1.
12.5% = what fraction?
Explanation
12.5% can be written as a fraction by dividing it by 100. Simplifying 12.5/100 gives us 1/8. Therefore, the fraction equivalent of 12.5% is 1/8.
2.
16.66% = what fraction?
Explanation
The given percentage, 16.66%, can be expressed as the fraction 1/6. This is because 16.66% is equivalent to the decimal 0.1666, which can be simplified to 1/6.
3.
37.5% = what fraction?
Explanation
The correct answer is 3/8 because 37.5% can be written as a fraction by dividing it by 100. When we divide 37.5 by 100, we get 0.375. This decimal can be simplified to a fraction by moving the decimal point two places to the right, resulting in 3/8. Therefore, 37.5% is equivalent to the fraction 3/8.
4.
62.5% = what fraction?
Explanation
The fraction 5/8 is equivalent to 62.5% because when you convert a percentage to a fraction, you divide the percentage by 100 and simplify if possible. In this case, 62.5 divided by 100 is 0.625, which can be simplified to 5/8 by dividing both the numerator and denominator by 0.125. Therefore, 62.5% is equal to 5/8.
5.
66.66% = what fraction?
Explanation
The given question asks for the fraction equivalent to 66.66%. To convert a percentage to a fraction, we divide the percentage by 100. In this case, dividing 66.66 by 100 gives us 0.6666. We can simplify this fraction by dividing both the numerator and denominator by 0.6666, which gives us 2/3. Therefore, the fraction equivalent to 66.66% is 2/3.
6.
83.33% = what fraction?
Explanation
The fraction 5/6 is equivalent to 83.33% because when we convert 5/6 to a decimal, we get 0.8333. Multiplying this decimal by 100 gives us 83.33%. Therefore, 5/6 is the fraction that represents 83.33%.
7.
87.5% = what fraction?
Explanation
The fraction 7/8 is equivalent to 87.5%. To convert a percentage to a fraction, we divide the percentage value by 100 and simplify the fraction if possible. In this case, 87.5 divided by 100 equals 0.875. Simplifying 0.875 gives us 7/8, which is the equivalent fraction.
8.
1/8 = what percent?
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, 1/8 is equal to 12.5%.
9.
1/6 = what percent?
Explanation
The given question is asking 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, resulting in 16.66%. Therefore, the correct answer is 16.66%.
10.
3/8 = what percent?
Explanation
The given question asks for the percentage equivalent of the fraction 3/8. To find this, we can convert the fraction to a decimal by dividing the numerator (3) by the denominator (8), which equals 0.375. To express this as a percentage, we multiply the decimal by 100. Therefore, 0.375 multiplied by 100 equals 37.5%. So, the correct answer is 37.5%.
11.
5/8 = what percent?
Explanation
The fraction 5/8 can be converted to a percent by dividing the numerator (5) by the denominator (8) and then multiplying by 100. This calculation gives us 0.625, which when multiplied by 100 equals 62.5%. Therefore, 5/8 is equal to 62.5%.
12.
5/6 = what percent?
Explanation
To find the percentage of a fraction, we can multiply the fraction by 100. In this case, multiplying 5/6 by 100 gives us 500/6, which is approximately 83.33%. Therefore, the correct answer is 83.33%.
13.
7/8 = what percent?
Explanation
The given question asks for the percentage equivalent of the fraction 7/8. To find this, we divide the numerator (7) by the denominator (8) and multiply the result by 100. This calculation gives us 87.5%. Therefore, the correct answer is 87.5%.
14.
11^{2}=?
15.
12^{2}=?
16.
13^{2}=?
Explanation
The given equation is asking for the value of 132. The answer provided is 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 given equation "93=?" implies that 93 is equal to something. The answer provided is 729, which means that 93 is equal to 729.
25.
√2 ≈ ?
Explanation
The given value of 1.4 is an approximation of the square root of 2. The square root of 2 is an irrational number, meaning it cannot be expressed as a fraction or a terminating or repeating decimal. The decimal representation of the square root of 2 goes on infinitely without a pattern. However, 1.4 is a close approximation of the square root of 2 and is commonly used in calculations where an exact value is not necessary.
26.
√3 ≈ ?
27.
Ratio_{Isoceles∆ Sides? }_{(answer format }_{x:y:z}_{√ = option+v)}
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, and the third side, which is the base, may have a different length. The ratio 1:1:√2 indicates that the two equal sides have a length of 1 unit each, while the length of the base is √2 units. This ratio is commonly used to describe the sides of a 45-45-90 degree triangle, where the two equal angles are 45 degrees each and the right angle is 90 degrees.
28.
Complete the ratio_{Right∆:}3:4:x
Explanation
The ratio is given as 3:4:x. To find the value of x, we can set up a proportion using the given information. The ratio of the first two terms is 3/4, and the ratio of the second and third terms is 4/x. We can cross multiply and solve for x. 3x = 4*4, which simplifies to 3x = 16. Dividing both sides by 3, we get x = 16/3. However, since the answer is given as 5, it does not match the calculated value. Therefore, the question may be incomplete or the given answer may be incorrect.
29.
0!=?
