GMAT Memorization Trivia Test! Quiz Questions

1. Complete the idiom:
I must have either chocolate ice cream __ carrot cake to complete a great meal.

The correct answer is "or" because the sentence is presenting two options for completing a great meal - either chocolate ice cream or carrot cake. "Or" is used to indicate a choice between two alternatives.

Explanation

The correct answer is "or" because the sentence is presenting two options for completing a great meal - either chocolate ice cream or carrot cake. "Or" is used to indicate a choice between two alternatives.

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2. Complete the idiom:
When given the choice, I choose both ice cream __ cake.

The correct answer is "and" because the idiom "I choose both ice cream and cake" implies that the person wants to have both options and cannot decide between them. The word "and" is used to connect the two options, indicating that the person wants both ice cream and cake.

Explanation

The correct answer is "and" because the idiom "I choose both ice cream and cake" implies that the person wants to have both options and cannot decide between them. The word "and" is used to connect the two options, indicating that the person wants both ice cream and cake.

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3. Complete the idiom:
The chimpanzee is much more intelligent __ the orangutan.

The given answer "than" completes the idiom "The chimpanzee is much more intelligent than the orangutan." This idiom is used to compare the intelligence levels of two different animals, stating that the chimpanzee is more intelligent than the orangutan. "Than" is a comparative conjunction used to introduce the second element being compared in a sentence. In this case, it is used to show the comparison between the intelligence of the chimpanzee and the orangutan.

Explanation

The given answer "than" completes the idiom "The chimpanzee is much more intelligent than the orangutan." This idiom is used to compare the intelligence levels of two different animals, stating that the chimpanzee is more intelligent than the orangutan. "Than" is a comparative conjunction used to introduce the second element being compared in a sentence. In this case, it is used to show the comparison between the intelligence of the chimpanzee and the orangutan.

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6. What percentage is the fourth distribution sextile of a normal bell curve?

The fourth distribution sextile of a normal bell curve represents the percentage of data that falls within one standard deviation above the mean. In a normal distribution, approximately 34% of the data falls within this range. Therefore, the answer is 34%.

Explanation

The fourth distribution sextile of a normal bell curve represents the percentage of data that falls within one standard deviation above the mean. In a normal distribution, approximately 34% of the data falls within this range. Therefore, the answer is 34%.

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7. What percentage is the fifth distribution sextile of a normal bell curve?

The fifth distribution sextile of a normal bell curve represents the percentage of data points that fall within that specific range. In this case, the answer is 14% or 14, indicating that 14% of the data falls within the fifth distribution sextile.

Explanation

The fifth distribution sextile of a normal bell curve represents the percentage of data points that fall within that specific range. In this case, the answer is 14% or 14, indicating that 14% of the data falls within the fifth distribution sextile.

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8. What percentage is the sixth distribution sextile of a normal bell curve?

The sixth distribution sextile of a normal bell curve represents the percentage of data points that fall within that specific range. In this case, the answer is 2% because the sixth sextile represents the middle 2% of the data. The number 2 is also correct as it represents the value of the sixth sextile, which is 2%.

Explanation

The sixth distribution sextile of a normal bell curve represents the percentage of data points that fall within that specific range. In this case, the answer is 2% because the sixth sextile represents the middle 2% of the data. The number 2 is also correct as it represents the value of the sixth sextile, which is 2%.

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9. What is the formula for rate of speed?
(d=distance, t=time)

The formula for rate of speed is given by dividing the distance traveled by the time taken. This can be represented as r = d/t. In this equation, r represents the rate of speed, d represents the distance traveled, and t represents the time taken. By dividing the distance by the time, we can determine the rate at which an object is moving.

Explanation

The formula for rate of speed is given by dividing the distance traveled by the time taken. This can be represented as r = d/t. In this equation, r represents the rate of speed, d represents the distance traveled, and t represents the time taken. By dividing the distance by the time, we can determine the rate at which an object is moving.

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10. What is the formula for the probability of event A and the probability of event B?
(Pa=probability of event A, Pb=probability of event B)

The formula for the probability of event A and the probability of event B is simply multiplying the probability of event A (Pa) by the probability of event B (Pb). This is because when two independent events occur, the probability of both events happening is the product of their individual probabilities.

Explanation

The formula for the probability of event A and the probability of event B is simply multiplying the probability of event A (Pa) by the probability of event B (Pb). This is because when two independent events occur, the probability of both events happening is the product of their individual probabilities.

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11. 66.66% = what fraction?

The given decimal 66.66% can be converted to a fraction by dividing it by 100. This gives us 0.6666. Simplifying this fraction, we get 2/3. Therefore, the fraction equivalent of 66.66% is 2/3.

Explanation

The given decimal 66.66% can be converted to a fraction by dividing it by 100. This gives us 0.6666. Simplifying this fraction, we get 2/3. Therefore, the fraction equivalent of 66.66% is 2/3.

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12. 1/6 = what percent?

This question is asking for the percentage equivalent of the fraction 1/6. To find this, we divide 1 by 6 and then multiply the result by 100 to convert it into a percentage. The result is 0.1666, which when rounded to two decimal places is 16.66%. Therefore, the correct answer is 16.66%.

Explanation

This question is asking for the percentage equivalent of the fraction 1/6. To find this, we divide 1 by 6 and then multiply the result by 100 to convert it into a percentage. The result is 0.1666, which when rounded to two decimal places is 16.66%. Therefore, the correct answer is 16.66%.

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13. 5/6 = what percent?

The fraction 5/6 can be converted to a percentage by dividing the numerator (5) by the denominator (6) and then multiplying by 100. This calculation results in 83.33%.

Explanation

The fraction 5/6 can be converted to a percentage by dividing the numerator (5) by the denominator (6) and then multiplying by 100. This calculation results in 83.33%.

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14. 7/8 = what percent?

The fraction 7/8 can be converted to a percentage by multiplying it by 100. When we do this, we get 87.5%. Therefore, 7/8 is equal to 87.5%.

Explanation

The fraction 7/8 can be converted to a percentage by multiplying it by 100. When we do this, we get 87.5%. Therefore, 7/8 is equal to 87.5%.

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16. 12²=?

The given question is asking for a number that is equal to 122. The answer provided is 144, which is not equal to 122. Therefore, the answer is incorrect.

Explanation

The given question is asking for a number that is equal to 122. The answer provided is 144, which is not equal to 122. Therefore, the answer is incorrect.

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25. 9³=?

The equation 93 = 729 is not a mathematical equation as it is missing an operation or a variable. Therefore, it is not possible to find a logical explanation for this answer.

Explanation

The equation 93 = 729 is not a mathematical equation as it is missing an operation or a variable. Therefore, it is not possible to find a logical explanation for this answer.

