Graduate Recruitment Aptitude Test

1. 11²=?

The given equation is asking for the value of 112. However, the answer provided is 121, which is not equal to 112. Therefore, the given answer is incorrect and there is no valid explanation for it.

Explanation

The given equation is asking for the value of 112. However, the answer provided is 121, which is not equal to 112. Therefore, the given answer is incorrect and there is no valid explanation for it.

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6. 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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7. 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 means that memorizing idioms is not as enjoyable or entertaining as playing bingo. The word "as" is used to compare the level of fun between the two activities.

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 means that memorizing idioms is not as enjoyable or entertaining as playing bingo. The word "as" is used to compare the level of fun between the two activities.

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8. Complete the idiom:

I forbid you __ call me before noon.

The correct answer is "to". This completes the idiom "I forbid you to call me before noon." The phrase "forbid someone to do something" means to prohibit or disallow someone from doing a specific action. In this case, the speaker is instructing the other person not to call them before noon.

Explanation

The correct answer is "to". This completes the idiom "I forbid you to call me before noon." The phrase "forbid someone to do something" means to prohibit or disallow someone from doing a specific action. In this case, the speaker is instructing the other person not to call them before noon.

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

If you take the GMAT enough times, you might develop the ability to choose the credited responses without reading the questions. This means that by repeatedly taking the GMAT, one can become so familiar with the format and content of the test that they can accurately select the correct answers without needing to read the questions thoroughly. This implies a high level of expertise and understanding of the exam, allowing for efficient and accurate decision-making.

Explanation

If you take the GMAT enough times, you might develop the ability to choose the credited responses without reading the questions. This means that by repeatedly taking the GMAT, one can become so familiar with the format and content of the test that they can accurately select the correct answers without needing to read the questions thoroughly. This implies a high level of expertise and understanding of the exam, allowing for efficient and accurate decision-making.

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

In this idiom, "take off your hat" means to remove your hat. The word "to" is used to indicate that removing the hat is necessary or required before entering the house.

Explanation

In this idiom, "take off your hat" means to remove your hat. The word "to" is used to indicate that removing the hat is necessary or required before entering the house.

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

The idiom "have a responsibility to" means that someone is obligated or has a duty to do something. In this case, the correct answer "to" completes the sentence by indicating that the person has a responsibility to take care of the child.

Explanation

The idiom "have a responsibility to" means that someone is obligated or has a duty to do something. In this case, the correct answer "to" completes the sentence by indicating that the person has a responsibility to take care of the child.

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12. Complete the idiom:

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

The correct answer is "to". In this idiom, "permit" means to allow or give permission. The sentence is stating that the speaker does not allow or give permission for their children to play with knives in the living room.

Explanation

The correct answer is "to". In this idiom, "permit" means to allow or give permission. The sentence is stating that the speaker does not allow or give permission for their children to play with knives in the living room.

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

This question is asking for the completion of the idiom "I must have either chocolate ice cream __ carrot cake to complete a great meal." The correct answer is "or." In this context, "or" is used to indicate a choice between two options. The sentence suggests that either chocolate ice cream or carrot cake would be a suitable choice to complete a great meal.

Explanation

This question is asking for the completion of the idiom "I must have either chocolate ice cream __ carrot cake to complete a great meal." The correct answer is "or." In this context, "or" is used to indicate a choice between two options. The sentence suggests that either chocolate ice cream or carrot cake would be a suitable choice to complete a great meal.

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

The correct answer is "than". This is because the phrase "much more intelligent" is comparing the intelligence of the chimpanzee to that of the orangutan. The word "than" is used to indicate the comparison between the two.

Explanation

The correct answer is "than". This is because the phrase "much more intelligent" is comparing the intelligence of the chimpanzee to that of the orangutan. The word "than" is used to indicate the comparison between the two.

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16. 1/8 = what percent?

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

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17. 3/8 = what percent?

The fraction 3/8 can be converted to a percentage by multiplying it by 100. So, 3/8 * 100 = 37.5%. Therefore, the correct answer is 37.5%.

Explanation

The fraction 3/8 can be converted to a percentage by multiplying it by 100. So, 3/8 * 100 = 37.5%. Therefore, the correct answer is 37.5%.

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18. 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, the correct answer is 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, the correct answer is 87.5%.

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25. 3!=?

The expression "3!" represents the factorial of 3, which means multiplying 3 by all the positive integers less than it. In this case, 3! is calculated as 3 x 2 x 1, which equals 6.

Explanation

The expression "3!" represents the factorial of 3, which means multiplying 3 by all the positive integers less than it. In this case, 3! is calculated as 3 x 2 x 1, which equals 6.

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

The correct answer is "as". In this idiom, "as" is used to compare or liken euthanasia to an escape from pain. It suggests that many individuals perceive euthanasia as a means to relieve themselves from suffering or agony.

Explanation

The correct answer is "as". In this idiom, "as" is used to compare or liken euthanasia to an escape from pain. It suggests that many individuals perceive euthanasia as a means to relieve themselves from suffering or agony.

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27. 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 specific context, it implies that the person being addressed has a duty or obligation towards the child, possibly in terms of taking care of them or 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 specific context, it implies that the person being addressed has a duty or obligation towards the child, possibly in terms of taking care of them or ensuring their well-being.

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

This idiom is used to express that Democrats and Republicans in the US are similar or have similarities. It implies that despite their different political ideologies and policies, there are still commonalities or shared characteristics between the two parties.

