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

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

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New post 02 Jun 2015, 05:25
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Question Stats:

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

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New post 02 Jun 2015, 08:13
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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.

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

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New post 03 Jun 2015, 00:37
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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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New post 03 Jun 2015, 05:35
1
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


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

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

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New post 04 Jun 2015, 07:50
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.
Adding those together yields 20.
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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New post 04 Jun 2015, 18:15
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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Re: When positive integer m is divided by positive integer x, the reminder  [#permalink]

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New post 08 Jun 2015, 05:22
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.

Answer: C.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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

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