GMAT Math : Problem-Solving Questions

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Example Questions

Example Question #2 : Understanding Decimals

Which of the following is the square of twenty seven one-thousandths?

Possible Answers:

Seven hundred twenty-nine one-millionths

The correct answer is not among the other responses.

Fifty-four one-hundred-thousandths

Fifty-four one-millionths

Seven hundred twenty-nine one-hundred-thousandths

Correct answer:

Seven hundred twenty-nine one-millionths

Explanation:

Twenty-seven one-thousandths = 0.027

Its square is

$0.027^{2} = 0.027 \times 0.027$

Multiply without regard to the decimals first:

$27 \times 27 = 729$

0.027 and 0.027 have a total of six digits to the right of their decimal points, so position the decimal point in the answer so that there are six digits to its right.

$0.027 \times 0.027= 0.000729$

This is seven hundred twenty-nine one-millionths.

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Example Question #3 : Understanding Decimals

Which of the following is the cube of fifteen one-hundredths?

Possible Answers:

The correct answer is not among the other responses.

Three thousand three hundred seventy-five one-hundred-thousandths

Three thousand three hundred seventy-five one-millionths

Forty-five one-hundred-thousandths

Forty-five one-millionths

Correct answer:

Three thousand three hundred seventy-five one-millionths

Explanation:

Fifteen one-hundredths = 0.15

Its cube is $0.15 ^{3} =0.15 \times 0.15 \times 0.15$

Multiply without regard to the decimals first:

$15 \times 15 \times 15 = 3,375$

0.15, 0.15, and 0.15 have a total of six digits to the right of their decimal points, so position the decimal point in the answer so that there are six digits to its right.

$0.15 \times 0.15 \times 0.15= 0.003375$

This is three thousand three hundred seventy-five one-millionths.

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Example Question #2 : Understanding Decimals

Subtract nine hundred six ten-thousandths from four tenths.

Possible Answers:

Three hundred ninety-four ten-thousandths

Three hundred ninety-four thousandths

Five hundred six thousandths

Three thousand nine hundred four ten-thousandths

Three thousand ninety-four ten-thousandths

Correct answer:

Three thousand ninety-four ten-thousandths

Explanation:

Nine hundred six ten-thousandths = 0.0906

Four tenths = 0.4, or 0.4000

The difference:

$\begin{matrix} \; \; \; 0.4000\\ - \underline{0.0906} \\ \; \; \; 0.3094\end{matrix}$

This is three thousand ninety-four ten-thousandths.

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Example Question #3 : Decimals

Which of these equations is not correct?

Possible Answers:

$\frac{4}{3} =1.333333333333333333.......$

$\frac{1}{12} = .0833333333333........$

$\frac{573}{999} = .573$

100/1000 = .1

$\frac{4}{5}=.8$

Correct answer:

$\frac{573}{999} = .573$

Explanation:

Although tempting, a calculator is not required to spot the correct answer.

$\frac{573}{1000}$ is equal to as it is 573 parts of 1000 . And therefore $\frac{573}{999}$ must be slightly different. (It's it actually .573573573573....... )

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Example Question #3 : Understanding Decimals

If we divide 10 by 3, what is the 10th digit after the decimal point of the quotient?

Possible Answers:

Correct answer:

Explanation:

$\frac{10}{3}=3.3333333333333$

The tenth digit after the decimal point is 3.

When dividing 1 by 3 or 10 by 3, we get repeating 3s. So, there must be a 3 in the tenths digit.

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Example Question #2 : Decimals

If and are positive integers such that $\frac{x}{y}$ = 4.46, which of the following numbers could be the remainder when is divided by ?

Possible Answers:

184

206

163

151

145

Correct answer:

184

Explanation:

Given that

$\frac{x}{y}=4.46$

it follows that x=4.46y .

We don't need to know or , the only important information is that:

$y \times 0.46 = remainder$

Where the remainder is any one of the answer choices. This is because the remainder for any divisor/dividend pair is the product of the decimal portion of the quotient and the divisor.

Since we don't know y, our answer choice for the remainder is any answer that satisfies the above equation for a positive interger, since is specified as such in the problem.

The only answer choice that satisfies the constraints on is 184:

$y \times 0.46 = 184$ ==> $y = \frac{184}{0.46}$ ==> y = 400

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Example Question #401 : Arithmetic

Solve $\dpi{100} \small 2x-3> 0$ for x.