Explanation

This idiom is used to express that Democrats and Republicans in the US are similar or have similarities. It implies that despite their different political ideologies and policies, there are still commonalities or shared characteristics between the two parties.

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

This question is asking to complete the idiom "Many amusing quips are attributed __ Dorothy Parker." The correct answer is "to." This means that many amusing quips are credited or associated with Dorothy Parker. The idiom implies that Dorothy Parker is well-known for making witty and humorous remarks.

Explanation

This question is asking to complete the idiom "Many amusing quips are attributed __ Dorothy Parker." The correct answer is "to." This means that many amusing quips are credited or associated with Dorothy Parker. The idiom implies that Dorothy Parker is well-known for making witty and humorous remarks.

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

This question asks for the completion of the idiom "Most politicians prefer not to be associated __ the Mafia." The correct answer is "with." This means that politicians generally do not want to be connected or linked to the Mafia, as it could damage their reputation and credibility.

Explanation

This question asks for the completion of the idiom "Most politicians prefer not to be associated __ the Mafia." The correct answer is "with." This means that politicians generally do not want to be connected or linked to the Mafia, as it could damage their reputation and credibility.

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

The idiom "I can distinguish between black and white" means that the person is able to differentiate between right and wrong, good and bad, or truth and lies. It implies that the person has a clear understanding and can make accurate judgments or decisions.

Explanation

The idiom "I can distinguish between black and white" means that the person is able to differentiate between right and wrong, good and bad, or truth and lies. It implies that the person has a clear understanding and can make accurate judgments or decisions.

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32. 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" means that the person wants to have both options rather than just one. They prefer not to make a choice between the two and would like to have both items.

Explanation

The correct answer is "and" because the idiom "I choose both ice cream and cake" means that the person wants to have both options rather than just one. They prefer not to make a choice between the two and would like to have both items.

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33. 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 the result by 100. In this case, 5 divided by 8 is 0.625, and when multiplied by 100, it gives 62.5%. 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 the result by 100. In this case, 5 divided by 8 is 0.625, and when multiplied by 100, it gives 62.5%. Therefore, the correct answer is 62.5%.

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34. 2!=?

The given question is asking for the factorial of 2, which is denoted by 2!. The factorial of a number is the product of all positive integers less than or equal to that number. In this case, the factorial of 2 is equal to 2 * 1, which equals 2. Therefore, the correct answer is 2.

Explanation

The given question is asking for the factorial of 2, which is denoted by 2!. The factorial of a number is the product of all positive integers less than or equal to that number. In this case, the factorial of 2 is equal to 2 * 1, which equals 2. Therefore, the correct answer is 2.

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35. 4!=?

The question is asking for the value of 4! (4 factorial). The exclamation mark denotes factorial, which means multiplying a number by all the positive integers less than it down to 1. In this case, 4! is equal to 4 x 3 x 2 x 1, which equals 24.

Explanation

The question is asking for the value of 4! (4 factorial). The exclamation mark denotes factorial, which means multiplying a number by all the positive integers less than it down to 1. In this case, 4! is equal to 4 x 3 x 2 x 1, which equals 24.

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36. 5!=?

The question asks for the value of 5 factorial, which is denoted as 5!. Factorial means multiplying a number by all of the positive integers less than it. So, 5! can be calculated as 5 x 4 x 3 x 2 x 1, which equals 120.

Explanation

The question asks for the value of 5 factorial, which is denoted as 5!. Factorial means multiplying a number by all of the positive integers less than it. So, 5! can be calculated as 5 x 4 x 3 x 2 x 1, which equals 120.

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37. 6!=?

The question is asking for the value of 6 factorial, which is denoted by 6!. Factorial is a mathematical operation that multiplies a number by all 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 by 6!. Factorial is a mathematical operation that multiplies a number by all 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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38. Complete the idiom:
If you worry too much ___ the GMAT, you'll develop an ulcer.

This idiom suggests that excessive worry or stress about the GMAT exam can lead to the development of an ulcer. The word "about" is used to indicate the specific subject or focus of the worry, which in this case is the GMAT. The idiom implies that it is important to strike a balance between preparation and stress management in order to avoid negative health consequences.

Explanation

This idiom suggests that excessive worry or stress about the GMAT exam can lead to the development of an ulcer. The word "about" is used to indicate the specific subject or focus of the worry, which in this case is the GMAT. The idiom implies that it is important to strike a balance between preparation and stress management in order to avoid negative health consequences.

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39. 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". The word "prohibited" suggests that someone was not allowed to do something. In this case, the person was not allowed to enter the public library. The reason for this prohibition is given in the rest of the sentence, which explains that the person accidentally set the dictionary on fire with a magnifying glass. Therefore, the person was prohibited from entering the public library.

Explanation

The correct answer is "from". The word "prohibited" suggests that someone was not allowed to do something. In this case, the person was not allowed to enter the public library. The reason for this prohibition is given in the rest of the sentence, which explains that the person accidentally set the dictionary on fire with a magnifying glass. Therefore, the person was prohibited from entering the public library.

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

The word "that" is the correct answer to complete the idiom. The phrase "He was so late that he missed the main course" implies that the person was extremely late, to the point where they arrived after the main course had already been served or eaten. The word "that" is used to introduce a clause that explains the consequence or result of being late.

