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Overview of formulas, arithmetic, and idioms to memorize for the GMAT.

• 1.

### 12.5% = what fraction?

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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• 2.

### 16.66% = what fraction?

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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• 3.

### 37.5% = what 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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• 4.

### 62.5% = what 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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• 5.

### 66.66% = what 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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• 6.

### 83.33% = what fraction?

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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• 7.

### 87.5% = what fraction?

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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• 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, the correct answer is 12.5%.

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• 9.

### 1/6 = what percent?

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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• 10.

### 3/8 = what percent?

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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• 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 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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• 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), 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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• 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, the correct answer is 87.5%.

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• 14.

### 112=?

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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• 15.

• 16.

• 17.

• 18.

• 19.

• 20.

• 21.

• 22.

### 73=?

Explanation
The given question is incomplete and not readable.

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• 23.

• 24.

• 25.

### √2 ≈ ?

Explanation
The value of √2 is approximately 1.4.

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• 26.

• 27.

### RatioIsoceles∆ 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. 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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• 28.

### Complete the ratioRight∆:3:4:x

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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• 29.

### 0!=?

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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• 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.

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• 31.

### 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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• 32.

### 3!=?

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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• 33.

### 4!=?

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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• 34.

### 5!=?

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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• 35.

### 6!=?

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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• 36.

### 7!=?

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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• 37.

### Factor (x+y)2(Note: x2 = x2)

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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• 38.

### Factor (x-y)2(Note: x2 = x2)

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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• 39.

### Factor (x+y)(x+y)(Note: x2 = x2)

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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• 40.

### Factor (x+y)(x-y)(Note: x2 = x2)

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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• 41.

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

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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• 42.

### Complete the idiom:My GMAT teacher defines the conclusion __ 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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• 43.

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

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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• 44.

### Complete the idiom:He is not so much smart __ 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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• 45.

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

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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• 46.

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

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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• 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 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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• 48.

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

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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• 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 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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• 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 "targeted" suggests a deliberate and focused approach in order to appeal to this specific demographic.

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