GRE Math Question (Set 1 of 6 explained)

GRE Question Set 1.6 EXPLAINED.pages

1. The ratio 7 to 5 The numerator

The denominator

A.The quantity on the left is greater B. The quantity on the right is greater C. Both are equal D. The relationship cannot be determined without further information Correct: A Explanation: A fraction is a number of the form a/b where a and b are integers and b ! 0. The integer a is called the numerator of the fraction, and b is called the denominator. For example, the ratio 7 to 5 is 7/5. 7/5 is a fraction in which 7 is the numerator and 5 is the denominator. Such numbers are also called rational numbers.

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GRE Question Set 1.6 EXPLAINED.pages

2. s and t are positive quantities s/t

The ratio of t to s

A.The quantity on the left is greater B. The quantity on the right is greater C. Both are equal D. The relationship cannot be determined without further information Correct: D Explanation: Without knowing values for s and t, we can’t determine if one reciprocal has more value than its coordinating reciprocal.

The ratio of one quantity to another is a way to express their relative sizes, often in the form of a fraction, where the first quantity is the numerator and the second quantity is the denominator. Thus, if s and t are positive quantities, then the ratio of s to t can be written as the fraction s. The notation “s to t” or “s:t” is also used to t express this ratio. For example, if there are 2 apples and 3 oranges in a basket, we

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GRE Question Set 1.6 EXPLAINED.pages

can say that the ratio of the number of apples to the number of oranges is 2 or that 3 it is 2 to 3 or that it is 2:3. Like fractions, ratios can be reduced to lowest terms. For example, if there are 8 apples and 12 oranges in a basket, then the ratio of the num- bers of apples to oranges is still 2 to 3. Similarly, the ratio 9 to 12 is equivalent to the ratio 3 to 4.

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GRE Question Set 1.6 EXPLAINED.pages

3. If s > 0 and t < 0 s:t

t to s

A.The quantity on the left is greater B. The quantity on the right is greater C. Both are equal D. The relationship cannot be determined without further information Correct: D Explanation: Without knowing the absolute values of both s and t, we canâ&#x20AC;&#x2122;t determine which fraction is greater. Both fractions will be negative.

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GRE Question Set 1.6 EXPLAINED.pages

4. There are 2 figs and 3 tomatoes and no other food in a basket.

The ratio of the number of The ratio of the number of figs to the number of tomatoes to the number of tomatoes food

A.The quantity on the left is greater B. The quantity on the right is greater C. Both are equal D. The relationship cannot be determined without further information Correct: A Explanation: The left side has a value of 2/3.

The right side has a value of 3/5.

2/3 = 66.7% 3/5 = 60.0%

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GRE Question Set 1.6 EXPLAINED.pages

5. There are 8 apples and 12 oranges and no other food in a basket.

2/3

The ratio of the number of apples to oranges

A.The quantity on the left is greater B. The quantity on the right is greater C. Both are equal D. The relationship cannot be determined without further information Correct: C Explanation: The left side has a value of 66.7%.

The right side has a value of 8/12 = 2/3 = 66.7%

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GRE Question Set 1.6 EXPLAINED.pages

6.

9 to 12

3/4

A.The quantity on the left is greater B. The quantity on the right is greater C. Both are equal D. The relationship cannot be determined without further information Correct: C Explanation: The left side has a value of 9/12 = 3/4.

The right side has a value of 3/4.

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GRE Question Set 1.6 EXPLAINED.pages

7. r, s, and t are positive numbers.

r to s to t

r÷s÷t

A.The quantity on the left is greater B. The quantity on the right is greater C. Both are equal D. The relationship cannot be determined without further information Correct: C Explanation: If three or more positive quantities are being considered, say r, s, and t, then their relative sizes can also be expressed as a ratio with the notation “r to s to t.” For, example, if there are 5 apples, 30 pears, and 20 oranges in a basket, then the ratio of the numbers of apples to pears to oranges is 5 to 30 to 20. This ratio can be reduced to 1 to 6 to 4 by dividing each number by the greatest common divisor of 5, 30, and 20, which is 5.