Explanation

The word "that" is the correct answer to complete the idiom. The phrase "He was so late that he missed the main course" implies that the person was extremely late, to the point where they arrived after the main course had already been served or eaten. The word "that" is used to introduce a clause that explains the consequence or result of being late.

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

The idiom "not mean-spirited but merely flippant" suggests that the review in question was not intended to be malicious or hurtful, but rather it was lighthearted and lacked seriousness. The word "but" is used to contrast the two characteristics of the review, emphasizing that while it may have been flippant, it was not mean-spirited.

Explanation

The idiom "not mean-spirited but merely flippant" suggests that the review in question was not intended to be malicious or hurtful, but rather it was lighthearted and lacked seriousness. The word "but" is used to contrast the two characteristics of the review, emphasizing that while it may have been flippant, it was not mean-spirited.

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

The word "nor" is used in the idiom to indicate that Jenny was unable to do two things - leave the house and use the telephone. "Nor" is a coordinating conjunction that is used to connect two negative alternatives. In this context, it emphasizes that both actions were not possible for Jenny due to being grounded.

Explanation

The word "nor" is used in the idiom to indicate that Jenny was unable to do two things - leave the house and use the telephone. "Nor" is a coordinating conjunction that is used to connect two negative alternatives. In this context, it emphasizes that both actions were not possible for Jenny due to being grounded.

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43. Complete the ratio_Right∆:

3:4:x

The ratio is given as 3:4:x. To find the value of x, we can use the given information that the ratioRight∆ is equal to 5. Since the ratioRight∆ is the first term in the ratio, we can set up the equation as 3/5 = x/4. Cross-multiplying, we get 3*4 = 5*x, which simplifies to 12 = 5x. Dividing both sides by 5, we find that x = 12/5 = 2.4. Therefore, the value of x is 2.4.

Explanation

The ratio is given as 3:4:x. To find the value of x, we can use the given information that the ratioRight∆ is equal to 5. Since the ratioRight∆ is the first term in the ratio, we can set up the equation as 3/5 = x/4. Cross-multiplying, we get 3*4 = 5*x, which simplifies to 12 = 5x. Dividing both sides by 5, we find that x = 12/5 = 2.4. Therefore, the value of x is 2.4.

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44. Factor (x+y)(x+y)
(Note: x2 = x²)

The given expression is a product of two binomials, (x+y) and (x+y). When we multiply these two binomials, we use the distributive property to multiply each term of the first binomial by each term of the second binomial. In this case, we have (x+y) multiplied by (x+y), which gives us x^2 + 2xy + y^2. Therefore, the correct answer is x^2 + 2xy + y^2.

Explanation

The given expression is a product of two binomials, (x+y) and (x+y). When we multiply these two binomials, we use the distributive property to multiply each term of the first binomial by each term of the second binomial. In this case, we have (x+y) multiplied by (x+y), which gives us x^2 + 2xy + y^2. Therefore, the correct answer is x^2 + 2xy + y^2.

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

The word "as" is used to define the relationship between the conclusion and the main point of the argument. It indicates that the conclusion is synonymous with or represents the main point of the argument.

Explanation

The word "as" is used to define the relationship between the conclusion and the main point of the argument. It indicates that the conclusion is synonymous with or represents the main point of the argument.

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

The word "as" is used in this idiom to compare the Mona Lisa to other great works of art. It implies that art historians consider the Mona Lisa to be on the same level or in the same category as other renowned and highly esteemed works of art. The use of "as" emphasizes the high regard and admiration that art historians have for the Mona Lisa.

Explanation

The word "as" is used in this idiom to compare the Mona Lisa to other great works of art. It implies that art historians consider the Mona Lisa to be on the same level or in the same category as other renowned and highly esteemed works of art. The use of "as" emphasizes the high regard and admiration that art historians have for the Mona Lisa.

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

The correct answer is "with". In this idiom, "contrast with" means to compare two things that are different from each other. In this context, the speaker's father is comparing the grades of the speaker and their brother, highlighting the differences between them.

Explanation

The correct answer is "with". In this idiom, "contrast with" means to compare two things that are different from each other. In this context, the speaker's father is comparing the grades of the speaker and their brother, highlighting the differences between them.

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

The correct answer is "of" because the preposition "of" is used to indicate the relationship between Mel Gibson and Australia, stating that he is a native belonging to or originating from Australia.

Explanation

The correct answer is "of" because the preposition "of" is used to indicate the relationship between Mel Gibson and Australia, stating that he is a native belonging to or originating from Australia.

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49. 62.5% = what fraction?

The fraction 5/8 is equal to 62.5%. To convert a percentage to a fraction, we divide the percentage by 100 and simplify it if possible. In this case, dividing 62.5 by 100 gives us 0.625. Since 0.625 can be simplified by dividing both the numerator and denominator by 0.125, we get 5/8 as the simplified fraction.

Explanation

The fraction 5/8 is equal to 62.5%. To convert a percentage to a fraction, we divide the percentage by 100 and simplify it if possible. In this case, dividing 62.5 by 100 gives us 0.625. Since 0.625 can be simplified by dividing both the numerator and denominator by 0.125, we get 5/8 as the simplified fraction.

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50. 87.5% = what fraction?

The given question asks for the fraction equivalent of 87.5%. To find this, we convert the percentage to a fraction by dividing it by 100. So, 87.5/100 simplifies to 7/8. Therefore, the correct answer is 7/8.

