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.
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What is the smallest integer k for which 7^k > 14*7^15 ?
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- ceilidh.erickson
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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.
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
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
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- Jeff@TargetTestPrep
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We are given that 7^k > 14 x 7^15. Let's first simplify 14 x 7^15: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
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
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