GMAT Math : GMAT Quantitative Reasoning

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Example Questions

Example Question #2 : Dsq: Calculating Percents

Data sufficiency question- do not actually solve the question

How many male students are in a class?

1. There are 42 students in the class.

2. 55 percent of the students are female.

Possible Answers:

Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer the question

Each statement alone is sufficient

Statements 1 and 2 together are not sufficient, and additional data is neeeded to answer the question

Both statements taken together are sufficienct to answer the question, but neither statement alone is sufficient

Statement 2 alone is sufficient, but statement 1 along is not sufficient to answer the question

Correct answer:

Both statements taken together are sufficienct to answer the question, but neither statement alone is sufficient

Explanation:

In order to calculate the number of males in the class, you need to know the total number of students and the number of females (which can be calculated using the percentage).

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Example Question #3 : Percents

Data sufficiency question- do not actually solve the question

There are 20 cats in an animal shelter. How many black, female cats are in the shelter?

1. 14 of the cats are male

2. 25 percent of the cats are black

Possible Answers:

Statements 1 and 2 together are not sufficient, and additional data is needed to answer the question

Statement 2 alone is sufficient, but statement 1 is not sufficient to answer the question

Each statement alone is sufficient to answer the question

Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient

Statement 1 alone is sufficient, but statement 2 is not sufficient to answer the question

Correct answer:

Statements 1 and 2 together are not sufficient, and additional data is needed to answer the question

Explanation:

The information provided will allow you to calculate the number of females and the number of black cats, but there is not enough information to quantify the number of black, female cats

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Example Question #3 : Percents

A certain pet store sells cats and dogs. The number of dogs is 250% greater than the number of cats. How many cats are in the store?

1. There are 40 dogs in the store.

2. There are 56 cats and dogs in the store.

Possible Answers:

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

EACH statement ALONE is sufficient.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Statement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Correct answer:

EACH statement ALONE is sufficient.

Explanation:

$dogs = 2.5 \times cats$

Statement 1: sufficient

$40\: dogs = 2.5 \times cats$

$cats = \frac{40}{2.5}=16$

Statement 2: sufficient

$56 \, total = 2.5x + x= 3.5x$

$cats = x=\frac{56}{3.5}=16$

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Example Question #1 : Dsq: Calculating Percents

Mrs. Smith purchased groceries whose price, before tax, was $147.64. What was the tax rate on those groceries (nearest hundredth of a percent)?

1) The tax she paid was $9.23.

2) The total amount she paid was $156.87

Possible Answers:

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is not sufficient.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is not sufficient.

EITHER Statement 1 or Statement 2 ALONE is sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are NOT sufficient to answer the question.

Correct answer:

EITHER Statement 1 or Statement 2 ALONE is sufficient to answer the question.

Explanation:

To determine the tax rate, you need to know the purchase price, which is given, and the amount of tax paid. The amount of tax is given in Statement 1. Statement 2 alone, however, also allows you to find the amount of tax; just subtract:

$\$ 156.87 -\$ 147.64 = \$ 9.23$

Either way, you can now find the tax rate:

$\frac{9.23}{147.64} \cdot 100 \approx 0.0625 = 6.25\%$

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Example Question #3 : Dsq: Calculating Percents

Jared, a jewelry salesman, makes a 10% commission on the selling price of all the jewelry he sells. Last month, he earned $4,000 in commission. What is the total selling price of the jewelry he sold this month?

1. His sales this month were 25% more than his sales last month.

2. He earned $5,000 in commission this month.

Possible Answers:

BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.

Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

EACH statement ALONE is sufficient to answer the question asked.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.

Correct answer:

EACH statement ALONE is sufficient to answer the question asked.

Explanation:

Each statement has enough information to calculate the answer.

Using statement 1, we know that he sold 25% more than last month. Given in the question, last month he earned $4,000. If $4,000 is 10% of the total price of his jewelry sold last month, we do some math (below) to find he sold $40,000 worth of jewelry. Let be the total price of jewelry sold last month. Then,

$\$4000=0.10x$ so

x=40,000

Increasing that by 25% we see that

$40,000\cdot 1.25=50,000$

NOTE: when multiplying the percents, make sure you use the decimal values.

Using statement 2, we know that we can just calculate the total selling price of the jewelry he sold this month based on the commission percentage. So, if we let equal the total price of jewelry sold this month, we get $\$5000=.10y$

$y=\$50,000$

Therefore we see we can use either statement individually to find what we are looking for.

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Example Question #6 : Percents

A distributor ordered 3,250 chairs. 2,315 chairs were delivered. What percentage of the chairs have not yet been delivered?

