GRE Math : Decimal Operations

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Example Questions

Example Question #1 : How To Multiply Decimals

There are 3,500 people in group A and 5,000 people in group B:

Car Type	% in Group A Who Own	% in Group B Who Own
Motorbike	4	9
Sedan	35	25
Minivan	22	15
Van	9	12
Coupe	3	6

The number of people in group B who own a minivan is how much greater or less than the number of people in group A who own a minivan?

Possible Answers:

15 more

30 more

20 fewer

30 fewer

50 fewer

Correct answer:

20 fewer

Explanation:

In this question, simply take the percentage of each group that owns a minivan and compare the values. For minivans we look at the middle row which we recognize as a percent that must be converted to a decimal. Acknowledge that there's a different number of people between the groups A and B:

Group B: 0.15(5000) = 750

Group A: 0.22(3500) = 770

750 – 770 = –20; thus, group B has 20 fewer people who own minivans than group A.

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Example Question #12 : Decimals

Given that 0< x< y< 1 , which best describes the relationship between , $\frac{y}{x}$ , and (xy)^2 ?

Possible Answers:

$\small (xy) >\frac{y}{x }>(xy)^{2}$

$\small \frac{y}{x }>(xy)^{2}>(xy)$

$\small (xy)^{2} >\frac{y}{x }>(xy)$

$\small \frac{y}{x }>(xy)>(xy)^{2}$

$\small (xy)^{2} >(xy)>\frac{y}{x }$

Correct answer:

$\small \frac{y}{x }>(xy)>(xy)^{2}$

Explanation:

We must recognize that if x and y are both between 0 and 1, then they must be fractions (decimals). To determine their relationships, we can substitute values for x and y. Let's have $x=\frac{1}{4}$ and $y=\frac{1}{2}$ (because y must be greater than x).

If x and y are both between 0 and 1, then xy is also between 0 and 1 (though smaller than either x or y individually).

$xy=\frac{1}{4}*\frac{1}{2}=\frac{1}{8}$

The value of (xy)² will be less than (xy), since squaring any number between 0 and 1 gives a smaller result.

$(xy)^2=(\frac{1}{4}*\frac{1}{2})^2=(\frac{1}{8})^2=\frac{1}{64}$

Finally, $\frac{y}{x}$ is largest, since dividing a larger number by a smaller one gives a result greater than 1.

$\frac{y}{x}=\frac{\frac{1}{2}}{\frac{1}{4}}=\frac{1}{2}*\frac{4}{1}=2$

Note that the substituted values for x and y were purely hypothetical; any values that satisfy the given inequality could be used.

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Example Question #1373 : Act Math

You bought a dozen eggs marked at $\$2.29$ and received $\$2.55$ change from $\$5.00$ . What is the percent of sales tax?

Possible Answers:

$6\%$

$7\%$

$8\%$

$5\%$

Correct answer:

$7\%$

Explanation:

Set the equation up as

(x)($2.29)= $2.45

Solve for , which equals $\frac{2.45}{2.29}$

x=1.0698

Therefore the percent sales tax is:

$(1.0698-1) \times 100=6.98\% \approx 7\%$

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Example Question #13 : Decimal Operations

Solve for :

0.22b = 1.32

Possible Answers:

b = 6

b = .4

b = 4

b = .6

b = 7

Correct answer:

b = 6

Explanation:

To solve, first divide both sides of the equation by 0.22 , leaving you with:

$b = \frac{1.32}{0.22}$

Then simply divide the decimals, which will yield your answer:

b = 6 .

If you have trouble dividing the decimals, you can multiply both of the numbers by one followed by a number of zeroes equal to the number of digits beyond the decimal point (one hundred, in this case), then divide, then divide your result by the same number (one hundred again).

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Example Question #15 : Decimals

Solve for (round to the nearest hundredth if necessary)

0.8c = 1.3

Possible Answers:

c = 2.625

c =0 .625

c = 1.63

c = 1.625

c = 1.6

Correct answer:

c = 1.625

Explanation:

To solve, first divide both sides of the equation by :

$\frac{.8c}{.8} = \frac{1.3}{.8}$

$c = \frac{1.3}{.8}$

To do this division, you can divide as normal, or if you are having trouble, you can multiply both numbers by 10 to eliminate the decimal:

$\frac{1.3}{.8} = \frac{13}{8}$

$c = \frac{13}{8}$

c = 1.625

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Example Question #16 : Decimals

Solve for :

0.22q = 22.22

Possible Answers:

q = 11

q = 111

q = 10

q = 100

q = 101

Correct answer:

q = 101

Explanation:

To solve, first divide both sides of the equation by so you isolate the variable:

0.22q/0.22 = 22.22/0.22

q = 22.22/0.22

Then, divide the decimal--if you have trouble doing so, remember that you can multiply both numbers by 100 to eliminate the decimal, and then divide as normal:

q = 2222/22

q = 101

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Example Question #14 : Decimal Operations

Solve for :

0.25x = 6.5

Possible Answers:

x = 26

x = 2.6

x = 62

x = .26

x = 260

Correct answer:

x = 26

Explanation:

To solve, first divide both sides of the equation by so you can isolate the variable:

0.25x/0.25 = 6.5/0.25

x = 6.5/0.25

Now divide. If you have trouble dividing decimals, you may multiply both dividend and divisor by 100 to eliminate the decimal and divide normally:

x=6.5/0.25 = 650/25

x = 26

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Example Question #15 : Decimal Operations

Solve for :

0.3y = 3.33

Possible Answers:

y = 111.11

y = 1.111

y = 11.1

y = .111

y = 111

Correct answer:

y = 11.1

Explanation:

To solve, first divide both sides of the equation by so you isolate your variable:

0.3y/0.3 = 3.33/0.3

y = 3.33/0.3

Then, divide the decimals. If you have trouble with this, you can multiply both numbers by 100 to eliminate the decimals and then divide normally:

y = 3.33/0.3 = 333/30

y = 11.1

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GRE Math : Decimal Operations

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #1 : How To Multiply Decimals

Example Question #12 : Decimals

Example Question #1373 : Act Math

Example Question #13 : Decimal Operations

Example Question #15 : Decimals

Example Question #16 : Decimals

Example Question #14 : Decimal Operations

Example Question #15 : Decimal Operations

All GRE Math Resources

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