GMAT Math : Arithmetic

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Example Questions

Example Question #4 : Understanding Decimals

Subtract nine hundred six ten-thousandths from four tenths.

Possible Answers:

Three thousand ninety-four ten-thousandths

Five hundred six thousandths

Three thousand nine hundred four ten-thousandths

Three hundred ninety-four thousandths

Three hundred 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 #5 : 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 : Understanding 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:

206

184

163

145

151

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 #1 : Understanding Real Numbers

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

Possible Answers:

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

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

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

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

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

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:

$2 \sqrt[6]{2}$

$\sqrt[6]{8}$

$\sqrt[8]{8}$

$4 \sqrt[6]{4}$

$4 \sqrt[6]{2}$

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 : Understanding 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:

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

Not enough information is given to answer the question

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

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

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

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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Example Question #5 : Understanding Real Numbers

Today, Becky's age (B) is 3 times Charlie's age. In 3 years, what will Charlie's age be in terms of B?

Possible Answers:

$\small \frac{B}{3}+3$

$\small 3B+3$

$\small 3(B+3)$

$\small \frac{B+3}{3}$

$\small 3(B+3)$

$\small 3B+3$

Correct answer:

$\small \frac{B}{3}+3$

Explanation:

Today, $\small C=\frac{B}{3}$ . In 3 years, $\small C=\frac{B}{3}+3$ .

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Example Question #1 : Real Numbers

Given that $6 \leq A \leq 12$ and $4 \leq B \leq 6$ , what is the range of possible values for $\frac{A}{B}$ ?

Possible Answers:

$1 \leq \frac{A}{B} \leq 3$

$24 \leq \frac{A}{B} \leq 72$

$\frac{1}{2} \leq \frac{A}{B} \leq \frac{2}{3}$

$0 \leq \frac{A}{B} \leq 3$

$\frac{3}{2} \leq \frac{A}{B} \leq 2$

Correct answer:

$1 \leq \frac{A}{B} \leq 3$

Explanation:

The lowest possible value of $\frac{A}{B}$ is the lowest possible value of divided by the highest possible value of :

$\frac{A}{B} \geq 6 \div 6 = 1$

The highest possible value of $\frac{A}{B}$ is the highest possible value of divided by the lowest possible value of :

$\frac{A}{B} \leq 12 \div 4 = 3$

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GMAT Math : Arithmetic

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #4 : Understanding Decimals

Example Question #3 : Decimals

Example Question #5 : Understanding Decimals

Example Question #2 : Understanding Decimals

Example Question #1 : Understanding Real Numbers

Example Question #1 : Understanding Real Numbers

Example Question #3 : Understanding Real Numbers

Example Question #1 : Understanding Real Numbers

Example Question #5 : Understanding Real Numbers

Example Question #1 : Real Numbers

All GMAT Math Resources

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