Possible Answers:

$3.4\%$

$71.3\%$

$18.6\%$

$63.2\%$

$28.7\%$

Correct answer:

$28.7\%$

Explanation:

First let's find the number of chairs not delivered:

$3,250-2,315=935\ \textup{undelivered chairs}$

Therefore the fraction of chairs not delivered is $\frac{935}{3,250}$ .

Divide the numerator by the denominator to convert this fraction into a decimal:

$935\div 3,250=0.287$

Multiply by 100 to turn this decimal into a percentage:

$0.287\cdot 100=28.7\%$

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Example Question #291 : Arithmetic

What percent of a company's employees are women with a college degree?

(1) Of the women employed in the company, $40\%$ do not have a college degree.

(2) Of the men employed in the company, $80\%$ have a college degree.

Possible Answers:

Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient

Each statement ALONE is sufficient.

Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient

Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient

Both statements TOGETHER are not sufficient.

Correct answer:

Both statements TOGETHER are not sufficient.

Explanation:

Statement (1) indicates the percentage of women who do not have a college degree. From that statement, we know that 60% of the women in the company have a college degree. However, we do not know the total number of employees or the total number of women in the company. Therefore, statement (1) alone is not sufficient.

Statement (2) indicates the percentage of men who have a college degree but from that statement we cannot find the total number of employees or the total number of women with a college degree.

We need the total number of women and the total number of employees in order to calculate the percentage of employees who are women with a college degree. We show it with the following example:

If we assume that there are 100 women and 100 men working in the company, we can attempt to find the percentage of employees who are women with a college degree in the following way:

$\frac{(100-40)}{100+100}=\frac{60}{200}=\frac{30}{100}$

So in that example, 30% of the employees are women with a college degree.

However if we change the number of women to 500 and the number of men to 600, the percentage of employees who are women with a college degree is:

$\frac{(0.6\times 500)}{500+700}=\frac{300}{1200}=\frac{25}{100}$

The percentage of employees who are women with a college degree becomes 25%.

Therefore both statements together are not sufficient.

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Example Question #9 : Percents

is 30% of , and 60% of . and are positive integers.

True or false: is a positive integer.

Statement 1: is a multiple of 5.

Statement 2: is a multiple of 5.

Possible Answers:

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

Correct answer:

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

Explanation:

Statement 1 alone is inconclusive. For example, if N = 10 , then is 30% of 10 - that is,

$X = 0.30N = 0.30\cdot 10 = 3$ ,

an integer.

But if N = 15 , then is 30% of 15 - that is,

$X = 0.30N = 0.30\cdot 15 = 4.5$ ,

not an integer.

If Statement 2 alone is assumed, then Y = 5M for some integer . 60% of this is

$X = 0.60 \cdot 5M = 3M$ .

is three times an integer and is itself an integer.

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Example Question #11 : Percents

is 30% of , and is 30% of . is an integer. True or false: is an integer.

Statement 1: is an integer.

Statement 2: is divisible by 100.

Possible Answers:

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

Correct answer:

EITHER statement ALONE is sufficient to answer the question.

Explanation:

Assume Statement 1 alone.

If is 30% of and is 30% of , then:

B = 0.30 C

and

A = 0.30 B = 0.30 (0.30 C) = 0.09 C

$A = \frac{9}{100}C=9\cdot \frac{C}{100}$

is an integer; for to be an integer, must be divisible by 100. This makes Statement 2 a consequence of Statement 1, so we can now test Statement 2 alone.

If is divisible by 100, then for some integer , C= 100M . 30% of this is $B = 0.30 \cdot 100M = 30M$ . is 30 times some integer, and is therefore an integer itself.

Either statement alone answers the question.

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Example Question #12 : Percents

is 20% of , and is 20% of . is an integer. True or false: is an integer.

Statement 1: is not an integer.

Statement 2: is divisible by 72.

Possible Answers:

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Correct answer:

BOTH statements TOGETHER are insufficient to answer the question.

Explanation:

Assume both statements are true.

Case 1: C= 72 .

Then is 20% of this, so

$B = 0.20 \cdot 72 = 14.4$

is 20% of , so

$A = 0.20 \cdot 14.4= 2.88$

Case 2: C= 360

Then is 20% of this, so

$B = 0.20 \cdot 360 = 72$

is 20% of , so

$A = 0.20\cdot 72 = 14.4$

In both situations, the conditions of the problem, as well as both statements, are true, but in one case, is not an integer and in the other case, is an integer. The statements together are inconclusive.

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GMAT Math : GMAT Quantitative Reasoning

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #2 : Dsq: Calculating Percents

Example Question #3 : Percents

Example Question #3 : Percents

Example Question #1 : Dsq: Calculating Percents

Example Question #3 : Dsq: Calculating Percents

Example Question #6 : Percents

Example Question #291 : Arithmetic

Example Question #9 : Percents

Example Question #11 : Percents

Example Question #12 : Percents

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