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If x = 989 and y = 991, what is the remainder of xy/9?

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Bunuel
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If x = 989 and y = 991, what is the remainder of xy/9? [#permalink] New post   26 Apr 2016, 06:32
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If x = 989 and y = 991, what is the remainder of xy/9?

A. 8
B. 7
C. 6
D. 5
E. 4
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A
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Abhishek009
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Re: If x = 989 and y = 991, what is the remainder of xy/9? [#permalink] New post   26 Apr 2016, 08:28
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Bunuel wrote:
If x = 989 and y = 991, what is the remainder of xy/9?

A. 8
B. 7
C. 6
D. 5
E. 4


x / 9 = 989/9 will leave remainder 8

y/9 = 991/9 will leave remainder 1

Thus xy will be 8

8/9 remainder will be 8 ; hence answer will be (A) 8
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Re: If x = 989 and y = 991, what is the remainder of xy/9? [#permalink] New post   26 Apr 2016, 19:44
989 -> 990-1
991 -> 990+1

xy -> (990-1)(990+1) -> (990-1)^2
990/9 will leave no remainder, we add 9 to -1 and get 8. Answer A.

Is this a correct application?
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Re: If x = 989 and y = 991, what is the remainder of xy/9? [#permalink] New post   26 Apr 2016, 20:41
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lucalimoncelli wrote:
989 -> 990-1
991 -> 990+1

xy -> (990-1)(990+1) -> (990-1)^2
990/9 will leave no remainder, we add 9 to -1 and get 8. Answer A.

Is this a correct application?


Hi,
you have found a good method to answer the Q, but gone wrong in the highlighted portion..
\((990-1)(990+1) = 990^2 - 1^2\)..
now 990 will be div by 9 ..
so our answer is 0-1 = -1..
But remainders are always positive, so -1 will become 9-1 = 8..
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Re: If x = 989 and y = 991, what is the remainder of xy/9? [#permalink] New post   12 Feb 2019, 20:48
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Bunuel wrote:
If x = 989 and y = 991, what is the remainder of xy/9?

A. 8
B. 7
C. 6
D. 5
E. 4


Solution:

The remainder when 989 is divided by 9 is 8, and the remainder when 991 is divided by 9 is 1, so the remainder when 989 x 991 is divided by 9 is 8 x 1 = 8.

Answer: A
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Re: If x = 989 and y = 991, what is the remainder of xy/9? [#permalink] New post   05 Jul 2021, 16:28
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If x = 989 and y = 991, what is the remainder of xy/9? [#permalink]
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