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M31-27

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Math Expert
Joined: 02 Sep 2009
Posts: 56303

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14 Jun 2015, 13:42
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Difficulty:

45% (medium)

Question Stats:

67% (01:46) correct 33% (01:47) wrong based on 42 sessions

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When positive integer $$m$$ is divided by positive integer $$x$$, the reminder is 7 and when positive integer $$n$$ is divided by positive integer $$y$$, the reminder is 11. Which of the following is a possible value for $$x + y$$?

I. 18

II. 19

III. 20

A. I only
B. II only
C. III only
D. II and III only
E. None

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Math Expert
Joined: 02 Sep 2009
Posts: 56303

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14 Jun 2015, 13:42
1
Official Solution:

When positive integer $$m$$ is divided by positive integer $$x$$, the reminder is 7 and when positive integer $$n$$ is divided by positive integer $$y$$, the reminder is 11. Which of the following is a possible value for $$x + y$$?

I. 18

II. 19

III. 20

A. I only
B. II only
C. III only
D. II and III only
E. None

The remainder is ALWAYS less than the divisor, thus $$x > 7$$ and $$y > 11$$. Therefore the least values of $$x$$ and $$y$$ are 8 and 12, respectively, making the least value of $$x + y$$ equal to 20.

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Joined: 10 Dec 2015
Posts: 11
GMAT 1: 590 Q36 V35

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29 Sep 2016, 20:08
Hi! If x>7 and y>11, isn't it possible to say that x+y>18? Then, the answer could also be 19.
I understand that if we consider each equation separately, the answer has to be 20, but I wanted to check if we're allowed to combine the equations to get "19".
Math Expert
Joined: 02 Sep 2009
Posts: 56303

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30 Sep 2016, 06:19
nelliegu wrote:
Hi! If x>7 and y>11, isn't it possible to say that x+y>18? Then, the answer could also be 19.
I understand that if we consider each equation separately, the answer has to be 20, but I wanted to check if we're allowed to combine the equations to get "19".

The point is, we are told that x and y are positive integers. For positive integers x and y, where x > 7 and y > 11, it's not possible that x + y = 19.
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Joined: 10 Dec 2015
Posts: 11
GMAT 1: 590 Q36 V35

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02 Oct 2016, 13:04
Intern
Joined: 30 May 2017
Posts: 2

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08 Jul 2018, 19:50
If it would not have mentioned that its an integer then ??
Manager
Joined: 07 Feb 2017
Posts: 182

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08 Jul 2018, 20:01
m = xa+7 and x>7
n = yb + 11 and y>11
Eliminate I. and II.

Ex. for III.
m=15; a=1; x=8
n=23; b=1; y=12
Intern
Joined: 29 Jul 2017
Posts: 31
Location: India
Concentration: Operations, Finance
GPA: 3.94
WE: Design (Manufacturing)

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03 Jul 2019, 00:28
I think this is a high-quality question and I agree with explanation.
Re M31-27   [#permalink] 03 Jul 2019, 00:28
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