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Is 7^x greater than 2,500?

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Is 7^x greater than 2,500?

by M7MBA » Sun Dec 17, 2017 8:44 am
Is 7^x greater than 2,500?

(1) 7^(x+1) > 16,500
(2) 7^(x+2) = 7^x + 16464

The OA is B.

How can I use statement (2) to get an answer? I don't know how to solve this DS question.
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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Mon Dec 18, 2017 9:12 pm
M7MBA wrote:Is 7^x greater than 2,500?

(1) 7^(x+1) > 16,500
(2) 7^(x+2) = 7^x + 16464

The OA is B.

How can I use statement (2) to get an answer? I don't know how to solve this DS question.
(1) 7^(x+1) > 16,500

=> (7^x)*7 > 16500
(7^x) > 16500/7
7^x > 2357...

Case 1: If 2500 ≥ 7^x > 2357..., the answer is No.
Case 2: If 7^x > 2500, the answer is Yes. No unique answer. Insufficient.

(2) 7^(x+2) = 7^x + 16464

7^(x+2) - 7^x = 16464
(7^x)*7^2 - 7^x = 16464
7^x(7^2 - 1) = 16464
(7^x)*48 = 16464
7^x = 16464/48 = 343

Since 7^x = 343, we have 7^x is not greater than 2500. The answer is No. Sufficient.

The correct answer: B

Hope this helps!

-Jay
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