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What is the smallest integer k for which 7^k > 14*7^15 ?

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by M7MBA » Sat Apr 28, 2018 1:26 am
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What is the smallest integer k for which 7^k > 14*7^15?

A. 14
B. 15
C. 16
D. 17
E. 18

The OA is D.

How can I rewrite the given expression to solve this PS question? May someone helps me? Thanks in advance.
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by Vincen » Sat Apr 28, 2018 2:40 am
Hello gmat_mission.

Let's rewrite 14 as 2*7. Then we will get $$14\cdot7^{15} = 2\cdot7\cdot7^{15} = 2\cdot7^{16}.$$ Now, we want to find a value of k such that $$7^k>2\cdot7^{16}\ \Leftrightarrow\ \ 7^{k-16}>2.$$ Any value less or equal than 16 won't satisfy this condition. Then, the smallest integer is k=17. Therefore, the correct answer is the option [spoiler]D=17[/spoiler].
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by Jeff@TargetTestPrep » Thu May 03, 2018 3:34 pm
M7MBA wrote:What is the smallest integer k for which 7^k > 14*7^15?

A. 14
B. 15
C. 16
D. 17
E. 18
Simplifying, we have:

7^k > 2 x 7 x 7^15

7^k > 2 x 7^16

7^k/7^16 > 2

7^(k-16) > 2

We see that k must be at least 17.

Answer: D

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