If m 1 and n = 2^(m 1), then 4^m =

Question

If m > 1 and n = 2^(m −1), then 4^m =

A) 16n^2
B) 4n^2
C) n^2
D) n^2/4
E) n^2/16

Source: Chili Hot GMAT

omegacube · Answer

n = 2^(m −1)
=> n = 2^m/ 2
=> 2n = 2^m

Squaring both sides;
 4n^2 = 4^m

Hence B

amitshri15 · Answer

2^m = 2n.
4^m = 2^(2m) = (2^m)^2
=> (2n)^2 = 4n^2

Answer is B.

PareshGmat · Answer

Answer = B) 4n^2

n = 2^{m-1}

n = \frac{2^m}{2}

2^m = 2n

Squaring both sides

{(2^m)}^{2} = (2n)^2

2^{2m} = 4n^2

4^m = 4n^2

JJo · Answer

If m > 1 and n = 2^(m −1), then 4^m
Given m>1, so let's assume m=2
n=2^(m-1) = 2^(2-1) = 2, so n=2

hence, 4^m = 4^2 = 16
only 1 ans. choice can satisfy this:
A) 16n^2 --> clearly > 16
B) 4n^2 --> 4*2^2 = 16 (we can stop after this as there can be only 1 right answer)
C) n^2 --> clearly < 16
D) n^2/4 --> clearly < 16
E) n^2/16 --> clearly < 16

Ans. B) 4n^2

Bunuel · Answer

The correct answer is B.

erikvm · Answer

These steps I don't understand, could you please explain?

Why is it that you divide by 2.

Bunuel · Answer

This is basic staff:  2^{m-1}=2^m*2^{-1}=\frac{2^m}{2} .

erikvm · Answer

Ah thats right. Jeez, when something is slightly disguised, I get so thrown off.

It's because  2^m  * 2^-1 = 2^m * 1/2, correct?

Bunuel · Answer

______
Yes, 2^(-1) = 1/2.

EMPOWERgmatRichC · Answer

Hi All,

This question is perfect for TESTing VALUES....

We're told that M > 1 and N = 2^(M-1). We're asked for the value of 4^M

IF.....
M = 2
N = 2^(1) = 2
The value of 4^M = 4^2 = 16

So we're looking for an answer that = 16 when N = 2

Answer A: 16(2^2) = 64 This is NOT a match
Answer B: 4(2^2) = 16 This IS a match
Answer C: 2^2 = 4 This is NOT a match
Answer D: (2^2)/4 = 1 This is NOT a match
Answer E: (2^2)/16 = 1/4 This is NOT a match

Final Answer:  B

GMAT assassins aren't born, they're made,
Rich

stonecold · Answer

Excellent Question
Here 2^m = 2 x n 
now 4^m = 2^2m= (2^m)^2= 4n^2

BlueRocketAsh · Answer

n = 2^{(m −1)} 
 n=2^m*2^{-1} 
 n=\frac{2^m}{2} 
 2n=2^m 
 4^m=4n^2

Paras96 · Answer

n = 2^(m −1)
Simplifying,
=>n = 2^(m −1) = (2^m)/2
=>2n = (2^m)
Or =>(2^m) = 2n
Squaring both the sides 
=>(2^m)^2 = (2n)^2
=> 4^m=4n^2
Hence B

If m > 1 and n = 2^(m 1), then 4^m =

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