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

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Director
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G
Joined: 07 Dec 2014
Posts: 859

Kudos [?]: 291 [0], given: 16

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, 09:12
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Question Stats:

73% (01:55) correct 27% (01:09) wrong based on 44 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
[Reveal] Spoiler: OA

Last edited by gracie on 23 Aug 2017, 14:50, edited 5 times in total.

Kudos [?]: 291 [0], given: 16

1 KUDOS received
Intern
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S
Joined: 31 Mar 2017
Posts: 39

Kudos [?]: 5 [1], given: 16

GMAT 1: 710 Q45 V42
GMAT 2: 730 Q50 V39
GPA: 3.73
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, 14:27
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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

Kudos [?]: 5 [1], given: 16

1 KUDOS received
Intern
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B
Joined: 02 Sep 2016
Posts: 15

Kudos [?]: 1 [1], given: 1

GMAT 1: 660 Q50 V29
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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, 17:16
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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

Kudos [?]: 1 [1], given: 1

Re: x and y are two digit positive integers. When x is divided by 9 and y   [#permalink] 23 Aug 2017, 17:16
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x and y are two digit positive integers. When x is divided by 9 and y

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