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

Question

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

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

LeoN88 · Answer

Statement 1. x= 20 and 25 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

Mo2men · Answer

Hi,

25 is not an even number.

LeoN88 · Answer

Sorry, I wrote that in jiffy, consider another even such as 22.

varunverma · Answer

(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)

Basshead · Answer

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.

bumpbot · Answer

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

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