Given that 4^p + q = 64 and 4^p - q = 116, what is the value of pq =?

Given that 4^p + q = 64 and 4^p - q = 116, wh… | GMAT Sprint

Free Practice Question

PS · Problem Solving

sub-505

Exponents/Powers

Given that $4^{p + q} = 64$ and $4^{p - q} = \frac{1}{16}$ , what is the value of $\frac{p}{q} =$ ?

Answer Choices

Correct answer marked below

\frac{1}{6}

\frac{1}{5}

Correct

\frac{1}{3}

See the full step-by-step explanation

You can see the correct answer above. Sign in for free to unlock the complete worked solution.

Track your performance and improve

Get detailed analytics, unlock full explanations, and move up difficulty tiers as you practice.

Start for free Sign in

Explanation

Preview

Official Explanation

Official

The equation

4^{p + q} = 64

can be rewritten as

4^{p + q} = 4^3

. The second equation

4^{p - q} = \frac{1}{16}

can be expressed as

4^{p - q} = 4^{-2}

. From the first equation, we have

p + q = 3

, and from the second equation,

p - q = -2

. Solving these two equations, we can express

p

in terms of…

Read the full explanation

Create free account Sign in

Comments

WaheedMay 30, 2024

Tricky wording but good practice

RidaNov 1, 2024

thanks

SillyAug 15

thanks, this was a nice quick one to warm up with the exponent rules

JulietJun 18

got B. once you turn 64 into 4^3 and 1/16 into 4^-2 it basically solves itself

What this question tests

What it tests

Your grasp of exponent rules — multiplying and dividing powers, power-of-a-power, and negative/zero exponents.

Common trap

Adding exponents when multiplying bases that have the same exponent, or confusing (x^a)^b with x^(a·b).

Given that 4p+q=644^{p + q} = 644p+q=64 and 4p−q=1164^{p - q} = \frac{1}{16}4p−q=161​, what is the value of pq=\frac{p}{q} =qp​=?