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What is the value of k?

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Source: — Data Sufficiency |

by Brent@GMATPrepNow » Fri Dec 22, 2017 8:36 am
VJesus12 wrote:What is the value of k?

(1) 2^k = 1/8
(2) 4^(k + 3) = 1
Target question: What is the value of k?

Statement 1: 2^k = 1/8
Rewrite right side to get; 2^k = 2^(-3)
So, it must be the case that k = -3
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: 4^(k + 3) = 1
The only way that 4^something can equal 1 is when something = 0 (that is 4^0 = 1)
Rewrite right side to get; 4^(k + 3) = 4^0
So, we can conclude that k+3 = 0
This mean k = -3
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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