Possible Answers:

$\dpi{100} \small x\geq \frac{3}{2}$

$\dpi{100} \small x> \frac{-3}{2}$

$\dpi{100} \small x< \frac{3}{2}$

$\dpi{100} \small x> \frac{3}{2}$

$\dpi{100} \small x\leq \frac{3}{2}$

Correct answer:

$\dpi{100} \small x> \frac{3}{2}$

Explanation:

$\dpi{100} \small 2x-3> 0$

Add 3 to both sides: $\dpi{100} \small 2x> 3$

Divide both sides by 2: $\dpi{100} \small x> \frac{3}{2}$

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Example Question #1 : Understanding Real Numbers

Of 200 students, 80 take biology, 40 take chemistry, 60 take physics, 13 take two science courses, and no one takes three science courses. How many students are not taking a science course?

Possible Answers:

180

Correct answer:

Explanation:

To calculate the number of students taking at least 1 science course, add the number of students who are taking each course and subtract the number of students who are taking 2 (to ensure they're not counting twice).

$\small 80\ +\ 40\ +\ 60\ -\ 13\ =167$

To calculate the number of students NOT taking a class, subtract this number by the total number of students.

$\small 200\ -\ 167\ =\ 33$

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Example Question #3 : Understanding Real Numbers

Which of the following expressions is equal to $\sqrt[3]{4} \cdot \sqrt{2}$

Possible Answers:

$4 \sqrt[6]{2}$

$\sqrt[6]{8}$

$2 \sqrt[6]{2}$

$\sqrt[8]{8}$

$4 \sqrt[6]{4}$

Correct answer:

$2 \sqrt[6]{2}$

Explanation:

$\small \sqrt[3]{4} \cdot \sqrt{2} = 4^{\frac{1}{3}} \cdot 2^{\frac{1}{2}} = (2^{2})^{\frac{1}{3}} \cdot 2^{\frac{1}{2}} = 2^{2\; \cdot \frac{1}{3}} \cdot 2^{\frac{1}{2}}= 2^{ \frac{2}{3}} \cdot 2^{\frac{1}{2}}= 2^{ \frac{2}{3} + \frac{1}{2}}$

$\small = 2^{ \frac{7}{6} }} = \sqrt[6]{2^7} = 2\sqrt[6]{2}$

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Example Question #1 : Real Numbers

Given that $\small \small x + y = 9$ , $\small xy = 16$ , and $\small \small x < y$ , evaluate $\small \frac{1}{x}-\frac{1}{y}$ .

Possible Answers:

$\small \small \small \frac{{9}}{16}$

$\small \small \frac{{17}}{16}$

$\small \frac{\sqrt{17}}{16}$

$\small \small \small \small \frac{{3}}{16}$

Not enough information is given to answer the question

Correct answer:

$\small \frac{\sqrt{17}}{16}$

Explanation:

$\small \frac{1}{x}-\frac{1}{y} = \frac{y-x}{xy}$

To find $\small y - x$ :

$\small \small \small y + x = 9$ ,

so $\small \small \left (y + x \right )^{2} =y^{2} + 2xy +x^{2} = 81$

$\small \small y^{2} + 2xy +x^{2} - 4xy= 81 - 4 \cdot 16$

$\small \small y^{2} - 2xy +x^{2} = (y - x)^{2}= 17$

$\small \small y - x = \pm \sqrt{17}$

Since $\small \small x < y$ , $\small \small \small \small y - x > 0$

and we choose the positive square root

$\small \small \small y - x = \sqrt{17}$

$\small \small \small \frac{1}{x}-\frac{1}{y} = \frac{y-x}{xy}= \frac{\sqrt{17}}{16}$

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GMAT Math : Problem-Solving Questions

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #2 : Understanding Decimals

Example Question #3 : Understanding Decimals

Example Question #2 : Understanding Decimals

Example Question #3 : Decimals

Example Question #3 : Understanding Decimals

Example Question #2 : Decimals

Example Question #401 : Arithmetic

Example Question #1 : Understanding Real Numbers

Example Question #3 : Understanding Real Numbers

Example Question #1 : Real Numbers

All GMAT Math Resources

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