Explanation
The value of 0! (0 factorial) is 1. Factorial is a mathematical operation that multiplies a given number by all the positive integers less than it. By convention, 0! is defined as equal to 1. This is because there is only one way to arrange zero objects, and that is by not arranging them at all. Therefore, the answer to 0! is 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. Therefore, the answer is 1.
31.
2!=?
Explanation
The 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, 2! is equal to 2, because it is the product of 2 and 1, the only positive integers less than or equal to 2.
32.
3!=?
Explanation
The question is asking for the value of 3 factorial, which is denoted as 3!. Factorial is a mathematical operation that multiplies a number by all positive integers less than it. In this case, 3! is calculated as 3 x 2 x 1, which equals 6.
33.
4!=?
Explanation
The given question is asking for the value of 4 factorial, which is denoted as 4!. Factorial means multiplying a number by all the positive integers less than it down to 1. So, 4! is calculated as 4 x 3 x 2 x 1, which equals 24.
34.
5!=?
Explanation
The question is asking for the value of 5 factorial, which is denoted as 5!. Factorial is a mathematical operation that multiplies a number by all positive integers less than it down to 1. Therefore, 5! is calculated by multiplying 5 by 4, 3, 2, and 1. This results in the value of 120.
35.
6!=?
Explanation
The question is asking for the value of 6 factorial, which is represented by 6!. Factorial is a mathematical operation where you multiply a number by all the positive integers less than it. In this case, 6! is equal to 6 x 5 x 4 x 3 x 2 x 1, which equals 720.
36.
7!=?
Explanation
The given answer, 5040, is the factorial of 7. Factorial is a mathematical operation where you multiply a number by all the positive integers less than it. In this case, 7! is calculated as 7 x 6 x 5 x 4 x 3 x 2 x 1, which equals 5040.
37.
Factor (x+y)^{2}(Note: x2 = x^{2})
Explanation
The given expression is asking for the square of the sum of x and y. To find this, we use the formula (a+b)2 = a2 + 2ab + b2. In this case, a is x and b is y. Plugging in these values, we get x2 + 2xy + y2 as the correct answer.
38.
Factor (x-y)^{2}(Note: x2 = x^{2})
Explanation
The given expression is (x-y)², which represents the square of the difference between x and y. Expanding this expression using the formula (a-b)² = a² - 2ab + b², we get x² - 2xy + y². Therefore, the correct answer is x² - 2xy + y².
39.
Factor (x+y)(x+y)(Note: x2 = x^{2})
Explanation
The given expression (x+y)(x+y) can be expanded using the distributive property. Multiplying each term in the first set of parentheses by each term in the second set of parentheses, we get x*x + x*y + y*x + y*y. Simplifying this further, we combine like terms to obtain x^2 + 2xy + y^2. Therefore, the correct answer is x^2 + 2xy + y^2.
40.
Factor (x+y)(x-y)(Note: x2 = x^{2})
Explanation
The given expression is a product of three terms: (x+y), (x-y), and (x2-y2). The first two terms can be expanded using the difference of squares formula, which states that (a+b)(a-b) = a2-b2. Applying this formula to (x+y)(x-y) gives us x2-y2. Therefore, the correct answer is x2-y2.
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 someone worries excessively about the GMAT (Graduate Management Admission Test), it implies that they are overly stressed 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 indicate that the conclusion is the same as or equivalent to the main point of the argument. It suggests that the conclusion is a direct reflection or representation of the main point, emphasizing their close relationship.
43.
Complete the idiom:Art historians regard the Mona Lisa __ one of the greatest works of art.
Explanation
The idiom "regard as" means to consider or think of someone or something in a particular way. In this context, art historians view the Mona Lisa as one of the greatest works of art. This suggests that they hold a high opinion of the painting and recognize its significance and artistic value.
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 smart as cunning" implies that the person may not be highly intelligent, but they are very cunning or crafty.
45.
Complete the idiom:She is so beautiful __ exquisite.
Explanation
The correct answer is "as to be." This completes the idiom "She is so beautiful as to be exquisite." The phrase "as to be" is used to emphasize the extreme beauty of the person being described. It suggests that the person's beauty is so extraordinary that it reaches the level of being exquisite.
46.
Complete the idiom:Think of it more __ a promise than a threat.
Explanation
The correct answer is "of". This is because the idiom "think of it more of a promise than a threat" means to consider something as more of a commitment or assurance rather than a warning or intimidation. The word "of" is used to indicate the nature or characteristic of the thing being compared, in this case, emphasizing the positive aspect of the situation.
47.
Complete the idiom:Many people see euthanasia __ an escape from pain.
Explanation
The correct answer is "as." In this context, "as" is used to indicate that many people view euthanasia as an escape from pain. This means that they perceive euthanasia as a way to alleviate or avoid suffering.
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 indicate that the punishment given to the speaker is the same as the punishment given to the person they are speaking to. It implies that both individuals received equal consequences for their actions.
49.
Complete the idiom:Memorizing idioms is not as fun __ playing bingo.
Explanation
This question is asking for the completion of an idiom. The correct answer is "as." The idiom being completed is "Memorizing idioms is not as fun as playing bingo." This means that playing bingo is more enjoyable than memorizing idioms.
50.
Complete the idiom:The commercials were obviously targeted __ teenage boys.
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 "at" indicates the direction or focus of the targeting, implying that the commercials were intended for this particular demographic.