Explanation

The given question asks for the fraction equivalent of 87.5%. To find this, we convert the percentage to a fraction by dividing it by 100. So, 87.5/100 simplifies to 7/8. Therefore, the correct answer is 7/8.

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51. 7!=?

The given answer, 5040, is the factorial of 7. Factorial is a mathematical operation that multiplies a number by all positive integers less than it down to 1. In this case, 7! is calculated as 7 x 6 x 5 x 4 x 3 x 2 x 1, which equals 5040.

Explanation

The given answer, 5040, is the factorial of 7. Factorial is a mathematical operation that multiplies a number by all positive integers less than it down to 1. In this case, 7! is calculated as 7 x 6 x 5 x 4 x 3 x 2 x 1, which equals 5040.

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52. 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). By using the identity for the difference of squares, we can simplify the expression 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). By using the identity for the difference of squares, we can simplify the expression to x^2-y^2. Therefore, the correct answer is x^2-y^2.

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

The correct answer is "that". The idiom "the hypothesis that" is used to introduce a statement or belief that is being discussed. In this case, the phrase "the hypothesis that aspartame causes brain tumors" is being used to indicate that there is a belief or theory about the potential link between aspartame and brain tumors, but it has not been proven yet.

Explanation

The correct answer is "that". The idiom "the hypothesis that" is used to introduce a statement or belief that is being discussed. In this case, the phrase "the hypothesis that aspartame causes brain tumors" is being used to indicate that there is a belief or theory about the potential link between aspartame and brain tumors, but it has not been proven yet.

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54. 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." In this context, "to be" is used to indicate that the estimated time he has spent impersonating Elvis is longer than the time Elvis himself spent performing. This phrase is commonly used in idiomatic expressions to express estimation or speculation.

Explanation

The correct answer is "to be." In this context, "to be" is used to indicate that the estimated time he has spent impersonating Elvis is longer than the time Elvis himself spent performing. This phrase is commonly used in idiomatic expressions to express estimation or speculation.

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55. Complete the idiom:
I can distinguish day __ night.

The correct answer is "from". The idiom "distinguish between" is commonly used to differentiate or recognize the difference between two things. In this case, the phrase is completed by adding "from" to indicate that the speaker is able to distinguish or tell apart day and night.

Explanation

The correct answer is "from". The idiom "distinguish between" is commonly used to differentiate or recognize the difference between two things. In this case, the phrase is completed by adding "from" to indicate that the speaker is able to distinguish or tell apart day and night.

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56. 12.5% = what fraction?

12.5% is equivalent to the fraction 1/8. This is because 12.5% can be written as a decimal as 0.125. To convert this decimal to a fraction, we can write it as 125/1000, which can be simplified to 1/8.

Explanation

12.5% is equivalent to the fraction 1/8. This is because 12.5% can be written as a decimal as 0.125. To convert this decimal to a fraction, we can write it as 125/1000, which can be simplified to 1/8.

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57. 37.5% = what fraction?

The fraction equivalent to 37.5% is 3/8. To convert a percentage to a fraction, we divide the percentage by 100 and simplify the resulting fraction. In this case, dividing 37.5 by 100 gives us 0.375, which can be simplified to 3/8. Therefore, 37.5% is equal to 3/8 as a fraction.

Explanation

The fraction equivalent to 37.5% is 3/8. To convert a percentage to a fraction, we divide the percentage by 100 and simplify the resulting fraction. In this case, dividing 37.5 by 100 gives us 0.375, which can be simplified to 3/8. Therefore, 37.5% is equal to 3/8 as a fraction.

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58. Factor (x+y)²
(Note: x2 = x²)

The given expression is asking for the factor of (x+y) squared. When we expand (x+y) squared, we get x squared plus 2xy plus y squared. Therefore, the correct answer is x squared plus 2xy plus y squared.

Explanation

The given expression is asking for the factor of (x+y) squared. When we expand (x+y) squared, we get x squared plus 2xy plus y squared. Therefore, the correct answer is x squared plus 2xy plus y squared.

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

The phrase "had a dispute over money" means that the men were arguing or disagreeing about money. They were likely in a conflict or disagreement regarding the use, distribution, or ownership of money. The word "over" indicates that the dispute was centered around the topic of money.

Explanation

The phrase "had a dispute over money" means that the men were arguing or disagreeing about money. They were likely in a conflict or disagreement regarding the use, distribution, or ownership of money. The word "over" indicates that the dispute was centered around the topic of money.

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

This question is asking for the completion of the idiom comparing the quality of the pasta sauce to the mother-in-law's. The correct answer "to" is used to indicate that the pasta sauce is of a much higher quality or better than the mother-in-law's sauce.

Explanation

This question is asking for the completion of the idiom comparing the quality of the pasta sauce to the mother-in-law's. The correct answer "to" is used to indicate that the pasta sauce is of a much higher quality or better than the mother-in-law's sauce.

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61. 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 both divisible by 2, the sum will also be divisible by 2. Therefore, the answer to the equation "Even + Even" 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 both divisible by 2, the sum will also be divisible by 2. Therefore, the answer to the equation "Even + Even" is "Even".

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63. (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 = x^3 and x2 * -2 = -2x^2. Therefore, the expression simplifies to x^3 - 2x^2. However, the question asks for the value of this expression when it equals 1. So, we need to solve the equation x^3 - 2x^2 = 1. This equation does not have a simple solution, so it cannot be simplified further. Therefore, the answer is 1.

