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When positive integer m is divided by positive integer x, the reminder

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Math Expert
Joined: 02 Sep 2009
Posts: 55681
When positive integer m is divided by positive integer x, the reminder  [#permalink]

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02 Jun 2015, 06:25
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18
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Difficulty:

75% (hard)

Question Stats:

55% (01:40) correct 45% (01:58) wrong based on 164 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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Joined: 12 Nov 2014
Posts: 62
When positive integer m is divided by positive integer x, the reminder  [#permalink]

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02 Jun 2015, 09:13
1
1
Euclid's Division Lemma states that "Given positive integers a and b, there exists unique integers q and r satisfying
a = bq+ r where 0 ≤ r < b" (q is quotient and r is remainder)

From the question :
m = x *q1 + 7 So from theorem 7< x ; x > 7
n = y *q2 + 11 So from theorem 11< y ; y > 11

So the least value of x = 8 & least value of y = 12
Least value of x+y = 20.

Out of given choices only III is possible.

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Re: When positive integer m is divided by positive integer x, the reminder  [#permalink]

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03 Jun 2015, 01:37
2
Bunuel wrote:
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

Since the reminders are 7 & 11 respectively, the minimum values for x & y are 8 and 12 respectively (y>11) (x>7)

Value of x+y = 12+8 =20. Hence C.
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Re: When positive integer m is divided by positive integer x, the reminder  [#permalink]

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03 Jun 2015, 06:35
1
3
Bunuel wrote:
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

TIP FOR SUCH QUESTIONS: Make Algebraic Equation in the beginning to understand how to proceed further. Then Start thinking the possible values of variables asked about

i.e. "When positive integer m is divided by positive integer x, the reminder is 7" can be understood as

m = ax +7 which means the value of x must be greater than 7 as the remainder 7 is possible only when the Divisor is bigger than the Remainder 7

i.e. Min Value of x = 8

AND

i.e. "When positive integer n is divided by positive integer y, the reminder is 11" can be understood as

n = by +11 which means the value of y must be greater than 11 as the remainder 11 is possible only when the Divisor is bigger than the Remainder 11

i.e. Min Value of y = 12

i.e. Minimum Value of x+y = 8+12 = 20

Hence III only can be True

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Joined: 04 May 2014
Posts: 29
Re: When positive integer m is divided by positive integer x, the reminder  [#permalink]

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04 Jun 2015, 08:50
3
Maybe I'm going in too fast without thinking of the alternatives.
But when m/x yields remainder 7, you can assume x > 7
Similarly when n/y yields remainder 11, you can assume y > 11

Therefore the least possible would be x=8 and y=12.
Only answer satisfying this would be C.

But like I said, maybe I overlooked things.
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Re: When positive integer m is divided by positive integer x, the reminder  [#permalink]

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04 Jun 2015, 19:15
Hi tjerkrintjema,

You've handled this question perfectly. As you can see from the other posts, there are a variety of different ways to approach this prompt (most GMAT questions can be approached in more than one way). Beyond the immediate goal of trying to get a question correct, an additional goal should always be to take an approach that is fastest/easiest; you've done that here.

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Math Expert
Joined: 02 Sep 2009
Posts: 55681
Re: When positive integer m is divided by positive integer x, the reminder  [#permalink]

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08 Jun 2015, 06:22
1
1
Bunuel wrote:
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

OFFICIAL SOLUTION:

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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Re: When positive integer m is divided by positive integer x, the reminder  [#permalink]

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27 Apr 2019, 03:17
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Re: When positive integer m is divided by positive integer x, the reminder   [#permalink] 27 Apr 2019, 03:17
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