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27. Ratio_{Isoceles∆ Sides?}
_{(answer format}
_x:y:z
_{√ = option+v)}

The ratio of the sides of an isosceles triangle is 1:1:√2. This means that the two equal sides of the triangle have a length of 1 unit each, while the third side (the base) has a length of √2 units.

Explanation

The ratio of the sides of an isosceles triangle is 1:1:√2. This means that the two equal sides of the triangle have a length of 1 unit each, while the third side (the base) has a length of √2 units.

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28. Complete the ratio_Right∆:

3:4:x

The ratio given is "ratioRight∆:3:4:x". The ratio is incomplete as it does not provide any numerical values for "ratioRight∆" and "x". Therefore, without this information, it is not possible to determine the value of "x" or provide a complete explanation.

Explanation

The ratio given is "ratioRight∆:3:4:x". The ratio is incomplete as it does not provide any numerical values for "ratioRight∆" and "x". Therefore, without this information, it is not possible to determine the value of "x" or provide a complete explanation.

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29. 0!=?

The factorial of 0 is defined as 1. This is because factorial is a mathematical operation that calculates the product of all positive integers less than or equal to a given number. Since there are no positive integers less than or equal to 0, the product is considered to be 1.

Explanation

The factorial of 0 is defined as 1. This is because factorial is a mathematical operation that calculates the product of all positive integers less than or equal to a given number. Since there are no positive integers less than or equal to 0, the product is considered to be 1.

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30. 3!=?

The question is asking for the value of 3 factorial, denoted as 3!. Factorial is a mathematical operation that multiplies a number by all of the positive integers less than it. In this case, 3! is equal to 3 x 2 x 1, which equals 6. Therefore, the correct answer is 6.

Explanation

The question is asking for the value of 3 factorial, denoted as 3!. Factorial is a mathematical operation that multiplies a number by all of the positive integers less than it. In this case, 3! is equal to 3 x 2 x 1, which equals 6. Therefore, the correct answer is 6.

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31. 4!=?

The question is asking for the factorial of 4, which is denoted by 4!. Factorial means multiplying a number by all of the positive integers less than it. In this case, 4! would be equal to 4 x 3 x 2 x 1, which equals 24.

Explanation

The question is asking for the factorial of 4, which is denoted by 4!. Factorial means multiplying a number by all of the positive integers less than it. In this case, 4! would be equal to 4 x 3 x 2 x 1, which equals 24.

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32. 6!=?

The question is asking for the value of 6 factorial, which is denoted as 6!. Factorial is a mathematical operation where you multiply a number by all of the positive integers less than it. In this case, 6! is calculated as 6 x 5 x 4 x 3 x 2 x 1, which equals 720.

Explanation

The question is asking for the value of 6 factorial, which is denoted as 6!. Factorial is a mathematical operation where you multiply a number by all of the positive integers less than it. In this case, 6! is calculated as 6 x 5 x 4 x 3 x 2 x 1, which equals 720.

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33. 7!=?

The given question asks for the value of 7 factorial, denoted as 7!. Factorial means multiplying a number by all the positive integers less than it. So, to find 7!, we multiply 7 by 6, then by 5, then by 4, then by 3, then by 2, and finally by 1. The result is 5040.

Explanation

The given question asks for the value of 7 factorial, denoted as 7!. Factorial means multiplying a number by all the positive integers less than it. So, to find 7!, we multiply 7 by 6, then by 5, then by 4, then by 3, then by 2, and finally by 1. The result is 5040.

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34. Factor (x+y)(x+y)
(Note: x2 = x²)

The given expression is a result of multiplying (x+y) by itself twice. When we expand the expression, we use the distributive property to multiply each term in the first set of parentheses (x+y) by each term in the second set of parentheses (x+y). This results in x multiplied by x (x^2), x multiplied by y (xy), y multiplied by x (xy), and y multiplied by y (y^2). Combining like terms, we get the final answer x^2+2xy+y^2.

Explanation

The given expression is a result of multiplying (x+y) by itself twice. When we expand the expression, we use the distributive property to multiply each term in the first set of parentheses (x+y) by each term in the second set of parentheses (x+y). This results in x multiplied by x (x^2), x multiplied by y (xy), y multiplied by x (xy), and y multiplied by y (y^2). Combining like terms, we get the final answer x^2+2xy+y^2.

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35. Complete the idiom:
My GMAT teacher defines the conclusion __ the main point of the argument.

The word "as" is used to show the relationship between the conclusion and the main point of the argument. It indicates that the conclusion is the same or equivalent to the main point.

Explanation

The word "as" is used to show the relationship between the conclusion and the main point of the argument. It indicates that the conclusion is the same or equivalent to the main point.

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36. Complete the idiom:
He is not so much smart __ cunning.

The correct answer is "as". This idiom is used to compare two qualities or characteristics of a person or thing. In this case, it is comparing the level of intelligence and cunningness of someone. The phrase "not so much...as" is used to indicate that the first quality mentioned is not as strong or prevalent as the second quality. Therefore, the correct completion of the idiom is "He is not so much smart as cunning." This means that the person being referred to is more cunning than they are smart.

Explanation

The correct answer is "as". This idiom is used to compare two qualities or characteristics of a person or thing. In this case, it is comparing the level of intelligence and cunningness of someone. The phrase "not so much...as" is used to indicate that the first quality mentioned is not as strong or prevalent as the second quality. Therefore, the correct completion of the idiom is "He is not so much smart as cunning." This means that the person being referred to is more cunning than they are smart.

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37. Complete the idiom:
Think of it more __ a promise than a threat.

The idiom "think of it more of a promise than a threat" implies that the speaker wants the listener to view a particular situation or statement as more positive and reassuring rather than negative or intimidating. By using "of" in this idiom, it suggests that the speaker wants the listener to consider the situation or statement as being in the category of a promise, which typically conveys a sense of commitment and reliability, rather than in the category of a threat, which usually implies danger or harm.

Explanation

The idiom "think of it more of a promise than a threat" implies that the speaker wants the listener to view a particular situation or statement as more positive and reassuring rather than negative or intimidating. By using "of" in this idiom, it suggests that the speaker wants the listener to consider the situation or statement as being in the category of a promise, which typically conveys a sense of commitment and reliability, rather than in the category of a threat, which usually implies danger or harm.

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38. Complete the idiom:
Many people see euthanasia __ an escape from pain.

The correct answer is "as". In this idiom, "as" is used to indicate that many people perceive euthanasia as a means to escape from pain. It suggests that euthanasia is viewed as a solution or relief from suffering by those who support it.

Explanation

The correct answer is "as". In this idiom, "as" is used to indicate that many people perceive euthanasia as a means to escape from pain. It suggests that euthanasia is viewed as a solution or relief from suffering by those who support it.

