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

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by M7MBA » Sun Oct 29, 2017 7:39 am
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 could I solve this PS question without using a calculator? Experts, may you help me?
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by ceilidh.erickson » Sun Oct 29, 2017 11:27 am
Like most EXPONENT questions on the GMAT, this question is not asking you to calculate anything. It's testing whether you understand exponent rules.

First, simplify (14)(7^15) ---> (2)(7)(7^15) ---> (2)(7^16)
When we multiply two terms with the same base, we add the exponents: (7^1)(7^15) = 7^16

If 7^k > (2)(7^16), then k must be greater than 16. If k = 16, then (2)(7^16) would be greater than 7^16. So k must be some number greater than 16.

The answer is D.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
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by Jeff@TargetTestPrep » Thu Dec 07, 2017 6:40 am
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
We are given that 7^k > 14 x 7^15. Let's first simplify 14 x 7^15:

14 x 7^15 = 2^1 x 7^1 x 7^15 = 2 x 7^16

Thus, 7^k > 2 x 7^16 when k = 17 since 7^17 = 7 x 7^16, which is greater than 2 x 7^16.

Answer: D

Jeffrey Miller
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