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M31-27

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M31-27  [#permalink]

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New post 14 Jun 2015, 13:42
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72% (01:05) correct 28% (00:52) wrong based on 50 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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Re M31-27  [#permalink]

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New post 14 Jun 2015, 13:42
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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.


Answer: C
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: M31-27  [#permalink]

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New post 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".
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Re: M31-27  [#permalink]

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New post 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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: M31-27  [#permalink]

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New post 02 Oct 2016, 13:04
I had missed that, thanks.
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Re: M31-27  [#permalink]

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New post 08 Jul 2018, 19:50
If it would not have mentioned that its an integer then ??
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Re: M31-27  [#permalink]

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New post 08 Jul 2018, 20:01
m = xa+7 and x>7
n = yb + 11 and y>11
Eliminate I. and II.
Answer C or E

Ex. for III.
m=15; a=1; x=8
n=23; b=1; y=12
Answer C
Re: M31-27 &nbs [#permalink] 08 Jul 2018, 20:01
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