If n is a non-negative integer such that 6^n is a divisor of

Question

If n is a non-negative integer such that 6^n is a divisor of 5,178,791, what is the value of n^6 – 6^n?

A. - 11
B. - 1
C. 0
D. 1
E. 11

Bunuel · Accepted Answer

If n is a non-negative integer such that 6^n is a divisor of 5,178,791, what is the value of n^6 – 6^n?

A. - 11
B. - 1
C. 0
D. 1
E. 11

6^n is a divisor of 5,178,791 --> as far as n is non-negative integer (given) the only value of n is 0 (5,178,791 is not even, thus it can not be divided by 6 in any power but 0)

n = 0

0^6 - 6^0 = 0 - 1 = -1

Answer: B.

PerfectScores · Answer

Let us say that n = 0 then 6^0 = 1 which is a divisor of any number.

Now the question is asking the value of 0^6 - 6^0 = -1

seemachandran · Answer

Dear Bunuel/Others

When its 'non-negative' in the question ; dosent this mean '0' or other positive values?

Bunuel · Answer

Yes, non-negative numbers include 0 and positive numbers.

JeffTargetTestPrep · Answer

Since 5,178,791 is odd, it is not divisible by 6^n (which is an even number), except when n = 0.

Therefore, 0^6 - 6^0 = 0 - 1 = -1.

Answer: B

CrackverbalGMAT · Answer

6^n is a divisor of 5,178,791

Any positive integral power of 6 must end with a 6

5,178,791 has a units digit of 1 and not 6. The Q.stem provides us that n is a non-negative integer and hence we can thus substitute n as 0.

If n = 0, n^6 – 6^n = 0^6 - 6^0

= - 1

(option b)

D.S
GMAT SME

bumpbot · Answer

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If n is a non-negative integer such that 6^n is a divisor of

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