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# If x is an integer greater than 1, what is the units digit of 6^x − 6^

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Joined: 02 Sep 2009
Posts: 51229
If x is an integer greater than 1, what is the units digit of 6^x − 6^  [#permalink]

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22 May 2018, 03:29
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Difficulty:

5% (low)

Question Stats:

94% (00:43) correct 6% (00:36) wrong based on 57 sessions

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If x is an integer greater than 1, what is the units digit of $$6^x − 6^{(x−1)}$$?

A. 0
B. 1
C. 3
D. 6
R. It cannot be determined.

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If x is an integer greater than 1, what is the units digit of 6^x − 6^  [#permalink]

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22 May 2018, 03:49
Bunuel wrote:
If x is an integer greater than 1, what is the units digit of $$6^x − 6^{(x−1)}$$?

A. 0
B. 1
C. 3
D. 6
R. It cannot be determined.

It does not matter how many times 6 is multiplied by 6. The unit's digit is always 6 (unless x is 0 or -ve).
Hence , Units digit of both $$6^x$$ & $$6^{(x−1)}$$ is $$6$$.
Hence after subtraction the units digit is 0.
Hence , I would go for option A.
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If x is an integer greater than 1, what is the units digit of 6^x − 6^  [#permalink]

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22 May 2018, 03:56
Bunuel wrote:
If x is an integer greater than 1, what is the units digit of $$6^x − 6^{(x−1)}$$?

A. 0
B. 1
C. 3
D. 6
R. It cannot be determined.

If $$x=1$$, then the units digit of $$6^x − 6^{(x−1)}$$ is $$6-1=5$$

For all other cases $$...6-...6 = ...0$$

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Re: If x is an integer greater than 1, what is the units digit of 6^x − 6^  [#permalink]

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22 May 2018, 04:15

Solution

Given:
• The value of the integer x is greater than 1

To find:
• The unit digit of the expression $$6^x$$ – $$6^{(x-1)}$$

Approach and Working:
• If we observe the unit digit pattern of 6, we can see for any positive power of 6, the number will always end with 6 only
o $$6^1$$ = 6
o $$6^2$$ = 36
o $$6^3$$ = 216 etc.
• As x > 1, x-1 > 0
o Hence, $$6^x$$ and $$6^{(x-1)}$$ will always end with the unit digit 6
• Therefore, $$6^x$$ - $$6^{(x-1)}$$ will end with 0
Hence, the correct answer is option A.

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Re: If x is an integer greater than 1, what is the units digit of 6^x − 6^ &nbs [#permalink] 22 May 2018, 04:15
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