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39. Complete the idiom:
Memorizing idioms is not as fun __ playing bingo.

This question is asking for the completion of the idiom "Memorizing idioms is not as fun __ playing bingo." The correct answer is "as." This is because the idiom is comparing the level of fun between two activities, memorizing idioms and playing bingo. The word "as" is commonly used in idioms to indicate a comparison or similarity between two things. In this case, it suggests that playing bingo is more enjoyable or fun than memorizing idioms.

Explanation

This question is asking for the completion of the idiom "Memorizing idioms is not as fun __ playing bingo." The correct answer is "as." This is because the idiom is comparing the level of fun between two activities, memorizing idioms and playing bingo. The word "as" is commonly used in idioms to indicate a comparison or similarity between two things. In this case, it suggests that playing bingo is more enjoyable or fun than memorizing idioms.

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40. Complete the idiom:
Democrats are not so different __ Republicans in the US.

The correct answer is "from". This is because the idiom "not so different from" is used to compare two things and highlight their similarities. In this case, it suggests that Democrats and Republicans in the US have more similarities than differences.

Explanation

The correct answer is "from". This is because the idiom "not so different from" is used to compare two things and highlight their similarities. In this case, it suggests that Democrats and Republicans in the US have more similarities than differences.

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41. Complete the idiom:
He was so late __ he missed the main course.

The word "that" is used to complete the idiom "He was so late that he missed the main course." This idiom is used to express that someone was extremely late, to the point that they missed an important event or opportunity. In this case, the person was so late that they arrived after the main course had already been served and missed the opportunity to have it.

Explanation

The word "that" is used to complete the idiom "He was so late that he missed the main course." This idiom is used to express that someone was extremely late, to the point that they missed an important event or opportunity. In this case, the person was so late that they arrived after the main course had already been served and missed the opportunity to have it.

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42. Complete the idiom:
The hypothesis __ aspartame causes brain tumors has not been proven yet.

The correct answer is "that". In this idiom, "that" is used to introduce a clause that explains or provides more information about the hypothesis. It indicates that the claim or belief that aspartame causes brain tumors has not been proven yet.

Explanation

The correct answer is "that". In this idiom, "that" is used to introduce a clause that explains or provides more information about the hypothesis. It indicates that the claim or belief that aspartame causes brain tumors has not been proven yet.

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43. Complete the idiom:

The time he has spent impersonating Elvis is estimated __ longer than the time Elvis himself spent performing.

The correct answer is "to be." This phrase is used to indicate that the estimated time spent impersonating Elvis is longer than the time Elvis himself spent performing. It suggests that the person has spent a significant amount of time impersonating Elvis, possibly indicating a deep passion or dedication to the act.

Explanation

The correct answer is "to be." This phrase is used to indicate that the estimated time spent impersonating Elvis is longer than the time Elvis himself spent performing. It suggests that the person has spent a significant amount of time impersonating Elvis, possibly indicating a deep passion or dedication to the act.

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44. Complete the idiom:

I forbid you __ call me before noon.

The correct answer is "to". In this idiom, "forbid" means to prohibit or not allow something. The phrase "forbid you to" is used to express a strong command or order, indicating that the speaker does not want the person to do a certain action. In this case, the speaker is specifically forbidding the person from calling them before noon.

Explanation

The correct answer is "to". In this idiom, "forbid" means to prohibit or not allow something. The phrase "forbid you to" is used to express a strong command or order, indicating that the speaker does not want the person to do a certain action. In this case, the speaker is specifically forbidding the person from calling them before noon.

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45. Complete the idiom:
If you take the GMAT enough times, you might develop the ability __ choose the credited responses without reading the questions.

The correct answer "to" completes the idiom "develop the ability to". This means that if you take the GMAT multiple times, you may eventually acquire the skill or capability to choose the credited responses without even reading the questions. The word "to" indicates the purpose or result of developing this ability.

Explanation

The correct answer "to" completes the idiom "develop the ability to". This means that if you take the GMAT multiple times, you may eventually acquire the skill or capability to choose the credited responses without even reading the questions. The word "to" indicates the purpose or result of developing this ability.

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46. Complete the idiom:
Many amusing quips are attributed __ Dorothy Parker.

The correct answer is "to." In this idiom, the word "attributed" means to credit or assign something to someone. Therefore, the sentence means that many amusing quips are credited or assigned to Dorothy Parker.

Explanation

The correct answer is "to." In this idiom, the word "attributed" means to credit or assign something to someone. Therefore, the sentence means that many amusing quips are credited or assigned to Dorothy Parker.

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47. Complete the idiom:
You have a responsibility __ take care of the child.

The correct answer is "to." In this idiom, "to" is used to indicate the purpose or duty of having a responsibility. It implies that the person has an obligation or duty to take care of the child. The word "to" connects the responsibility and the action of taking care, showing the relationship between them.

Explanation

The correct answer is "to." In this idiom, "to" is used to indicate the purpose or duty of having a responsibility. It implies that the person has an obligation or duty to take care of the child. The word "to" connects the responsibility and the action of taking care, showing the relationship between them.

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48. Complete the idiom:
My pasta sauce is far superior __ my mother-in-law's.

The correct answer is "to." The idiom is comparing the quality of the speaker's pasta sauce to the quality of their mother-in-law's sauce. By using "to," it implies that the speaker's sauce is of higher quality or better in some way compared to their mother-in-law's sauce.

Explanation

The correct answer is "to." The idiom is comparing the quality of the speaker's pasta sauce to the quality of their mother-in-law's sauce. By using "to," it implies that the speaker's sauce is of higher quality or better in some way compared to their mother-in-law's sauce.

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49. Complete the idiom:
Try __ stay awake during the essay section of the test.

The correct answer is "to". This is because the idiom "try to" is used to express an attempt or effort to do something. In this context, the phrase "try to stay awake" means making an effort to remain awake during the essay section of the test.

Explanation

The correct answer is "to". This is because the idiom "try to" is used to express an attempt or effort to do something. In this context, the phrase "try to stay awake" means making an effort to remain awake during the essay section of the test.

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50. Complete the idiom:
Many people credit Christopher Columbus __ the discovery of America, but Native Americans were here first.

Many people credit Christopher Columbus with the discovery of America, but Native Americans were here first.

Explanation

Many people credit Christopher Columbus with the discovery of America, but Native Americans were here first.

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51. Complete the idiom:
Most politicians prefer not to be associated __ the Mafia.

The correct answer is "with". In this idiom, "to be associated with" means to be connected or linked to something or someone, usually in a negative way. The sentence suggests that politicians generally do not want to be connected or affiliated with the Mafia, indicating a desire to distance themselves from any association with organized crime.

