GMAT Math : Problem-Solving Questions

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Example Questions

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:

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

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

$\small 3(B+3)$

$\small 3B+3$

$\small 3(B+3)$

$\small 3B+3$

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:

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

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

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

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

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

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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Example Question #4 : Real Numbers

If and are composite integers, which of the following can be prime?

Possible Answers:

$x\cdot y$

x^2+y^2

None of these can be prime.

x^2-y^2

x^2y+2y

Correct answer:

x^2+y^2

Explanation:

x^2-y^2 = (x-y)(x+y) so this is a composite number for all and .

$x\cdot y$ is by definition a composite number.

$x^2y+2y = y\cdot (x^2+2)$ the product of 2 numbers.

This leaves just x^2+y^2 . For a number to be prime, it must be odd (except for 2) so we need to have either or be odd (but not both). The first composite odd number is 9. 9^2 = 81 . The smallest composite number is 4. 4^2 = 16 .

81+16 = 97 is a prime number.

So the answer is x^2+y^2

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Example Question #2 : Number Theory

If $\frac{122}{x-3}$ is a real number, which of the following CANNOT be a value for x?

Possible Answers:

-3

122

125

-122

Correct answer:

Explanation:

The definition of the set of real numbers is the set of all numbers that can fit into a/b where a and b are both integers and b does not equal 0.

So, since we see a fraction here, we know a non-real number occurs if the denominator is 0. Therefore we can find where the denominator is 0 by setting x-3 =0 and solving for x. In this case, x=3 would create a non-real number. Thus our answer is that x CANNOT be 3 for our expression to be a real number.

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Example Question #1963 : Problem Solving Questions

Let be the product of integers from 18 to 33, inclusive. If g=2x , how many more unique prime factors does have than ?

Possible Answers:

Greater than

Not enough information given.

Correct answer:

Explanation:

This question does not require any calculation. Given that 32 (an even number) is a factor of , then 2 must be a prime factor. If is then multiplied by 2 (to get ) then has no additional unique prime factors (its only additional prime factor, 2, is NOT unique).

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Example Question #1 : Understanding Real Numbers

If $\dpi{100} \small x\ and\ y$ are both negative, then $\dpi{100} \small \frac{x+y}{-xy}$ could NOT be equal to....

Possible Answers:

$\dpi{100} \small 5$

$\dpi{100} \small -5$

$\dpi{100} \small \frac{\sqrt{8}}{4}$

$\dpi{100} \small \frac{3}{4}$

Correct answer:

$\dpi{100} \small -5$

Explanation:

$\dpi{100} \small x+y$ is negative and $\dpi{100} \small xy$ is positive

$\dpi{100} \small \frac{Negative}{-Positive} = \frac{Negative}{Negative} = Positive$

Therefore, the solution cannot be negative.

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Example Question #2 : Real Numbers

If $\frac{873}{x^3-8}$ is a real number, which one of these cannot be a value of ?

Possible Answers:

Correct answer:

Explanation:

For the expression to be defined, the denominator needs to be different from 0. Therefore:

$x^{3}-8=0$

$x^3 = 8 \Leftrightarrow x = \sqrt[3]{8} \Leftrightarrow x = (2^{3})^{\frac{1}{3}} = 2$

So the correct answer is 2.

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Example Question #1961 : Problem Solving Questions

If x<y , and 2y<10 , and x<1 , what can we say for sure about x+y ?

Possible Answers:

x+y>4

x+y is positive

x+y is negative

None of the other answers.

x+y=0

Correct answer:

None of the other answers.

Explanation:

To show the other answers aren't always true, we need to choose 2 numbers that satisfy the given inequalities but also contradict each answer one-by-one.

Let x =0, y =4 this choice shows that sometimes x +y = 4 , which rules out the answers x +y>4 , x+y is negative, and x+y = 0

Now Let x=-3, y=-2 , this will still satisfy the given inequalities, but now x+y = -5 . This means that the answer " x+y is positive" isn't always true either.

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Example Question #1961 : Problem Solving Questions

Which of the following is equal to the sum of thirty-three one-thousandths and three hundred three ten-thousandths?

Possible Answers:

Six hundred thirty-three ten-thousandths

Three hundred sixty-six ten-thousandths

Six hundred six ten-thousandths

Three hundred thirty-six ten-thousandths

Six hundred three ten-thousandths

Correct answer:

Six hundred thirty-three ten-thousandths

Explanation:

The one-thousandths and ten-thousandths places are the third places and the fourth places, respectively, to the right of the decimal point. Therefore:

Thirty-three one-thousandths = 0.033

Three hundred three ten-thousandths = 0.0303

Add:

$\begin{matrix} \: \: \: 0.0330\\ +\underline{0.0303}\\ \: \: \: 0.0633 \end{matrix}$

The last nonzero digit ends at the ten-thousandths place, so this is $\frac{633}{10,000}$ , or

six hundred thirty-three ten-thousandths.

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Example Question #1962 : Problem Solving Questions

Which of the following is equal to 0.0407?

Possible Answers:

Four hundred seven ten-thousandths

Four hundred seven one-thousandths

Four hundred seventy ten-thousandths

Four hundred seventy one-thousandths

Forty-seven ten-thousandths

Correct answer:

Four hundred seven ten-thousandths

Explanation:

The last nonzero digit is located in the fourth place right of the decimal point - the ten-thousandths place. Put the number, without decimal point or leading zeroes, over 10,000. This number is $\frac{407}{10,000}$ , or four hundred seven ten-thousandths.

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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 #5 : Understanding Real Numbers

Example Question #1 : Real Numbers

Example Question #4 : Real Numbers

Example Question #2 : Number Theory

Example Question #1963 : Problem Solving Questions

Example Question #1 : Understanding Real Numbers

Example Question #2 : Real Numbers

Example Question #1961 : Problem Solving Questions

Example Question #1961 : Problem Solving Questions

Example Question #1962 : Problem Solving Questions

All GMAT Math Resources

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