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GRE Question Set 1.6 EXPLAINED.pages

8. If there are 5 apples, 30 pears, and 20 oranges in a basket The ratio of the number of The greatest common pears to apples divisor of 5, 30, and 20

A.The quantity on the left is greater B. The quantity on the right is greater C. Both are equal D. The relationship cannot be determined without further information Correct: A Explanation: The left side has a value of 30/5 = 6/1 The right side has a maximum value of only 5. The greatest divisor of 5 is 5.

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GRE Question Set 1.6 EXPLAINED.pages

9.

5 to 30 to 20

1 to 6 to 4

A.The quantity on the left is greater B. The quantity on the right is greater C. Both are equal D. The relationship cannot be determined without further information Correct: C Explanation: 5 to 30 to 20; this ratio can be reduced to 1 to 6 to 4

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GRE Question Set 1.6 EXPLAINED.pages

10. x / 49 = 3 / 21

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x/1

A.The quantity on the left is greater B. The quantity on the right is greater C. Both are equal D. The relationship cannot be determined without further information Correct: C Explanation: To find a number x so that the ratio of x to 49 is the same as the ratio of 3 to 21, you can write X/49 = 3/21 Then cross multiply to get 21x = (3)(49), and solve for x to get x = (3)(49)/21 = 7 A proportion is an equation relating two ratios; for example, 9/12 = 3/4 . To solve a problem involving ratios, you can often write a proportion and solve it by cross multiplication.

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GRE Question Set 1.6 EXPLAINED.pages

11.

The number of ratios in a proportion

3

A.The quantity on the left is greater B. The quantity on the right is greater C. Both are equal D. The relationship cannot be determined without further information Correct: B Explanation: A proportion is an equation relating two ratios; for example, 9/12 = 3/4 is two ratios combined about an equal sign to form a proportion.

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GRE Question Set 1.6 EXPLAINED.pages

12. 9 / (a)(b)(c) = 3 / 4

(a) / 1

9 / (a)(b)(c)

A.The quantity on the left is greater B. The quantity on the right is greater C. Both are equal D. The relationship cannot be determined without further information Correct: D Explanation: (a) can have infinitely many possible values, as long as (b) and (c) collude to produce 12 from the combination of all three.

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GRE Question Set 1.6 EXPLAINED.pages

13. 3 American stamp are worth 57 Indian stamps. British stamps are worth 4 American Stamps. 2 American Stamps are worth 7 Chinese stamps.

British Stamps to Indian British Stamps to Chinese Stamps Stamps

A.The quantity on the left is greater B. The quantity on the right is greater C. Both are equal D. The relationship cannot be determined without further information Correct: B Explanation: The left has a value of 1/76 The right has a value of 1/14 3A : 57I; and 4A : 1B; and 2A:7C For the left, make a proportion from the two ratios at attention.

3A : 57I; and 4A : 1B

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GRE Question Set 1.6 EXPLAINED.pages

Find a common denominator for the shared variable, A, in this case.

3A : 57I 4A : 1B 12A : 228I 12A : 3B 3B : 228I 1B : 76I For the right, make a proportion from the two ratios with the relevant variables.

4A : 1B; and 2A:7C 4A : 1B 2A : 7C 4A : 1B 4A : 14C 1B : 14C

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GRE Question Set 1.6 EXPLAINED.pages

14.

1 calorie : 1 Degree of body temperature achieved.

1 Fat gram : 9 calories.

1 Glucose gram : 4 calories.

1 Protein gram : 4 calories.

1 Meal : 3 Glucose gram + 3 Protein gram + 1 Fat gram The minimum number of meals, to have 100 degrees of body temperature achieved

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A.The quantity on the left is greater B. The quantity on the right is greater C. Both are equal D. The relationship cannot be determined without further information Correct: A Explanation: The left is slightly above 3.

1 Meal : 3 Glucose gram + 3 Protein gram + 1 Fat gram 1 Meal : 12 calories + 12 calories + 9 calories 1 Meal : 33 Calories 3 Meals : 99 Calories

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