Explanation

The correct answer is "with". In this idiom, "to be associated with" means to be connected or linked to something or someone, usually in a negative way. The sentence suggests that politicians generally do not want to be connected or affiliated with the Mafia, indicating a desire to distance themselves from any association with organized crime.

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52. Complete the idiom:
My father likes to contrast my grades __ my brother's.

The correct answer is "with". In this idiom, "contrast" means to compare or highlight the differences between two things. In this context, it means that the father likes to compare the grades of the speaker with the grades of their brother. The word "with" is used to indicate the object of comparison.

Explanation

The correct answer is "with". In this idiom, "contrast" means to compare or highlight the differences between two things. In this context, it means that the father likes to compare the grades of the speaker with the grades of their brother. The word "with" is used to indicate the object of comparison.

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53. Complete the idiom:

You are responsible __ the child.

The correct answer is "for". In this idiom, "responsible for" means being accountable or in charge of something or someone. In this context, it suggests that the person being addressed is accountable for taking care of the child and ensuring their well-being.

Explanation

The correct answer is "for". In this idiom, "responsible for" means being accountable or in charge of something or someone. In this context, it suggests that the person being addressed is accountable for taking care of the child and ensuring their well-being.

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54. Complete the idiom:

I don't permit my children __ play with knives in the living room.

The correct answer is "to". In this context, "to" is used to indicate the purpose or intention of not permitting the children to play with knives in the living room. It shows that the action of not allowing the children to play with knives is the intended outcome or goal.

Explanation

The correct answer is "to". In this context, "to" is used to indicate the purpose or intention of not permitting the children to play with knives in the living room. It shows that the action of not allowing the children to play with knives is the intended outcome or goal.

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55. Complete the idiom:
I can distinguish between black __ white.

The correct answer is "and". This is because the idiom "to distinguish between black and white" means to differentiate or understand the difference between two contrasting things or ideas. In this case, the speaker is able to discern or recognize the distinctions between black and white.

Explanation

The correct answer is "and". This is because the idiom "to distinguish between black and white" means to differentiate or understand the difference between two contrasting things or ideas. In this case, the speaker is able to discern or recognize the distinctions between black and white.

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56. Complete the idiom:
Because Jenny was grounded, she could neither leave the house __ use the telephone.

The correct answer for completing the idiom is "nor". This is because "nor" is used to connect two negative alternatives in a sentence. In this case, it is used to show that Jenny was unable to do both leaving the house and using the telephone because she was grounded.

Explanation

The correct answer for completing the idiom is "nor". This is because "nor" is used to connect two negative alternatives in a sentence. In this case, it is used to show that Jenny was unable to do both leaving the house and using the telephone because she was grounded.

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57. 12.5% = what fraction?

The fraction that is equivalent to 12.5% is 1/8. This can be determined by converting the percentage to a fraction by dividing it by 100. In this case, 12.5 divided by 100 equals 0.125. Simplifying this decimal gives us 1/8.

Explanation

The fraction that is equivalent to 12.5% is 1/8. This can be determined by converting the percentage to a fraction by dividing it by 100. In this case, 12.5 divided by 100 equals 0.125. Simplifying this decimal gives us 1/8.

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58. 1/8 = what percent?

The fraction 1/8 can be converted to a percentage by multiplying it by 100. When we do this calculation, we get 12.5%. Therefore, the correct answer is 12.5%.

Explanation

The fraction 1/8 can be converted to a percentage by multiplying it by 100. When we do this calculation, we get 12.5%. Therefore, the correct answer is 12.5%.

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59. 5!=?

The given question is asking for the factorial of 5, which is denoted as 5!. The factorial of a number is the product of all positive integers from 1 to that number. In this case, 5! is calculated as 5 x 4 x 3 x 2 x 1, which equals 120. Therefore, the correct answer is 120.

Explanation

The given question is asking for the factorial of 5, which is denoted as 5!. The factorial of a number is the product of all positive integers from 1 to that number. In this case, 5! is calculated as 5 x 4 x 3 x 2 x 1, which equals 120. Therefore, the correct answer is 120.

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60. Complete the idiom:
If you worry too much ___ the GMAT, you'll develop an ulcer.

The correct answer is "about". This is because the idiom "worry about" means to be concerned or anxious about something. In this context, if you worry too much about the GMAT (Graduate Management Admission Test), it implies that you are excessively concerned or anxious about it, which can lead to developing an ulcer.

Explanation

The correct answer is "about". This is because the idiom "worry about" means to be concerned or anxious about something. In this context, if you worry too much about the GMAT (Graduate Management Admission Test), it implies that you are excessively concerned or anxious about it, which can lead to developing an ulcer.

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61. Complete the idiom:
Art historians regard the Mona Lisa __ one of the greatest works of art.

The correct answer is "as". In this sentence, "as" is used to compare the Mona Lisa to other great works of art. It indicates that art historians consider the Mona Lisa to be one of the greatest works of art.

Explanation

The correct answer is "as". In this sentence, "as" is used to compare the Mona Lisa to other great works of art. It indicates that art historians consider the Mona Lisa to be one of the greatest works of art.

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62. Complete the idiom:
The review was not mean-spirited __ merely flippant.

The review was not mean-spirited but merely flippant. This means that while the review may have been flippant or lacking seriousness, it was not intended to be malicious or hurtful. The word "but" is used to contrast the two qualities, emphasizing that the review was not mean-spirited despite being flippant.

Explanation

The review was not mean-spirited but merely flippant. This means that while the review may have been flippant or lacking seriousness, it was not intended to be malicious or hurtful. The word "but" is used to contrast the two qualities, emphasizing that the review was not mean-spirited despite being flippant.

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64. 62.5% = what fraction?

The given question asks for the fraction equivalent of 62.5%. To convert a percentage to a fraction, we divide the percentage by 100 and simplify the fraction if possible. In this case, dividing 62.5 by 100 gives us 0.625. To simplify the fraction, we can divide both the numerator and denominator by 0.125, which results in 5/8. Therefore, the fraction equivalent of 62.5% is 5/8.

Explanation

The given question asks for the fraction equivalent of 62.5%. To convert a percentage to a fraction, we divide the percentage by 100 and simplify the fraction if possible. In this case, dividing 62.5 by 100 gives us 0.625. To simplify the fraction, we can divide both the numerator and denominator by 0.125, which results in 5/8. Therefore, the fraction equivalent of 62.5% is 5/8.

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65. 87.5% = what fraction?

The given question asks for the fraction that is equivalent to 87.5%. To convert a percentage to a fraction, we divide the percentage by 100 and simplify if possible. In this case, 87.5 divided by 100 equals 0.875. To simplify this fraction, we can see that both the numerator and denominator are divisible by 0.125. Dividing both by 0.125 gives us 7/8, which is the simplified fraction equivalent to 87.5%.

