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If x and y are positive integers, what is the units digit ....

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If x and y are positive integers, what is the units digit ....  [#permalink]

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If x and y are positive integers, what is the units digit of \(7^{xy+y}\)?

1) \(\frac{x}{16}\)=n, where n is a positive integer.

2) \(\frac{y}{8}\)=m, where m is a positive integer.

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Re: If x and y are positive integers, what is the units digit ....  [#permalink]

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New post 06 Sep 2018, 08:03
CAMANISHPARMAR wrote:
If x and y are positive integers, what is the units digit of \(7^{xy+y}\)?

1) \(\frac{x}{16}\)=n, where n is a positive integer.

2) \(\frac{y}{8}\)=m, where m is a positive integer.



Cyclicity of unit's digit of 7 is 7,9,3,1,7,9,3,1......
\(7^{xy+y}\)=\(7^{(x+1)y}\)

Let us see the statements..

1) \(\frac{x}{16}\)=n, where n is a positive integer.
So x is a multiple of 16
\(7^{(x+1)y}\)=\(7^{(16+1)y}\)
If y is 2, it will be 9..
If y=4, it will be 1..and so on
Insufficient

2) \(\frac{y}{8}\)=m, where m is a positive integer
\(7^{(x+1)y}\)
Y is a multiple of 8, so \(7^{(x+1)y}\)=\(7^{(x+1)8}\)
So power of 7 is a multiple of 8..
Thus irrespective of x ANS will be 1
Sufficient

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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html


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Re: If x and y are positive integers, what is the units digit ....   [#permalink] 06 Sep 2018, 08:03
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If x and y are positive integers, what is the units digit ....

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