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# If x is a positive integer, what is the digit at the units place

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If x is a positive integer, what is the digit at the units place [#permalink]
Mo2men wrote:
LeoN88 wrote:
GMATMBA5 wrote:
If x is a positive integer, what is the digit at the units place in the expansion of x^40?

(1) x is even
(2) x is not a multiple of five

Statement 1. x= 20 and25 will have different unit digits. Insufficient.

Statement 2. 12 and 13 will have different unit digits. Insufficient.

1+2, x must be ending with 2/4/6/8 for all these 4 possibilities of x the last digit in the for the format x^4n is 6. Sufficient C
Last Digit
2^4-6
4^4-6
6^4-6
8^4-6

Hi,

25 is not an even number.

Sorry, I wrote that in jiffy, consider another even such as 22.
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If x is a positive integer, what is the digit at the units place [#permalink]
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(A) x is even
the unit digits of
2: 2486
4: 4646
6:6666
8: 8246
0: 0000

So, any even number with a unit digit of 0 raised to the power 40 will have a unit digit of zero and other even numbers raised to the power 40 will have a unit digit of 6
A is insufficient

(B) if x is not a multiple of 5 then it can either be odd or even. Insufficient

(A) and (B)
even numbers ending with 2,4,6,8 are not multiples of 0 and all have unit digit 6 at the end of the cyclic pattern (set of 4 numbers repeating) and ends with 6 as 40 is divisible by 4.
Sufficient (C)
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Re: If x is a positive integer, what is the digit at the units place [#permalink]
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If x is a positive integer, what is the digit at the units place in the expansion of x^40?

(1) x is even

Cyclicity of 4: 4, 6
Cyclicity of 6: 6, 6
Cyclicity of 8: 8, 4, 2, 6
Cyclicity of 0: 0

Insufficient; can be 0 or 6.

(2) x is not a multiple of five

Cyclicity of 3 = 3, 9, 7, 1
Cyclicity of 2 = 2, 4, 8, 6

We can get different answers. Insufficient.

(1&2) If x is even and not a multiple of 5, we can conclude that the units digit is 6. Sufficient.
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Re: If x is a positive integer, what is the digit at the units place [#permalink]
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Re: If x is a positive integer, what is the digit at the units place [#permalink]
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