GRE Math Question Set 1.7 EXPLAINED.pages
1.
1 Part out of 100 parts
1 percent
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 term percent means per hundred, or hundredths. Percents are ratios that are often used to represent parts of a whole, where the whole is considered as having 100 parts. 1 percent means 1 part out of 100 parts, or 1/100. 32 percent means 32 parts out of 100 parts, or 32/100.
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GRE Math Question Set 1.7 EXPLAINED.pages
2.
32 Parts out of 100 parts
32 / 100
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 The part is the numerator of the ratio and the whole (A.K.A. Base) is the denominator. Percents are often written with the % symbol; fractional and decimal equivalents are often used as well but without the % symbol.
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GRE Math Question Set 1.7 EXPLAINED.pages
3.
1/2
50 parts out of 100 parts
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: 50 percent means 50 parts out of 100 parts, or 1/2.
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GRE Math Question Set 1.7 EXPLAINED.pages
4.
100%
100 / 100
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 ‘ % ‘ symbol is the same as ‘ /100’ . 100% = 100/100.
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GRE Math Question Set 1.7 EXPLAINED.pages
5.
1%
0.1
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: B Explanation: Be careful not to confuse 0.01 with 0.01%. The percent symbol matters. For example, 0.01 = 1% but 0.01% = 0.01 / 100 = 0.0001
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GRE Math Question Set 1.7 EXPLAINED.pages
6.
0.003
0.3%
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: C Explanation: 0.3% is the same as writing 0.3 / 100. And, 0.3 / 100 = 0.003. Again, the percent symbol matters. For example, 0.01 = 1% but 0.01% = 0.01 / 100 = 0.0001
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GRE Math Question Set 1.7 EXPLAINED.pages
7.
0.01
0.01%
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: 0.01% is the same as writing 0.01 / 100. Thus, 0.01 / 100 = 0.00001. Adding a % symbol decreases the adjoining number by two magnitudes of ten. Nothing new here, just said differently.
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GRE Math Question Set 1.7 EXPLAINED.pages
8.
0.01 / 100
0.0001
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: 0.01% is the same as writing 0.01 / 100. And, 0.01 / 100 = 0.00001.
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GRE Math Question Set 1.7 EXPLAINED.pages
9. Assume the whole is 20 and the part is 13.
The percent
The decimal equivalent
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: 13/20 = 0.65 = 65% The value of the left (the percent) is 65 The value of the right (the decimal equivalent) is 0.65 Note that the part is the numerator of the ratio and the whole is the denominator. Percents are often written with the % symbol; fractional and decimal equivalents are often used as well but without the % symbol, as follows. To compute a percent, given the part and the whole, divide the part by the whole. The result will be the decimal equivalent, so multiply the result by 100 to convert to percent.
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GRE Math Question Set 1.7 EXPLAINED.pages
10.
13 / 20
66.7%
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: 13/20 = 0.65 = 65% The left is 65 The right is 66.7 Note that the part is the numerator of the ratio and the whole is the denominator. Percents are often written with the % symbol; fractional and decimal equivalents are often used as well but without the % symbol, as follows. To compute a percent, given the part and the whole, divide the part by the whole. The result will be the decimal equivalent, so multiply the result by 100 to convert to percent.
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GRE Math Question Set 1.7 EXPLAINED.pages
11. The percent of 150 that is 12.9
0.086
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 The left is 8.6 The right is 0.086 Here the whole is 150 and the part is 12.9. Part / Whole = 12.9 / 150 = 0.086 = 8.6% A quick way to figure out long division: Use half the value of the base, 75 in this case, and half the value of the numerator, 6.5 in this case. 7.5 is exactly 10% of 75, thus 6.5 is estimated to be less than 10% of 75. To find the part that is a certain percent of a whole, you can either multiply the whole by the decimal equivalent of the percent or set up a proportion to find the part.
