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What is the digit at the unit's place in the expansion

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What is the digit at the unit's place in the expansion  [#permalink]

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New post 10 Apr 2018, 13:19
1
1
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

45% (00:42) correct 55% (00:53) wrong based on 49 sessions

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What is the digit at the unit's place in the expansion of \(X^{40}\)?

1. X is even
2. X is not a multiple of five

Source: Experts Global

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Re: What is the digit at the unit's place in the expansion  [#permalink]

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New post 10 Apr 2018, 15:24
Statement 1
x is even --> units digit of x can be 0,2,4,6,8
if units digit is 0, then x^40 has units digit 0
if units digit is 2, then x^40 has units digit 6 because 2 raised to a power that's a multiple of 4 has 6 as the units digit.
if units digit is 4, then x^40 has units digit 6 because 4=2^2 --> (2^2)^40=2^80 --> 80 is a multiple of 4
if units digit is 6, then x^40 has units digit 6
if units digit is 8, then x^40 has units digit 6 because 8=2^3 --> (2^3)^40=2^120 --> 120 is a multiple of 4
So units digit of x^40 can be 0 or 6.
Not sufficient

Statement 2
x is not a multiple of 5 --> units digit of x can be 1,2,3,4,6,7,8,9
Not sufficient

Combining 1&2
Units digit of x can be 2,4,6,8, thus x^40 will have 6 as the units digit.
Sufficient

Answer: C
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Re: What is the digit at the unit's place in the expansion  [#permalink]

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New post 11 Apr 2018, 08:07
imo C

st 1 gives 0&6
St2 insufficient
Both gives 6
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Re: What is the digit at the unit's place in the expansion  [#permalink]

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New post 19 Apr 2018, 22:52
I)X is even . For every even to power 4 always give 6 except the ones which include 5 eg 20 or 10 which will end with zero.

So not sufficient.

II)not multiple of 5 includes 2,3 etc which have 6 and 1 values when raise to power 4.
Not sufficient.

Combining 1 and 2
Even nos excluding multiple of 5 will always end in 6.

So C is answer

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Re: What is the digit at the unit's place in the expansion &nbs [#permalink] 19 Apr 2018, 22:52
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