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# What is the remainder when x^2y is divided by 10?

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Math Expert
Joined: 02 Aug 2009
Posts: 6962
What is the remainder when x^2y is divided by 10?  [#permalink]

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28 Jul 2018, 00:34
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7
00:00

Difficulty:

85% (hard)

Question Stats:

30% (00:55) correct 70% (00:53) wrong based on 103 sessions

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What is the remainder when $$x^{2y}$$ is divided by 10?

(1) x=9
(2) y=2

New question!!!..

_________________

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

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Math Expert
Joined: 02 Aug 2009
Posts: 6962
Re: What is the remainder when x^2y is divided by 10?  [#permalink]

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28 Jul 2018, 01:02
5
axmanX wrote:
(Statement 1) x=9

when y is unknown, assuming even a positive value of y,

when y=1, x^2y=81, rem=1
when y=2, x^2y=6561, rem=1

you missed out y as fraction..

$$x^2y$$ divided by 10 MEANS units digit of x^2y

1) x=9..
if y is integer, units digit will always be 1
if y is a fraction say 1/2, units digit will be 9
insuff

2) y = 2
will depend on x
x is 1, ans is 1
x is 2 ans is 6
insuff

combined
ans is 1
suff

C

NOTE - always work for integer and fraction and 0 unless specified
_________________

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

GMAT online Tutor

##### General Discussion
Intern
Joined: 08 Jul 2018
Posts: 22
Location: India
Concentration: General Management, Marketing
GPA: 4
Re: What is the remainder when x^2y is divided by 10?  [#permalink]

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28 Jul 2018, 00:57
(Statement 1) x=9

when y is unknown, assuming even a positive value of y,

when y=1, x^2y=81, rem=1
when y=2, x^2y=6561, rem=1

We can see a pattern forming here, for all positive values of y, even powers of 9 will leave a remainder = 1, when divided by 10.
So, statement 1 is SUFFICIENT

(Statement 2) y=2
knowing just y without x is not sufficient for us to even find out the unit digit of the resulting value, statement 2 is thus INSUFFICIENT.

Intern
Joined: 08 Jul 2018
Posts: 22
Location: India
Concentration: General Management, Marketing
GPA: 4
Re: What is the remainder when x^2y is divided by 10?  [#permalink]

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28 Jul 2018, 16:00
chetan2u wrote:
axmanX wrote:
(Statement 1) x=9

when y is unknown, assuming even a positive value of y,

when y=1, x^2y=81, rem=1
when y=2, x^2y=6561, rem=1

you missed out y as fraction..

$$x^2y$$ divided by 10 MEANS units digit of x^2y

1) x=9..
if y is integer, units digit will always be 1
if y is a fraction say 1/2, units digit will be 9
insuff

2) y = 2
will depend on x
x is 1, ans is 1
x is 2 ans is 6
insuff

combined
ans is 1
suff

C

NOTE - always work for integer and fraction and 0 unless specified

Makes sense. Thanks for correcting me!
Intern
Joined: 23 Aug 2017
Posts: 26
Re: What is the remainder when x^2y is divided by 10?  [#permalink]

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31 Jul 2018, 06:55
Statement 1:

The Pattern is:
When the exponent is odd the unit digit is 9, when it is even the unit digit is 1. As we don't know whether Y is an integer or even whether if Y > 0, then inssuficient.

Statement 2:
We need to know the value of X. Not Sufficient.

1) & 2) As we know now that Y is an integer greater than zero the remainder will be 1. Sufficient.

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Re: What is the remainder when x^2y is divided by 10? &nbs [#permalink] 31 Jul 2018, 06:55
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