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GRE Math Question Set 1.7 EXPLAINED.pages
12.
30% of 350
10.5
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: To find 30% of 350, multiply 350 by the decimal equivalent of 30%, or 0.3, as follows. x = (350)(0.3) = 105 To use a proportion, you need to find the number of parts of 350 that yields the same ratio as 30 out of 100 parts. You want a number x that satisfies the proportion part / whole 30 / 100 X/350 = 30/100 X = (350)(30)/100 = 105
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GRE Math Question Set 1.7 EXPLAINED.pages
13. The number of parts of 350 that yields the same ratio as 30 out of 100 parts
1/100 รท 1/(30)(350)
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 value of the left is 105. Translating, 30% of 350 is 105. The value of the right is (1/100) x (30)(350) = (1/100) x (10,500) = 105 Given the percent and the part, you can calculate the whole. To do this you can either use the decimal equivalent of the percent or you can set up a proportion and solve it.
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GRE Math Question Set 1.7 EXPLAINED.pages
14. The number that 15 is 60% of
60/15 x 100
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: 15 is 60% of 25. You can calculate this as (15 / 60) x 100. 15 / 60 = 0.25. 0.25 x 100 = 25. 60 / 15 is the reciprocal of 15 / 60. 60 / 15 = 4. 4 x 100 = 400 Use the decimal equivalent of 60%. Because 60% of some number Z is 15, multiply z by the decimal equivalent of 60%, or 0.6. 0.6Z = 15 Now solve for z by dividing both sides of the equation by 0.6 as follows. Z= 15/0.6 =25 Using a proportion, look for a number z such that part / whole 60 / 100 15/Z = 60/100 Z = (15)(100)/60 = 1,500/60 = 25
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GRE Math Question Set 1.7 EXPLAINED.pages
15. 300/100
The base
The part
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 The base is the denominator, 100 in this case. The part is the numerator, 300 in this case. Percent assumes a context of a part and a whole, it is not necessary that the part be less than the whole. In general, the whole is called the base of the percent. When the numerator of a percent is greater than the base, the percent is greater than 100%. For example, 15 is 300% of 5, since 15/5 = 300/100
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GRE Math Question Set 1.7 EXPLAINED.pages
16.
250% of 16
(2.5)(40)
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: 250% of 16 is (250/100)(16) (250/100) reduces to (2.5). Calculating, (2.5)(16) = 40. Note that the decimal equivalent of 250% is 2.5. The value on the left is 40. The value on the right is 100.
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GRE Math Question Set 1.7 EXPLAINED.pages
17. A quantity increases from 600 to 750.
The percent increase
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: When a quantity changes from an initial positive amount to another positive amount math calls it percent change. If a quantity increases from 600 to 750, then the percent increase is found by dividing the amount of increase, 150, by the base, 600. 150/600 25/100 {Reduce the fraction} 25/100 = 0.25 = 25%
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GRE Math Question Set 1.7 EXPLAINED.pages
18. A quantity doubled in size
100%
The percent increase
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 a quantity doubles in size, then the percent increase is 100%. For example, if a quantity changes from 150 to 300, then the percent increase is (300 - 150)/150 = 150/150 = 100%
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GRE Math Question Set 1.7 EXPLAINED.pages
19. A quantity decreases from 500 to 400.
The percent decrease
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: C Explanation: If a quantity decreases from 500 to 400, calculate the percent decrease as follows. Change/Base 500-400/500 100/500 20/100 {Reduce the fraction} 20/100 = 0.20 = 20% When computing a percent increase, the base is the smaller number. When computing a percent decrease, the base is the larger number. In either case, the base is the initial number, before the change.
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GRE Math Question Set 1.7 EXPLAINED.pages
20. A quantity increases from 600 to 750.
The base
750
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 base of this change is 600. When computing a percent increase, the base is the smaller number. When computing a percent decrease, the base is the larger number. In either case, the base is the initial number, before the change.