Explanation

The given expression is a multiplication of two terms: (x2) and (x-2). When we multiply these terms, we get x2 * x = x^3 and x2 * -2 = -2x^2. Therefore, the expression simplifies to x^3 - 2x^2. However, the question asks for the value of this expression when it equals 1. So, we need to solve the equation x^3 - 2x^2 = 1. This equation does not have a simple solution, so it cannot be simplified further. Therefore, the answer is 1.

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64. 0!=?

The question is asking for the value of 0! (0 factorial). By definition, the factorial of a number is the product of all positive integers less than or equal to that number. In this case, since there are no positive integers less than or equal to 0, the product is empty. However, by convention, 0! is defined to be equal to 1. This is because it simplifies certain mathematical formulas and provides consistency in calculations. Therefore, the correct answer is 1.

Explanation

The question is asking for the value of 0! (0 factorial). By definition, the factorial of a number is the product of all positive integers less than or equal to that number. In this case, since there are no positive integers less than or equal to 0, the product is empty. However, by convention, 0! is defined to be equal to 1. This is because it simplifies certain mathematical formulas and provides consistency in calculations. Therefore, the correct answer is 1.

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

The commercials were obviously targeted at teenage boys. This means that the commercials were specifically designed and aimed towards capturing the attention and interest of teenage boys. The word "targeted" suggests a deliberate and focused approach in order to appeal to this specific demographic.

Explanation

The commercials were obviously targeted at teenage boys. This means that the commercials were specifically designed and aimed towards capturing the attention and interest of teenage boys. The word "targeted" suggests a deliberate and focused approach in order to appeal to this specific demographic.

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67. 16.66% = what fraction?

The given percentage, 16.66%, can be written as a fraction by dividing it by 100. When we divide 16.66 by 100, we get 0.1666. To simplify this fraction, we can express it as 1/6, which means that 16.66% is equal to one-sixth.

Explanation

The given percentage, 16.66%, can be written as a fraction by dividing it by 100. When we divide 16.66 by 100, we get 0.1666. To simplify this fraction, we can express it as 1/6, which means that 16.66% is equal to one-sixth.

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68. 5/6 = what percent?

The fraction 5/6 can be converted to a percentage by dividing the numerator (5) by the denominator (6), then multiplying the result by 100. This calculation gives us 83.33%, which is the equivalent percentage of the fraction 5/6. The answer 83.33 is also correct, as it represents the decimal form of the percentage.

Explanation

The fraction 5/6 can be converted to a percentage by dividing the numerator (5) by the denominator (6), then multiplying the result by 100. This calculation gives us 83.33%, which is the equivalent percentage of the fraction 5/6. The answer 83.33 is also correct, as it represents the decimal form of the percentage.

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69. (Even)(Even) = ?

Even

Odd

When multiplying two even numbers, the result will always be an even number. Therefore, the product of (Even)(Even) will be an even number.

Explanation

When multiplying two even numbers, the result will always be an even number. Therefore, the product of (Even)(Even) will be an even number.

70. Complete the ratio_Right∆:

5:x:13

The given ratio is "ratioRight∆:5:x:13". To complete the ratio, we need to find the value of "x". From the given information, we can see that the value of "x" is 12.

Explanation

The given ratio is "ratioRight∆:5:x:13". To complete the ratio, we need to find the value of "x". From the given information, we can see that the value of "x" is 12.

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71. Factor (x-y)²
(Note: x2 = x²)

The expression (x-y)2 can be expanded using the formula for the square of a binomial, which is (a-b)2 = a2 - 2ab + b2. In this case, a = x and b = y. Therefore, the expanded form of (x-y)2 is x2 - 2xy + y2.

Explanation

The expression (x-y)2 can be expanded using the formula for the square of a binomial, which is (a-b)2 = a2 - 2ab + b2. In this case, a = x and b = y. Therefore, the expanded form of (x-y)2 is x2 - 2xy + y2.

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72. 83.33% = what fraction?

The given question asks for the fraction equivalent of 83.33%. To find this fraction, we can convert the percentage to a decimal by dividing it by 100. So, 83.33% becomes 0.8333 as a decimal. To express this decimal as a fraction, we can write it as 8333/10000. Simplifying this fraction gives us 5/6, which is the equivalent fraction of 83.33%.

Explanation

The given question asks for the fraction equivalent of 83.33%. To find this fraction, we can convert the percentage to a decimal by dividing it by 100. So, 83.33% becomes 0.8333 as a decimal. To express this decimal as a fraction, we can write it as 8333/10000. Simplifying this fraction gives us 5/6, which is the equivalent fraction of 83.33%.

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73. 1/6 = what percent?

The given question asks for the percentage equivalent of 1/6. To find this, we divide 1 by 6, which equals 0.1666. To convert this decimal to a percentage, we multiply it by 100, giving us 16.66%. Therefore, the correct answer is 16.66%.

Explanation

The given question asks for the percentage equivalent of 1/6. To find this, we divide 1 by 6, which equals 0.1666. To convert this decimal to a percentage, we multiply it by 100, giving us 16.66%. Therefore, the correct answer is 16.66%.

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

This idiom is commonly used to express that two or more people received the same punishment. In this case, the phrase "as to you" is used to compare the punishment given to the speaker with the punishment given to the person they are addressing. It implies that both individuals were treated equally and received the same consequences for their actions.

