Divisibility of Exponential Difference

CAT 2002 Slot 1 · Quantitative Ability · Medium · Number System

This is a medium Quantitative Ability question from the CAT 2002 Slot 1 paper. It tests Number System. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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$7^{6n} - 6^{6n}$ , where $n$ is an integer $> 0$ , is divisible by:

A.
13
B.
127
C.
559
D.
All of these

Answer

Explanation

For $n = 1$ , $7^6 - 6^6 = (7^3 - 6^3)(7^3 + 6^3) = (343 - 216)(343 + 216) = 127 \times 559$ . Also, $559 = 13 \times 43$ . Thus, $7^{6n} - 6^{6n}$ is divisible by $13$ , $127$ , and $559$ . Hence, 'All of these' is the correct answer.

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Divisibility of Exponential Difference

Explanation

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