Explanation

The given question asks for the fraction that is equivalent to 87.5%. To convert a percentage to a fraction, we divide the percentage by 100 and simplify if possible. In this case, 87.5 divided by 100 equals 0.875. To simplify this fraction, we can see that both the numerator and denominator are divisible by 0.125. Dividing both by 0.125 gives us 7/8, which is the simplified fraction equivalent to 87.5%.

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66. 3/8 = what percent?

The fraction 3/8 can be converted to a percentage by dividing the numerator (3) by the denominator (8) and then multiplying by 100. This calculation gives us 0.375, which when multiplied by 100 equals 37.5%. Therefore, the correct answer is 37.5%.

Explanation

The fraction 3/8 can be converted to a percentage by dividing the numerator (3) by the denominator (8) and then multiplying by 100. This calculation gives us 0.375, which when multiplied by 100 equals 37.5%. Therefore, the correct answer is 37.5%.

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67. Factor (x+y)(x-y)
(Note: x2 = x²)

The given expression is a product of three factors: (x+y), (x-y), and (x^2-y^2). The first two factors are the difference of squares, which can be simplified to x^2-y^2. Therefore, the correct answer is x^2-y^2.

Explanation

The given expression is a product of three factors: (x+y), (x-y), and (x^2-y^2). The first two factors are the difference of squares, which can be simplified to x^2-y^2. Therefore, the correct answer is x^2-y^2.

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68. Complete the idiom:
The commercials were obviously targeted __ teenage boys.

The idiom "targeted at" is commonly used to indicate that something is aimed or directed towards a specific group or audience. In this case, the commercials were clearly designed and intended for teenage boys, suggesting that they were created with the purpose of attracting their attention and interest.

Explanation

The idiom "targeted at" is commonly used to indicate that something is aimed or directed towards a specific group or audience. In this case, the commercials were clearly designed and intended for teenage boys, suggesting that they were created with the purpose of attracting their attention and interest.

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69. Complete the idiom:
The men had a dispute __ money.

The idiom "to have a dispute over money" means that the men were arguing or disagreeing about money. The word "over" indicates that the dispute was centered around the topic of money.

Explanation

The idiom "to have a dispute over money" means that the men were arguing or disagreeing about money. The word "over" indicates that the dispute was centered around the topic of money.

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70. Complete the idiom:
Mel Gibson is a native __ Australia.

The correct answer is "of" because the phrase "native of" is used to indicate someone's place of origin or birth. In this case, it is stating that Mel Gibson is originally from Australia.

Explanation

The correct answer is "of" because the phrase "native of" is used to indicate someone's place of origin or birth. In this case, it is stating that Mel Gibson is originally from Australia.

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71. Complete the idiom:
She is not only beautiful, __ smart.

The idiom "She is not only beautiful, but also smart" is used to emphasize that the person being referred to is not just beautiful, but also intelligent. The phrase "but also" is used to introduce an additional quality or characteristic that the person possesses. In this case, it highlights that the person is not only physically attractive but also intellectually capable.

Explanation

The idiom "She is not only beautiful, but also smart" is used to emphasize that the person being referred to is not just beautiful, but also intelligent. The phrase "but also" is used to introduce an additional quality or characteristic that the person possesses. In this case, it highlights that the person is not only physically attractive but also intellectually capable.

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72. Complete the ratio_Right∆:

5:x:13

The given ratio is "ratioRight∆:5:x:13". The ratio is complete up to the third term, with "ratioRight∆:5:x". To find the missing term, we can use the fact that the ratio is complete and balanced. Since the ratio is balanced, we can set up a proportion: ratioRight∆/5 = x/13. Cross-multiplying, we get ratioRight∆ * 13 = 5 * x. Simplifying further, we have ratioRight∆ = (5 * x) / 13. Substituting the given value of 12 for ratioRight∆, we can solve for x: 12 = (5 * x) / 13. Multiplying both sides by 13 and then dividing by 5, we find x = 12 * 13 / 5 = 12. Therefore, the missing term is 12.

Explanation

The given ratio is "ratioRight∆:5:x:13". The ratio is complete up to the third term, with "ratioRight∆:5:x". To find the missing term, we can use the fact that the ratio is complete and balanced. Since the ratio is balanced, we can set up a proportion: ratioRight∆/5 = x/13. Cross-multiplying, we get ratioRight∆ * 13 = 5 * x. Simplifying further, we have ratioRight∆ = (5 * x) / 13. Substituting the given value of 12 for ratioRight∆, we can solve for x: 12 = (5 * x) / 13. Multiplying both sides by 13 and then dividing by 5, we find x = 12 * 13 / 5 = 12. Therefore, the missing term is 12.

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73. What is the measure of the side of an Isoceles_Right∆with a hypotenuse of x√2

The measure of the side of an isosceles right triangle with a hypotenuse of x√2 is x. In an isosceles right triangle, the two legs are congruent, so if the hypotenuse is x√2, each leg must also be x. Therefore, the measure of the side is x.

Explanation

The measure of the side of an isosceles right triangle with a hypotenuse of x√2 is x. In an isosceles right triangle, the two legs are congruent, so if the hypotenuse is x√2, each leg must also be x. Therefore, the measure of the side is x.

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74. 37.5% = what fraction?

37.5% can be written as a fraction by dividing it by 100. Simplifying 37.5/100 gives us 3/8. Therefore, 37.5% is equivalent to the fraction 3/8.

Explanation

37.5% can be written as a fraction by dividing it by 100. Simplifying 37.5/100 gives us 3/8. Therefore, 37.5% is equivalent to the fraction 3/8.

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75. (x²)(x^-2)=?

The given expression is a multiplication of two terms, (x2) and (x-2). When we multiply these terms, we get x2(x-2). Expanding this expression further, we get x3 - 2x2. However, the question asks for the value of the expression when it is equal to 1. Therefore, the correct answer is 1 when the expression x3 - 2x2 is equal to 1.

Explanation

The given expression is a multiplication of two terms, (x2) and (x-2). When we multiply these terms, we get x2(x-2). Expanding this expression further, we get x3 - 2x2. However, the question asks for the value of the expression when it is equal to 1. Therefore, the correct answer is 1 when the expression x3 - 2x2 is equal to 1.

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76. 1!=?

The factorial of a number is the product of all positive integers less than or equal to that number. In this case, 1! (read as "1 factorial") is equal to 1 because there is only one positive integer less than or equal to 1, which is 1 itself.

Explanation

The factorial of a number is the product of all positive integers less than or equal to that number. In this case, 1! (read as "1 factorial") is equal to 1 because there is only one positive integer less than or equal to 1, which is 1 itself.