Explanation

This idiom is commonly used to express that two or more people received the same punishment. In this case, the phrase "as to you" is used to compare the punishment given to the speaker with the punishment given to the person they are addressing. It implies that both individuals were treated equally and received the same consequences for their actions.

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

The correct answer is "as". In this idiom, "not so much...as" is used to compare two qualities or characteristics, indicating that the first quality is not as strong or prevalent as the second one. In this case, it suggests that the person being referred to is not as smart as they are cunning.

Explanation

The correct answer is "as". In this idiom, "not so much...as" is used to compare two qualities or characteristics, indicating that the first quality is not as strong or prevalent as the second one. In this case, it suggests that the person being referred to is not as smart as they are cunning.

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

The phrase "Think of it more of a promise than a threat" means that one should consider the situation or statement as more of a guarantee or assurance rather than a warning or intimidation. By using the preposition "of," it emphasizes the idea that the intention behind the statement is not to cause harm or instill fear, but rather to convey a sense of reliability or commitment.

Explanation

The phrase "Think of it more of a promise than a threat" means that one should consider the situation or statement as more of a guarantee or assurance rather than a warning or intimidation. By using the preposition "of," it emphasizes the idea that the intention behind the statement is not to cause harm or instill fear, but rather to convey a sense of reliability or commitment.

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80. 66.66% = what fraction?

The given question asks for the fraction equivalent of 66.66%. To find this, we convert the percentage to a fraction by dividing it by 100. So, 66.66/100 = 0.6666. This decimal can be simplified to 2/3, which is the equivalent fraction.

Explanation

The given question asks for the fraction equivalent of 66.66%. To find this, we convert the percentage to a fraction by dividing it by 100. So, 66.66/100 = 0.6666. This decimal can be simplified to 2/3, which is the equivalent fraction.

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

The given idiom "She is not only beautiful, but also smart" is used to emphasize that the person being described is not just beautiful, but also intelligent. The phrase "but also" is used to add another quality or characteristic to the statement. In this case, it is used to highlight the person's intelligence in addition to their beauty.

Explanation

The given idiom "She is not only beautiful, but also smart" is used to emphasize that the person being described is not just beautiful, but also intelligent. The phrase "but also" is used to add another quality or characteristic to the statement. In this case, it is used to highlight the person's intelligence in addition to their beauty.

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

The given expression (za)(zb) can be simplified by multiplying the two terms together. According to the rules of multiplication, when multiplying two terms with the same base, you add the exponents. In this case, the base is "z" and the exponents are "a" and "b". Therefore, the answer is za+b.

Explanation

The given expression (za)(zb) can be simplified by multiplying the two terms together. According to the rules of multiplication, when multiplying two terms with the same base, you add the exponents. In this case, the base is "z" and the exponents are "a" and "b". Therefore, the answer is za+b.

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84. Even + Odd = ?

Even

Odd

When we add an even number and an odd number together, the result will always be an odd number. This is because even numbers are always divisible by 2, while odd numbers are not. When we add an even number (which can be expressed as 2n, where n is an integer) and an odd number (which can be expressed as 2n+1), the sum will be (2n) + (2n+1) = 4n + 1, which is always an odd number. Therefore, the answer is odd.

Explanation

When we add an even number and an odd number together, the result will always be an odd number. This is because even numbers are always divisible by 2, while odd numbers are not. When we add an even number (which can be expressed as 2n, where n is an integer) and an odd number (which can be expressed as 2n+1), the sum will be (2n) + (2n+1) = 4n + 1, which is always an odd number. Therefore, the answer is odd.

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

Christopher Columbus is often credited with the discovery of America, but it is important to acknowledge that Native Americans were already present in America before Columbus arrived. The word "with" in the idiom implies that Columbus is given recognition or acknowledgment for the discovery, despite the fact that Native Americans were the original inhabitants of the land.

Explanation

Christopher Columbus is often credited with the discovery of America, but it is important to acknowledge that Native Americans were already present in America before Columbus arrived. The word "with" in the idiom implies that Columbus is given recognition or acknowledgment for the discovery, despite the fact that Native Americans were the original inhabitants of the land.

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86. 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, then each leg must also be x. Therefore, the measure of the side of the triangle 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, then each leg must also be x. Therefore, the measure of the side of the triangle is x.

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87. 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 points that fall within that range. In a normal distribution, each sextile represents approximately 13.6% of the data. Therefore, the fourth distribution sextile would represent 34% of the data. The answer provided, "34%", is the exact percentage, while "34" is the rounded value.

Explanation

The fourth distribution sextile of a normal bell curve represents the percentage of data points that fall within that range. In a normal distribution, each sextile represents approximately 13.6% of the data. Therefore, the fourth distribution sextile would represent 34% of the data. The answer provided, "34%", is the exact percentage, while "34" is the rounded value.

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88. 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. So when two odd numbers are added, we get (2n+1) + (2m+1) = 2(n+m+1), which is 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. So when two odd numbers are added, we get (2n+1) + (2m+1) = 2(n+m+1), which is an even number. Therefore, the correct answer is "Even".

89. 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 is parallel to the y-axis and intersects it at the point (c,0). Therefore, the correct answer is x=c.

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 is parallel to the y-axis and intersects it at the point (c,0). Therefore, the correct answer is x=c.

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

The second distribution sextile of a normal bell curve refers to the range between the 14th percentile and the 86th percentile. In other words, it represents the middle 72% of the data. Therefore, the answer is 14%.

