1.
12.5% = what fraction?
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.
2.
16.66% = what fraction?
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.
3.
37.5% = what fraction?
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.
4.
62.5% = what fraction?
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.
5.
66.66% = what fraction?
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.
6.
83.33% = what fraction?
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.
7.
87.5% = what fraction?
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%.
8.
1/8 = what percent?
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%.
9.
1/6 = what percent?
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%.
10.
3/8 = what percent?
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%.
11.
5/8 = what percent?
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%.
12.
5/6 = what percent?
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%.
13.
7/8 = what percent?
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%.
14.
11^{2}=?
Explanation
The given equation 112 = 121 is a statement of equality. It means that the value of 112 is equal to 121.
15.
12^{2}=?
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.
16.
13^{2}=?
Explanation
The given equation is 132 = ?. The answer is 169. This means that 132 is equal to 169.
17.
14^{2}=?
18.
15^{2}=?
19.
4^{3}=?
20.
5^{3}=?
21.
6^{3}=?
22.
7^{3}=?
23.
8^{3}=?
24.
9^{3}=?
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.
25.
âˆš2 â‰ˆ ?
Explanation
The square root of 2 is approximately equal to 1.4.
26.
âˆš3 â‰ˆ ?
27.
Ratio_{Isocelesâˆ† Sides? }_{(answer format }_{x:y:z}_{âˆš = option+v)}
Explanation
The ratio of the sides of an isosceles triangle is 1:1:âˆš2. 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 âˆš2 units.
28.
Complete the ratio_{Rightâˆ†:}3:4:x
Explanation
The ratio given is "ratioRightâˆ†:3:4:x". The ratio is incomplete as it does not provide any numerical values for "ratioRightâˆ†" and "x". Therefore, without this information, it is not possible to determine the value of "x" or provide a complete explanation.
29.
0!=?
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.
30.
1!=?
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.
31.
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.
32.
3!=?
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.
33.
4!=?
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.
34.
5!=?
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.
35.
6!=?
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.
36.
7!=?
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.
37.
Factor (x+y)^{2}(Note: x2 = x^{2})
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)Â² = aÂ² + 2ab + bÂ². Applying this formula to the given expression, we get xÂ² + 2xy + yÂ². Therefore, the correct answer is xÂ² + 2xy + yÂ².
38.
Factor (x-y)^{2}(Note: x2 = x^{2})
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.
39.
Factor (x+y)(x+y)(Note: x2 = x^{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.
40.
Factor (x+y)(x-y)(Note: x2 = x^{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.
41.
Complete the idiom:If you worry too much ___ the GMAT, you'll develop 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.
42.
Complete the idiom:My GMAT teacher defines the conclusion __ the main point of the argument.
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.
43.
Complete the idiom:Art historians regard the Mona Lisa __ 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.
44.
Complete the idiom:He is not so much smart __ cunning.
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.
45.
Complete the idiom:She is so beautiful __ 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.
46.
Complete the idiom:Think of it more __ a promise than a threat.
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.
47.
Complete the idiom:Many people see euthanasia __ an escape from pain.
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.
48.
Complete the idiom:Mom and dad gave the same punishment to me __ to you.
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.
49.
Complete the idiom:Memorizing idioms is not as fun __ playing bingo.
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.
50.
Complete the idiom:The commercials were obviously targeted __ teenage boys.
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.