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77. 2!=?

The expression "2!" represents the factorial of 2, which is calculated by multiplying 2 by all positive integers less than it. In this case, 2! equals 2 x 1, which equals 2. Therefore, the correct answer is 2.

Explanation

The expression "2!" represents the factorial of 2, which is calculated by multiplying 2 by all positive integers less than it. In this case, 2! equals 2 x 1, which equals 2. Therefore, the correct answer is 2.

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78. Complete the idiom:
He was prohibited __ entering the public library after he accidentally set the dictionary on fire with a magnifying glass.

The correct answer is "from." This preposition is used to indicate that someone is not allowed or forbidden to do something. In this context, the person is not allowed to enter the public library because of their previous accident with the dictionary.

Explanation

The correct answer is "from." This preposition is used to indicate that someone is not allowed or forbidden to do something. In this context, the person is not allowed to enter the public library because of their previous accident with the dictionary.

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79. Complete the idiom:
Before you enter the house you are required __ take off your hat.

Before you enter the house you are required to take off your hat. In this idiom, "to" is used as a preposition to indicate the required action of taking off one's hat before entering the house. It signifies a customary or expected behavior when entering someone's home as a sign of respect or politeness.

Explanation

Before you enter the house you are required to take off your hat. In this idiom, "to" is used as a preposition to indicate the required action of taking off one's hat before entering the house. It signifies a customary or expected behavior when entering someone's home as a sign of respect or politeness.

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80. 83.33% = what fraction?

The fraction that is equivalent to 83.33% is 5/6. This can be determined by converting the percentage to a fraction. To do this, we divide 83.33 by 100 to get 0.8333. Then, we simplify this decimal number to a fraction by placing it over 1 and multiplying the numerator and denominator by 10000 to remove the decimal. This gives us 8333/10000, which can be further simplified to 5/6.

Explanation

The fraction that is equivalent to 83.33% is 5/6. This can be determined by converting the percentage to a fraction. To do this, we divide 83.33 by 100 to get 0.8333. Then, we simplify this decimal number to a fraction by placing it over 1 and multiplying the numerator and denominator by 10000 to remove the decimal. This gives us 8333/10000, which can be further simplified to 5/6.

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81. Even + Even = ?

Even

Odd

When we add two even numbers together, the result is always an even number. This is because even numbers are divisible by 2, and when we add two numbers that are divisible by 2, the sum will also be divisible by 2. Therefore, the correct answer is "Even".

Explanation

When we add two even numbers together, the result is always an even number. This is because even numbers are divisible by 2, and when we add two numbers that are divisible by 2, the sum will also be divisible by 2. Therefore, the correct answer is "Even".

82. Factor (x+y)²
(Note: x2 = x²)

The given expression is a binomial squared, which means it represents the square of the sum of two terms (x and y in this case). To expand a binomial squared, we use the formula (a+b)² = a² + 2ab + b². Applying this formula to the given expression, we get x² + 2xy + y². Therefore, the correct answer is x² + 2xy + y².

Explanation

The given expression is a binomial squared, which means it represents the square of the sum of two terms (x and y in this case). To expand a binomial squared, we use the formula (a+b)² = a² + 2ab + b². Applying this formula to the given expression, we get x² + 2xy + y². Therefore, the correct answer is x² + 2xy + y².

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83. What is the formula for a vertical line, whose x-intercept is (c,0)?

The formula for a vertical line is x=c, where c is the x-coordinate of the x-intercept. This means that the line will have a constant x-value for all points on the line, while the y-value can vary. In this case, the x-intercept is (c,0), indicating that the line crosses the x-axis at the point (c,0) and is vertical.

Explanation

The formula for a vertical line is x=c, where c is the x-coordinate of the x-intercept. This means that the line will have a constant x-value for all points on the line, while the y-value can vary. In this case, the x-intercept is (c,0), indicating that the line crosses the x-axis at the point (c,0) and is vertical.

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84. 16.66% = what fraction?

The given percentage, 16.66%, can be expressed as a fraction by dividing it by 100. This results in 0.1666. To simplify this fraction, we can see that the decimal can be written as 1/6. Therefore, the fraction that represents 16.66% is 1/6.

Explanation

The given percentage, 16.66%, can be expressed as a fraction by dividing it by 100. This results in 0.1666. To simplify this fraction, we can see that the decimal can be written as 1/6. Therefore, the fraction that represents 16.66% is 1/6.

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85. Complete the idiom:
Mom and dad gave the same punishment to me __ to you.

The correct answer is "as". In this idiom, "as" is used to compare the punishment given to the speaker with the punishment given to someone else, in this case, "you". It suggests that both the speaker and "you" received the same punishment from mom and dad.

Explanation

The correct answer is "as". In this idiom, "as" is used to compare the punishment given to the speaker with the punishment given to someone else, in this case, "you". It suggests that both the speaker and "you" received the same punishment from mom and dad.

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87. Odd + Odd = ?

Even

Odd

When two odd numbers are added together, the sum will always be an even number. This is because odd numbers can be represented as 2n+1, where n is an integer. Adding two odd numbers (2n+1) + (2m+1) will result in 2n+2m+2, which can be simplified to 2(n+m+1), an even number. Therefore, the correct answer is Even.

Explanation

When two odd numbers are added together, the sum will always be an even number. This is because odd numbers can be represented as 2n+1, where n is an integer. Adding two odd numbers (2n+1) + (2m+1) will result in 2n+2m+2, which can be simplified to 2(n+m+1), an even number. Therefore, the correct answer is Even.

88. What is the formula to determine the length of the diagonal of a box?
(d=diagonal, l=length, w=width, h=height)

The formula to determine the length of the diagonal of a box is d^2 = l^2 + w^2 + h^2. This formula is derived from the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the length, width, and height of the box form the three sides of a right-angled triangle, with the diagonal being the hypotenuse. By applying the Pythagorean theorem, we can calculate the length of the diagonal of the box.

Explanation

The formula to determine the length of the diagonal of a box is d^2 = l^2 + w^2 + h^2. This formula is derived from the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the length, width, and height of the box form the three sides of a right-angled triangle, with the diagonal being the hypotenuse. By applying the Pythagorean theorem, we can calculate the length of the diagonal of the box.

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89. Factor (x-y)²
(Note: x2 = x²)

The expression (x-y)2 represents the square of the binomial (x-y). This means that we need to multiply (x-y) by itself. Using the formula for squaring a binomial, we get x2 - 2xy + y2. This is the expanded form of (x-y)2, which is the correct answer.

Explanation

The expression (x-y)2 represents the square of the binomial (x-y). This means that we need to multiply (x-y) by itself. Using the formula for squaring a binomial, we get x2 - 2xy + y2. This is the expanded form of (x-y)2, which is the correct answer.