Explanation

The second distribution sextile of a normal bell curve refers to the range between the 14th percentile and the 86th percentile. In other words, it represents the middle 72% of the data. Therefore, the answer is 14%.

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91. X^1/2=?
(option+v=√)

The given equation x1/2 = √x can be solved by taking the square root of both sides of the equation. The square root of x1/2 is equal to √x, which is the answer.

Explanation

The given equation x1/2 = √x can be solved by taking the square root of both sides of the equation. The square root of x1/2 is equal to √x, which is the answer.

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

The question is asking for the percentage value of the sixth distribution sextile of a normal bell curve. A normal bell curve is divided into six equal parts, known as sextiles. Each sextile represents a percentage of the total distribution. In this case, the answer is given as 2%, indicating that the sixth distribution sextile represents 2% of the total distribution. Additionally, the answer is also provided as simply "2", which may be interpreted as a shorthand way of expressing 2%.

Explanation

The question is asking for the percentage value of the sixth distribution sextile of a normal bell curve. A normal bell curve is divided into six equal parts, known as sextiles. Each sextile represents a percentage of the total distribution. In this case, the answer is given as 2%, indicating that the sixth distribution sextile represents 2% of the total distribution. Additionally, the answer is also provided as simply "2", which may be interpreted as a shorthand way of expressing 2%.

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93. 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 done, and t represents the time taken to do the work. This formula states that the work done is equal to the rate at which the work is done multiplied by the time taken.

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 done, and t represents the time taken to do the work. This formula states that the work done is equal to the rate at which the work is done multiplied by the time taken.

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

The first distribution sextile of a normal bell curve represents the percentage of data that falls within the first 16.67% of the distribution. Since there are six sextiles in total, each sextile represents approximately 16.67% of the data. Therefore, the first distribution sextile represents 2% of the total data. The number "2" is not related to the percentage and seems unrelated to the question.

Explanation

The first distribution sextile of a normal bell curve represents the percentage of data that falls within the first 16.67% of the distribution. Since there are six sextiles in total, each sextile represents approximately 16.67% of the data. Therefore, the first distribution sextile represents 2% of the total data. The number "2" is not related to the percentage and seems unrelated to the question.

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

The slope of a line that is perpendicular to another line can be found by taking the negative reciprocal of the slope of the given line. In this case, the given line has a slope of x/y, so the perpendicular line will have a slope of -y/x.

Explanation

The slope of a line that is perpendicular to another line can be found by taking the negative reciprocal of the slope of the given line. In this case, the given 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 third distribution sextile of a normal bell curve?

The third distribution sextile of a normal bell curve represents the middle 34% of the data. This means that 34% of the data falls within this range, with 17% below and 17% above. Therefore, both the percentage (34%) and the numerical value (34) are correct answers.

Explanation

The third distribution sextile of a normal bell curve represents the middle 34% of the data. This means that 34% of the data falls within this range, with 17% below and 17% above. Therefore, both the percentage (34%) and the numerical value (34) are correct answers.

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

The fifth distribution sextile of a normal bell curve refers to the value that divides the data into six equal parts. In this case, the answer is 14% or 14, which means that 14% or 14 of the data falls below this value and the remaining 86% or 86 falls above it.

Explanation

The fifth distribution sextile of a normal bell curve refers to the value that divides the data into six equal parts. In this case, the answer is 14% or 14, which means that 14% or 14 of the data falls below this value and the remaining 86% or 86 falls above it.

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

The formula for rate of speed is determined by dividing the distance traveled (d) by the time taken to travel that distance (t). This is represented by the equation r=d/t.

Explanation

The formula for rate of speed is determined by dividing the distance traveled (d) by the time taken to travel that distance (t). This is represented by the equation r=d/t.

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99. (Even)(Odd)

Even

Odd

The given pattern suggests that when an even number is multiplied by any number (even or odd), the result is always an even number. Therefore, the correct answer is "Even".

Explanation

The given pattern suggests that when an even number is multiplied by any number (even or odd), the result is always an even number. Therefore, the correct answer is "Even".

100. 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 calculated by multiplying the probability of event A (Pa) with the probability of event B (Pb). This is because when two independent events occur, the probability of both events happening is equal to the product of their individual probabilities. Therefore, the correct answer is (Pa)(Pb).

Explanation

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

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101. 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 d2 = l2 + w2 + h2. This formula is derived from the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the diagonal) is equal to the sum of the squares of the lengths of the other two sides. In this case, the length (l), width (w), and height (h) of the box represent the three sides of the right-angled triangle, and by substituting these values into the formula, we can calculate the length of the diagonal (d).

Explanation

The formula to determine the length of the diagonal of a box is d2 = l2 + w2 + h2. This formula is derived from the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the diagonal) is equal to the sum of the squares of the lengths of the other two sides. In this case, the length (l), width (w), and height (h) of the box represent the three sides of the right-angled triangle, and by substituting these values into the formula, we can calculate the length of the diagonal (d).

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102. (Odd)(Odd) = ?

Even

Odd

The product of two odd numbers is always an odd number. Therefore, when multiplying two odd numbers, the result will be odd.

Explanation

The product of two odd numbers is always an odd number. Therefore, when multiplying two odd numbers, the result will be odd.

103. 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". The idiom "to be" is used to indicate that something is falsely claimed or misrepresented. In this context, it means that his friends do not believe that the ring he bought at the auction is truly Jackie O's; they think he was tricked into believing it was.

