GMAT Math : Arithmetic

Study concepts, example questions & explanations for GMAT Math

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Example Questions

Example Question #3 : Powers & Roots Of Numbers

Solve: \small (\sqrt{5}+\sqrt{4})^2

Possible Answers:

\small 20

\small 9+4\sqrt5

\small 20+4\sqrt5

\small 9

Correct answer:

\small 9+4\sqrt5

Explanation:

First, FOIL:

\small (\sqrt5+\sqrt4)^2=(\sqrt5+\sqrt4)(\sqrt5+\sqrt4)=5+\sqrt20+\sqrt20+4

\small =9+2\sqrt20

Factor out \small \sqrt4

\small =9+4\sqrt5

Example Question #1 : Understanding Powers And Roots

Solve: \small \frac{10^9-10^7}{99}

Possible Answers:

\small \frac{10^7}{99}

\small \frac{10}{99}

\small \frac{100}{99}

\small 10^7

Correct answer:

\small 10^7

Explanation:

First factor. \small \frac{10^9-10^7}{99}\ =\ \frac{(10^7)(10^2-1)}{99}

Simplify. \small \frac{(10^7)(10^2-1)}{99}\ =\ \frac{(10^7)(100-1)}{99}\ =\ \frac{(10^7)(99)}{99}\ =\ 10^7

Example Question #1 : Understanding Powers And Roots

If \small x^2=8, what is \small x^4?

Possible Answers:

Correct answer:

Explanation:

\small x^4=(x^2)^2=(8)^2=64

Example Question #6 : Powers & Roots Of Numbers

Evaluate: 

Possible Answers:

Correct answer:

Explanation:

Example Question #7 : Powers & Roots Of Numbers

Simplify this expression as much as possible:

Possible Answers:


The expression cannot be simplified further

Correct answer:

Explanation:

Example Question #1 : Understanding Powers And Roots

If the side length of a cube is tripled, how does the volume of the cube change?

Possible Answers:

Volume becomes 3 times larger.

Not enough informatin is given.

Volume becomes 27 times larger.

Volume becomes 9 times larger.

The volume doesn't change.

Correct answer:

Volume becomes 27 times larger.

Explanation:

The equation for the volume of a cube is .  If the length is tripled, it becomes , and , so the volume increases by 27 times the original size.

Example Question #9 : Powers & Roots Of Numbers

Simplify 

Possible Answers:

Correct answer:

Explanation:

This can either be done by brute force (slow) or by recognizing the properties of roots and exponents (fast).  Roots are simply fractional exponents: , , etc. so they can be done in any order.

 

So we see a cube root, we can immediately cancel that with the exponent of 3. taking us from here: to .  We now simplify to get

Example Question #10 : Powers & Roots Of Numbers

In the sequence 1, 3, 9, 27, 81, … , each term after the first is three times the previous term. What is the sum of the 9th and 10th terms in the sequence?

Possible Answers:

Correct answer:

Explanation:

We can rewrite the sequence as , , , , , … ,

and we can see that the 9th term in the sequence is and the 10th term in the sequence is . Therefore, the sum of the 9th and 10th terms would be


Example Question #11 : Understanding Powers And Roots

What is ?

Possible Answers:

Correct answer:

Explanation:

Example Question #12 : Understanding Powers And Roots

What is ?

Possible Answers:

Correct answer:

Explanation:

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