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90. Complete the idiom:
She is so beautiful __ exquisite.

The correct answer is "as to be." This idiom is used to emphasize the extreme beauty of someone or something. In this context, it suggests that the person being referred to is incredibly beautiful to the point of being exquisite.

Explanation

The correct answer is "as to be." This idiom is used to emphasize the extreme beauty of someone or something. In this context, it suggests that the person being referred to is incredibly beautiful to the point of being exquisite.

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91. What percentage is the third distribution sextile of a normal bell curve?

The third distribution sextile of a normal bell curve refers to the range that includes 34% of the data. This means that 34% of the data falls within this range, while the remaining 66% is distributed in other sections of the bell curve. Therefore, the correct answer is 34%.

Explanation

The third distribution sextile of a normal bell curve refers to the range that includes 34% of the data. This means that 34% of the data falls within this range, while the remaining 66% is distributed in other sections of the bell curve. Therefore, the correct answer is 34%.

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92. What is the formula for work?
(w=work, t=time, r=rate)

The formula for work is given by w=rt, where w represents the work done, r represents the rate at which the work is being done, and t represents the time taken to complete the work. This formula shows that work is equal to the product of the rate and the time.

Explanation

The formula for work is given by w=rt, where w represents the work done, r represents the rate at which the work is being done, and t represents the time taken to complete the work. This formula shows that work is equal to the product of the rate and the time.

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94. (Even)(Even) = ?

Even

Odd

When two even numbers are multiplied together, the result is always an even number. Therefore, the product of two even numbers is also an even number. In this case, since "Even" is an even number, when it is multiplied by another "Even" number, the answer will still be an even number.

Explanation

When two even numbers are multiplied together, the result is always an even number. Therefore, the product of two even numbers is also an even number. In this case, since "Even" is an even number, when it is multiplied by another "Even" number, the answer will still be an even number.

95. What is the slope of a line that is perpendicular to a line with slope x/y?

The slope of a line perpendicular to another line is the negative reciprocal of the slope of the original line. In this case, the original line has a slope of x/y, so the perpendicular line will have a slope of -y/x.

Explanation

The slope of a line perpendicular to another line is the negative reciprocal of the slope of the original line. In this case, the original line has a slope of x/y, so the perpendicular line will have a slope of -y/x.

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96. What percentage is the first distribution sextile of a normal bell curve?

The first distribution sextile of a normal bell curve refers to the area under the curve that falls within the first 16.67% of the total distribution. This can be calculated by dividing 100% by 6, since a normal distribution is divided into six equal parts called sextiles. Therefore, the first distribution sextile represents approximately 16.67% of the total distribution. In this case, the answer provided is 2%, which is incorrect. The correct answer should be approximately 16.67%.

Explanation

The first distribution sextile of a normal bell curve refers to the area under the curve that falls within the first 16.67% of the total distribution. This can be calculated by dividing 100% by 6, since a normal distribution is divided into six equal parts called sextiles. Therefore, the first distribution sextile represents approximately 16.67% of the total distribution. In this case, the answer provided is 2%, which is incorrect. The correct answer should be approximately 16.67%.

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97. 5/8 = what percent?

The fraction 5/8 can be converted to a percentage by dividing the numerator (5) by the denominator (8) and then multiplying by 100. This calculation gives us 0.625, which can be expressed as 62.5% in percentage form. Therefore, the correct answer is 62.5%.

Explanation

The fraction 5/8 can be converted to a percentage by dividing the numerator (5) by the denominator (8) and then multiplying by 100. This calculation gives us 0.625, which can be expressed as 62.5% in percentage form. Therefore, the correct answer is 62.5%.

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98. Even + Odd = ?

Even

Odd

When an even number is added to an odd number, the result is always an odd number. This is because an even number can be represented as 2n (where n is an integer), and an odd number can be represented as 2n+1. When we add these two expressions, we get 2n + 2n + 1 = 4n + 1, which is always an odd number. Therefore, the answer to the equation "Even + Odd" is always an odd number.

Explanation

When an even number is added to an odd number, the result is always an odd number. This is because an even number can be represented as 2n (where n is an integer), and an odd number can be represented as 2n+1. When we add these two expressions, we get 2n + 2n + 1 = 4n + 1, which is always an odd number. Therefore, the answer to the equation "Even + Odd" is always an odd number.

99. What is the ratio of the sides of a 30/60/90 right triangle?
(option+v=√)

In a 30/60/90 right triangle, the ratio of the sides is 1:√3:2. This means that the length of the side opposite the 30-degree angle is 1, the length of the side opposite the 60-degree angle is √3, and the length of the hypotenuse is 2. This ratio is derived from the properties of a 30/60/90 triangle, where the side opposite the 30-degree angle is half the length of the hypotenuse, and the side opposite the 60-degree angle is √3 times the length of the side opposite the 30-degree angle.

Explanation

In a 30/60/90 right triangle, the ratio of the sides is 1:√3:2. This means that the length of the side opposite the 30-degree angle is 1, the length of the side opposite the 60-degree angle is √3, and the length of the hypotenuse is 2. This ratio is derived from the properties of a 30/60/90 triangle, where the side opposite the 30-degree angle is half the length of the hypotenuse, and the side opposite the 60-degree angle is √3 times the length of the side opposite the 30-degree angle.

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100. (z^a)(z^b)=?

The given expression (za)(zb) can be simplified by applying the distributive property of multiplication. This property states that when multiplying a sum by a number, we can distribute the multiplication to each term within the sum. In this case, we have two terms, za and zb, being multiplied together. By applying the distributive property, we can multiply za by zb, resulting in za * zb. Therefore, the correct answer is za * zb, which can also be written as za+b.

Explanation

The given expression (za)(zb) can be simplified by applying the distributive property of multiplication. This property states that when multiplying a sum by a number, we can distribute the multiplication to each term within the sum. In this case, we have two terms, za and zb, being multiplied together. By applying the distributive property, we can multiply za by zb, resulting in za * zb. Therefore, the correct answer is za * zb, which can also be written as za+b.

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101. What percentage is the second distribution sextile of a normal bell curve?

The second distribution sextile of a normal bell curve is 14%. This means that 14% of the data falls within the range of the second sextile, which is one-sixth of the total distribution. This is a common way to divide and analyze data in statistics.

Explanation

The second distribution sextile of a normal bell curve is 14%. This means that 14% of the data falls within the range of the second sextile, which is one-sixth of the total distribution. This is a common way to divide and analyze data in statistics.

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102. Complete the idiom:
The kangaroo is native __ Australia.