Explanation

The correct answer is "to be". The idiom "to be" is used to indicate that something is falsely claimed or misrepresented. In this context, it means that his friends do not believe that the ring he bought at the auction is truly Jackie O's; they think he was tricked into believing it was.

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

The formula for calculating the volume of a cylinder is given by πr^2h, where π represents the mathematical constant pi, r is the radius of the cylinder's base, and h is the height of the cylinder. This formula is derived from the fact that the volume of a cylinder can be thought of as the area of the base (πr^2) multiplied by the height (h).

Explanation

The formula for calculating the volume of a cylinder is given by πr^2h, where π represents the mathematical constant pi, r is the radius of the cylinder's base, and h is the height of the cylinder. This formula is derived from the fact that the volume of a cylinder can be thought of as the area of the base (πr^2) multiplied by the height (h).

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

The phrase "as to be" is used to compare the beauty of the person to the level of being exquisite. It suggests that the person's beauty is of such high quality or intensity that it can be described as exquisite. The word "exquisite" means extremely beautiful or delicate, so this idiom emphasizes the exceptional beauty of the person in question.

Explanation

The phrase "as to be" is used to compare the beauty of the person to the level of being exquisite. It suggests that the person's beauty is of such high quality or intensity that it can be described as exquisite. The word "exquisite" means extremely beautiful or delicate, so this idiom emphasizes the exceptional beauty of the person in question.

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106. 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 takes into account the probabilities of both events A and B occurring, as well as the possibility of both events occurring at the same time. By subtracting the product of the probabilities of events A and B, we ensure that the overlapping probability is not counted twice.

Explanation

The formula for the probability of event A or the probability of event B is given by Pa+Pb-(PaPb). This formula takes into account the probabilities of both events A and B occurring, as well as the possibility of both events occurring at the same time. By subtracting the product of the probabilities of events A and B, we ensure that the overlapping probability is not counted twice.

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

The given answer 1:1:√2 represents the ratio of the sides of an isosceles triangle. In an isosceles triangle, two sides are equal in length. Here, the two equal sides have a ratio of 1:1, meaning they are of equal length. The third side, which is not equal to the other two sides, is represented by √2. This indicates that the length of the third side is the square root of 2 times the length of the equal sides.

Explanation

The given answer 1:1:√2 represents the ratio of the sides of an isosceles triangle. In an isosceles triangle, two sides are equal in length. Here, the two equal sides have a ratio of 1:1, meaning they are of equal length. The third side, which is not equal to the other two sides, is represented by √2. This indicates that the length of the third side is the square root of 2 times the length of the equal sides.

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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 is the formula for calculating the probability. The numerator represents the total number of ways to arrange the racers in the race, while the denominator represents the number of ways to arrange the racers in each winning position. By dividing the numerator by the denominator, we get the probability of a specific arrangement occurring.

Explanation

The given answer is the formula for calculating the probability. The numerator represents the total number of ways to arrange the racers in the race, while the denominator represents the number of ways to arrange the racers in each winning position. By dividing the numerator by the denominator, we get the probability of a specific arrangement occurring.

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109. 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. The formula is derived from dividing the equilateral triangle into two congruent right triangles, where the base of each right triangle is equal to half of one side of the equilateral triangle. By using the Pythagorean theorem and the properties of a right triangle, the formula simplifies to b^2√3/4.

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. The formula is derived from dividing the equilateral triangle into two congruent right triangles, where the base of each right triangle is equal to half of one side of the equilateral triangle. By using the Pythagorean theorem and the properties of a right triangle, the formula simplifies to b^2√3/4.

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

The coordinates of the y-intercept of a line are given by the point (-b/m, 0). This means that the y-intercept is located at the x-coordinate of -b/m and the y-coordinate of 0. The duplicate answer choice (-b/m,0) is redundant and unnecessary.

Explanation

The coordinates of the y-intercept of a line are given by the point (-b/m, 0). This means that the y-intercept is located at the x-coordinate of -b/m and the y-coordinate of 0. The duplicate answer choice (-b/m,0) is redundant and unnecessary.

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

The ratio of the sides of a 30/60/90 right triangle is 1:√3:2. In a 30/60/90 triangle, 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. Therefore, the ratio of the sides is 1:√3:2.

Explanation

The ratio of the sides of a 30/60/90 right triangle is 1:√3:2. In a 30/60/90 triangle, 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. Therefore, the ratio of the sides is 1:√3:2.

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112. 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(πr2) + (2πrh). This formula takes into account the two circular bases of the cylinder, which have an area of πr2 each, and the curved surface area of the cylinder, which is represented by the term 2πrh. By adding these two components together, we can calculate the total surface area of the cylinder.

Explanation

The formula for the surface area of a cylinder is 2(πr2) + (2πrh). This formula takes into account the two circular bases of the cylinder, which have an area of πr2 each, and the curved surface area of the cylinder, which is represented by the term 2πrh. By adding these two components together, we can calculate the total surface area of the cylinder.

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

The correct answer is "none, blank". In this idiom, "blank" means without any doubt or hesitation. Art historians consider the Mona Lisa as one of the greatest works of art without any doubt or hesitation.

Explanation

The correct answer is "none, blank". In this idiom, "blank" means without any doubt or hesitation. Art historians consider the Mona Lisa as one of the greatest works of art without any doubt or hesitation.

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