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

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Director
Joined: 11 Feb 2015
Posts: 721
If x and y are positive integers, what is the units digit ....  [#permalink]

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06 Sep 2018, 07:53
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Difficulty:

55% (hard)

Question Stats:

64% (01:32) correct 36% (02:28) wrong based on 36 sessions

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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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Manish

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

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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

B
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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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