GMAT Math : Arithmetic

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Example Questions

Example Question #21 : Understanding Fractions

Add three fourths of a number to one eighth of a number to get 56. What is the number?

Possible Answers:

The correct answer is not given among the other responses.

Correct answer:

Explanation:

If the number is , then the relation can be written as

$\frac{3}{4}N + \frac{1}{8}N = 56$

$\frac{6}{8}N + \frac{1}{8}N = 56$

$\frac{7}{8}N = 56$

$\frac{8} {7} \cdot \frac{7}{8} N =\frac{8} {7}\cdot 56$

N =64

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Example Question #1931 : Problem Solving Questions

Divide two sevenths of a number by one half to get 40. What is the number?

Possible Answers:

280

$91\frac{3}{7}$

$22\frac{6}{7}$

140

Correct answer:

Explanation:

If the number is , then the relation can be written as

$\frac{2}{7} N \div \frac{1}{2} = 40$

$\frac{2}{7} N \cdot \frac{2} {1}= 40$

$\frac{4}{7} N = 40$

$\frac{7} {4}\cdot \frac{4}{7}N = \frac{7} {4}\cdot40$

N = 70

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Example Question #382 : Arithmetic

Compute the following:

$(\frac{4}{5}\div \frac{20}{15} ) +\frac{16}{45}$

Possible Answers:

$\small \small \frac{4}{5}$

$\small \small \frac{4}{15}$

$\small \small \frac{41}{45}$

$\small 3 \frac{16}{45}$

$\small \frac{43}{45}$

Correct answer:

$\small \frac{43}{45}$

Explanation:

Consider that dividing two fractions is the same as multiplying the first fraction by the reciprocal of the second fraction. So, you can rewrite the presented expression:

$(\frac{4}{5}\div \frac{20}{15} ) +\frac{16}{45}$

like this:

$(\frac{4}{5}\ast \frac{15}{20} ) +\frac{16}{45}$

Now you can multiply across the numerators and denominators of the two fractions to find their product:

$\frac{60}{100} +\frac{16}{45}$

Each of these fractions can be reduced. Let's reduce the first fraction:

$\frac{3}{5}+\frac{16}{45}$

Now we can multiply the first fraction by $\frac{9}9{}$ to create a common denominator:

$(\frac{3}{5}\cdot\frac{9}{9})+\frac{16}{45}$

$\frac{27}{45}+\frac{16}{45}$

At this point, we can add the fractions together. Since the result cannot be simplified, it is the correct answer.

$\frac{43}{45}$

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Example Question #22 : Understanding Fractions

Which of the following is equal to $\frac{2}{3}$ ?

Possible Answers:

$\frac{15}{9}-1$

$\frac{4}{3}-\frac{1}{6}$

$\frac{5}{6}+\frac{2}{9}$

$\frac{8}{3}-\frac{5}{3}$

$\frac{7}{6}-\frac{4}{6}$

Correct answer:

$\frac{15}{9}-1$

Explanation:

Testing out all of the answer choices, the only solution that is equal to $\frac{2}{3}$ is $\frac{15}{9}-1=\frac{15}{9}-\frac{9}{9}=\frac{6}{9}=\frac{2}{3}$

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Example Question #22 : Understanding Fractions

Simplify the following expression: $\frac{5}{9}\div\frac{4}{3}$

Possible Answers:

$\frac{2}{3}$

$\frac{1}{2}$

$\frac{7}{12}$

$\frac{1}{3}$

$\frac{5}{12}$

Correct answer:

$\frac{5}{12}$

Explanation:

In order to simplify $\frac{5}{9}\div\frac{4}{3}$ , we must remember that dividing by a fraction is the same as multiplying by its reciprocal. Therefore:

$\frac{5}{9}\div\frac{4}{3}$

$=\frac{5}{9}\times \frac{3}{4}$

$=\frac{15}{36}$

$=\frac{5}{12}$

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Example Question #31 : Fractions

When positive integer is divided by 16, the remainder is 15. What is the remainder when is divided by 8 ?

Possible Answers:

Correct answer:

Explanation:

We can set up the following equation from what we are told in the question: n = 16q + 15 where is the quotient, then we divide by 8: $\frac{16q+7}{8}$ or $2q+\frac{7}{8}$ . From there we can see that $\frac{7}{8}$ will yield a remainder of , which is our final answer.

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Example Question #31 : Understanding Fractions

Simplify the following expression: $\frac{3}{4}-\frac{5}{8}+\frac{3}{16}$

Possible Answers:

$\frac{1}{2}$

$\frac{4}{3}$

$\frac{3}{2}$

$\frac{5}{8}$

$\frac{5}{16}$

Correct answer:

$\frac{5}{16}$

Explanation:

In order to simplify the expression $\frac{3}{4}-\frac{5}{8}+\frac{3}{16}$ , let's first change the terms to reflect a common denominator:

$\frac{3\times 4}{4\times 4}-\frac{5\times 2}{8\times 2}+\frac{3}{16}$

$=\frac{12}{16}-\frac{10}{16}+\frac{3}{16}$

$=\frac{12-10+3}{16}$

$=\frac{5}{16}$

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Example Question #33 : Understanding Fractions

When positive integer is divided by 12, the remainder is 7. What is the remainder when is divided by 3?

Possible Answers:

Correct answer:

Explanation:

The remainder cannot be greater or equal to the divisor, so we can already eliminate 3, 4 and 5. Then, we can set up an equation with the given information. We know that when is divided by 12, the remainder is 7 : n= 12q + 7 , where is the quotient. So, let's try to divide by 3 and we get : $\frac{12q+7}{3}$ or $4q + \frac{7}{3}$ . Therefore, the remainder must be one, since when 7 is divided by 3, the remainder is .

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Example Question #1941 : Problem Solving Questions

and are positive integers and $\frac{a}{b}= 36.24$ . What is the remainder?

Possible Answers:

Correct answer:

Explanation:

We are told that $\frac{a}{b}=36+0.24$ . In other words, the remainder can be expressed as follows:

$\frac{r}{b}=0.24$ or $\frac{r}{b}= \frac{24}{100}$

If we simplify, we get $\frac{r}{b}= \frac{6}{25}$ .

Therefore, we can see that is a multiple of . The only possible multiple of in the answer choice is .

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Example Question #31 : Understanding Fractions

What is $\frac{(5-2)!}{(3-3)!}$ ?

Possible Answers:

Does not exist

Correct answer:

Explanation:

Here we can be tempted to answer that the answer does not exist since there can be no division by 0; however, (3-3)!=0!=1 , or in other words, the factorial of 0 is 1. Therefore, the final answer is given by or .

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GMAT Math : Arithmetic

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #21 : Understanding Fractions

Example Question #1931 : Problem Solving Questions

Example Question #382 : Arithmetic

Example Question #22 : Understanding Fractions

Example Question #22 : Understanding Fractions

Example Question #31 : Fractions

Example Question #31 : Understanding Fractions

Example Question #33 : Understanding Fractions

Example Question #1941 : Problem Solving Questions

Example Question #31 : Understanding Fractions

All GMAT Math Resources

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