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GRE Math Question Set 1.7 EXPLAINED.pages
21. A quantity decreases from 500 to 400.
The base
500
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: When computing a percent increase, the base is the smaller number. When computing a percent decrease, the base is the larger number. In either case, the base is the initial number, before the change.
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GRE Math Question Set 1.7 EXPLAINED.pages
22. A $1,300 investment in a mutual fund increased 12% in one day. The value of the investment after the change
$1,556.00
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 percent increase is 12%. Therefore, the value of the increase is 12% of $1,300, or, using the decimal equivalent, the increase is (0.12)($1,300) = $156. Thus, the value of the investment after the change is $1,300 + $156 = $1,456 Because the final result is the sum of the initial investment— 100% of $1,300—and the increase—12% of $1,300—the final result is 100% + 12% = 112% of $1,300. Thus, another way to get the final result is to multiply the value of the investment by the decimal equivalent of 112%, which is 1.12: ($1,300)(1.12) = $1,456 A quantity may have several successive percent changes. The base of each successive percent change is the result of the preceding percent change. 22
GRE Math Question Set 1.7 EXPLAINED.pages
23. The monthly enrollment, E, at a preschool decreased by 8% during one month and increased by 6% during the next month. The cumulative percent change of E for the two months
100% - (1.06)(.92)
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 E is the enrollment before the first month, then the enrollment as a result of the 8% decrease can be found by multiplying the base, ‘E’ , by the decimal equivalent of 100% ! 8% = 92%, so that’s 0.92: 0.92E The enrollment as a result of the second percent change—the 6% increase—can be found by multiplying the new base, 0.92E, by the decimal equivalent of 100% + 6% = 106%, which is 1.06: (1.06)(0.92)E = 0.9752E
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GRE Math Question Set 1.7 EXPLAINED.pages
The percent equivalent of 0.9752 is 97.52%, which is 2.48% less than 100%. Thus, the cumulative percent change in the enrollment for the two months is a 2.48% decrease. Next, for the right, (1.06)(.92) is .9752. 100% is the same as 1. 1 - .9752 = .0248 .0248 = 2.48%
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GRE Math Question Set 1.7 EXPLAINED.pages
24. The monthly enrollment, E, at a preschool increased by 8% during one month and decreased by 6% during the next month. The cumulative percent change of E for the two months
100% + (1.06)(.92)
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 value of the left can be computed as 100% + (1.08)(.94) = 2.015 = 201.5% The value on the right is 100% + (1.06)(.92) = 1.9752 = 197.52%
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GRE Math Question Set 1.7 EXPLAINED.pages
25.
Which of the following is a FALSE statement?
A. The term percent means per hundred, or hundredths. B. Percents are ratios that are often used to represent parts of a whole, where the whole is considered as having 1 part. C. Note that the part is the numerator of the ratio and the whole is the denominator. D. To compute a percent, given the part and the whole, divide the part by the whole. The result will be the decimal equivalent, so multiply the result by 100 to convert to percent. E. To find the part that is a certain percent of a whole, you can either multiply the whole by the decimal equivalent of the percent or set up a proportion to find the part.
Correct: B Explanation: B is False. Percents are ratios that are often used to represent parts of a whole, where the whole is considered as having *100* part*s*.
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GRE Math Question Set 1.7 EXPLAINED.pages
26. Which of the following is a FALSE statement? A. Given the percent and the part, you can calculate the whole. To do this you can either use the decimal equivalent of the percent or you can set up a proportion and solve it. B. If a quantity doubles in size, then the percent increase is 100%. C.When computing a percent increase, the base is the smaller number. When computing a percent decrease, the base is the larger number. In either case, the base is the initial number, before the change. D. A quantity may have several successive percent changes. The base of each successive percent change is the result of the preceding percent change. E. 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 divisor and the second quantity is the factor. Correct: E Explanation: E is false. 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*.
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