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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] New post   26 May 2019, 23:21
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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
(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.
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If x is a positive integer, what is the digit at the units place [#permalink] New post   26 Sep 2020, 09:16
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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] New post   27 May 2019, 00:03
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

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.



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
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Re: If x is a positive integer, what is the digit at the units place [#permalink] New post   27 May 2019, 00:23
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.
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If x is a positive integer, what is the digit at the units place [#permalink] New post   27 May 2019, 00:48
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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Re: If x is a positive integer, what is the digit at the units place [#permalink] New post   29 Oct 2020, 08:22
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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] New post   24 Aug 2022, 18:23
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Re: If x is a positive integer, what is the digit at the units place [#permalink]
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