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x and y are two digit positive integers. When x is divided by 9 and y

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Joined: 07 Dec 2014
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x and y are two digit positive integers. When x is divided by 9 and y [#permalink]

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New post Updated on: 23 Aug 2017, 15:50
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Difficulty:

  25% (medium)

Question Stats:

71% (01:46) correct 29% (00:55) wrong based on 51 sessions

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x and y are two digit positive integers. When x is divided by 9 and y is divided by 6, the quotients are the same and the remainders are the same. If x+y is 16 times the quotient, what is the ratio between the quotient and the remainder?
A. 1:1
B. 2:1
C. 3:2
D. 3:1
E. 4:1

source:self

Originally posted by gracie on 23 Aug 2017, 10:12.
Last edited by gracie on 23 Aug 2017, 15:50, edited 5 times in total.
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Joined: 31 Mar 2017
Posts: 37
GMAT 1: 710 Q45 V42
GMAT 2: 730 Q50 V39
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Re: x and y are two digit positive integers. When x is divided by 9 and y [#permalink]

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New post 23 Aug 2017, 15:27
1
I'm not sure if this is the fastest way, but I just plugged in numbers and solved it pretty quickly

We are given
x = 9*q + r where q is the quotient and r is the remainder
y = 6*q + r
x + y = 16q

If q = 1, then 16q = 16 and x + y = 16
x = 9 + r and y = 6 + r
x + y = 15 + 2r
Since r is a remainder and must be an integer, then it is not possible for 15 + 2r to be 16.

If q = 2, then 16q = 32 and x + y = 32
x = 18 + r
y = 12 + r
x + y = 30 + 2r
30 + 2r = 32
Therefore r = 1

Therefore q = 2 and r = 1
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Re: x and y are two digit positive integers. When x is divided by 9 and y [#permalink]

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New post 23 Aug 2017, 18:16
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Given x=9q+r, y = 6q+r , where q & r are quotient and remainder respectively.

Also given x+y = 16q

It implies (9q+r)+ (6q+r) = 16q

15q+2r=16q

q=2r

q/r = 2/1
Re: x and y are two digit positive integers. When x is divided by 9 and y   [#permalink] 23 Aug 2017, 18:16
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