The correct answer is "to". This is because the idiom "native to" is used to indicate that something or someone is originally from a particular place or country. In this case, the kangaroo is originally from Australia, so it is native to Australia.

Explanation

The correct answer is "to". This is because the idiom "native to" is used to indicate that something or someone is originally from a particular place or country. In this case, the kangaroo is originally from Australia, so it is native to Australia.

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103. What is the formula for the area of an equilateral triangle?
(option+v = √. x2 = x*x. 1/2 = .5, b=base)

The formula for the area of an equilateral triangle is b^2√3/4. In this formula, "b" represents the length of one side of the equilateral triangle. To find the area, we square the length of one side (b^2), multiply it by the square root of 3 (√3), and then divide the result by 4. This formula is derived from the properties of equilateral triangles, where all sides are equal in length and all angles are equal to 60 degrees.

Explanation

The formula for the area of an equilateral triangle is b^2√3/4. In this formula, "b" represents the length of one side of the equilateral triangle. To find the area, we square the length of one side (b^2), multiply it by the square root of 3 (√3), and then divide the result by 4. This formula is derived from the properties of equilateral triangles, where all sides are equal in length and all angles are equal to 60 degrees.

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104. What is the formula for the surface area of a cylinder?
(option+p=π)

The formula for the surface area of a cylinder is 2(πr^2) + (2πrh). This formula consists of two parts: the first part, 2(πr^2), represents the area of the two circular bases of the cylinder, which are both equal to πr^2. The second part, (2πrh), represents the lateral surface area of the cylinder, which is the curved surface area wrapping around the sides of the cylinder. By adding these two parts together, we get the total surface area of the cylinder.

Explanation

The formula for the surface area of a cylinder is 2(πr^2) + (2πrh). This formula consists of two parts: the first part, 2(πr^2), represents the area of the two circular bases of the cylinder, which are both equal to πr^2. The second part, (2πrh), represents the lateral surface area of the cylinder, which is the curved surface area wrapping around the sides of the cylinder. By adding these two parts together, we get the total surface area of the cylinder.

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105. What is the formula for the probability of event A or the probability of event B?
(Pa=probability of event A, Pb=probability of event B)

The formula for the probability of event A or the probability of event B is given by Pa+Pb-(PaPb). This formula accounts for the possibility of both events A and B occurring at the same time by subtracting their joint probability (PaPb) from the sum of their individual probabilities (Pa+Pb). This ensures that the total probability does not exceed 1, which is the maximum possible probability.

Explanation

The formula for the probability of event A or the probability of event B is given by Pa+Pb-(PaPb). This formula accounts for the possibility of both events A and B occurring at the same time by subtracting their joint probability (PaPb) from the sum of their individual probabilities (Pa+Pb). This ensures that the total probability does not exceed 1, which is the maximum possible probability.

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106. (Odd)(Odd) = ?

Even

Odd

When multiplying two odd numbers together, the result is always an odd number. In this case, (Odd)(Odd) would result in an odd number. Therefore, the answer is odd.

Explanation

When multiplying two odd numbers together, the result is always an odd number. In this case, (Odd)(Odd) would result in an odd number. Therefore, the answer is odd.

107. X^1/2=?
(option+v=√)

The given equation x^(1/2) is equivalent to taking the square root of x. Therefore, the correct answer is √x, which represents the square root of x.

Explanation

The given equation x^(1/2) is equivalent to taking the square root of x. Therefore, the correct answer is √x, which represents the square root of x.

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108. There are X racers. If there are three winning positions for a race and A racers can come in first place, B racers can come in second place, C racers can come in third place, and D represents the left over racers who did not place, what is the probability?

The given answer, x!/a!b!c!d!,X!/A!B!C!D!, represents the probability of the different possible outcomes for the race. The numerator, x!, represents the number of ways the X racers can finish the race. The denominator, a!b!c!d!, represents the number of ways the winning positions can be filled by the A, B, C, and D racers. Dividing the numerator by the denominator gives the probability of the specific outcome occurring.

Explanation

The given answer, x!/a!b!c!d!,X!/A!B!C!D!, represents the probability of the different possible outcomes for the race. The numerator, x!, represents the number of ways the X racers can finish the race. The denominator, a!b!c!d!, represents the number of ways the winning positions can be filled by the A, B, C, and D racers. Dividing the numerator by the denominator gives the probability of the specific outcome occurring.

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109. Complete the idiom:
His friends do not believe the ring he bought at the auction __ Jackie O's; they all think he was tricked.

The correct answer is "to be". This idiom means that his friends do not believe that the ring he bought at the auction is actually Jackie O's, implying that they think he was deceived or fooled into thinking it was genuine.

Explanation

The correct answer is "to be". This idiom means that his friends do not believe that the ring he bought at the auction is actually Jackie O's, implying that they think he was deceived or fooled into thinking it was genuine.

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110. (Even)(Odd)

Even

Odd

The given question appears to be incomplete or not readable. The provided information does not provide any context or clear question to determine the correct answer. Therefore, an explanation cannot be generated.

Explanation

The given question appears to be incomplete or not readable. The provided information does not provide any context or clear question to determine the correct answer. Therefore, an explanation cannot be generated.

111. What is the formula for the volume of a cylinder?
(option+p=π)

The formula for the volume of a cylinder is given by multiplying the base area (πr^2) by the height (h). This is because the volume of a cylinder can be thought of as the area of the base (which is a circle with radius r) multiplied by the height of the cylinder. Thus, the correct formula for the volume of a cylinder is πr^2h.

Explanation

The formula for the volume of a cylinder is given by multiplying the base area (πr^2) by the height (h). This is because the volume of a cylinder can be thought of as the area of the base (which is a circle with radius r) multiplied by the height of the cylinder. Thus, the correct formula for the volume of a cylinder is πr^2h.

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112. What are the coordinates of the y-intercept of a line (if it exists)?
(b=y-intercept. m=slope)

The correct answer is (-b/m, 0), (-b/m,0). This answer suggests that the coordinates of the y-intercept of a line, if it exists, are (-b/m, 0). The "-b/m" represents the x-coordinate of the y-intercept, while the "0" represents the y-coordinate. The repetition of the answer choice may be a typographical error or redundancy.

Explanation

The correct answer is (-b/m, 0), (-b/m,0). This answer suggests that the coordinates of the y-intercept of a line, if it exists, are (-b/m, 0). The "-b/m" represents the x-coordinate of the y-intercept, while the "0" represents the y-coordinate. The repetition of the answer choice may be a typographical error or redundancy.

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113. Complete the idiom:
Art historians consider the Mona Lisa __ one of the greatest works of art.

Art historians consider the Mona Lisa to be one of the greatest works of art.

Explanation

Art historians consider the Mona Lisa to be one of the greatest works of art.

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