x, y, a, and b are positive integers. When x is divided by y : GMAT Problem Solving (PS)
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# x, y, a, and b are positive integers. When x is divided by y

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Director
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x, y, a, and b are positive integers. When x is divided by y [#permalink]

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19 Jan 2012, 16:07
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x, y, a, and b are positive integers. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 9. Which of the following is NOT a possible value for y + b?

A. 24
B. 21
C. 20
D. 17
E. 15

[Reveal] Spoiler:
My answer is A as I can get other values. But the OA is not given. What I am keen on asking is "I have solved this question by picking the values for x,y,a and b. Is there any shortcut and do you guys agree with my answer?
[Reveal] Spoiler: OA

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Best Regards,
E.

MGMAT 1 --> 530
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19 Jan 2012, 16:29
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enigma123 wrote:
x, y, a, and b are positive integers. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 9. Which of the following is NOT a possible value for y + b?
a)24
b)21
c)20
d)17
e)15

My answer is A as I can get other values. But the OA is not given. What I am keen on asking is "I have solved this question by picking the values for x,y,a and b. Is there any shortcut and do you guys agree with my answer?

Important note: remainder is ALWAYS less than divisor, thus y>6 and b>9 --> y+b>15.

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Director
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 536
Location: United Kingdom
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)
Followers: 74

Kudos [?]: 2955 [0], given: 217

Re: x, y, a, and b are positive integers. When x is divided by y [#permalink]

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24 Jan 2012, 17:35
Thanks for the tip.
_________________

Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730

Manager
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Kudos [?]: 28 [0], given: 7

Re: x, y, a, and b are positive integers. When x is divided by y [#permalink]

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25 Jan 2012, 01:01
Sometimes the answers is so easy. U just need to figure it out. Thanks Bunuel

I picked "E" too, but tried to figure it out by picking numbers. Took me ages
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Re: x, y, a, and b are positive integers. When x is divided by y [#permalink]

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25 Jan 2012, 03:59
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enigma123 wrote:
x, y, a, and b are positive integers. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 9. Which of the following is NOT a possible value for y + b?
a)24
b)21
c)20
d)17
e)15

My answer is A as I can get other values. But the OA is not given. What I am keen on asking is "I have solved this question by picking the values for x,y,a and b. Is there any shortcut and do you guys agree with my answer?

I would suggest you to analyze each statement as you read it. Often, you will find that you are very close to the answer by the time you read the last sentence of the question.

"When x is divided by y, the remainder is 6."
Here, I say to myself, "Ok, so y must be greater than 6 and x is either 6 or at least 6 greater than y."

If you are not sure how I deduced this, check out these posts:
http://www.veritasprep.com/blog/2011/04 ... unraveled/
http://www.veritasprep.com/blog/2011/04 ... y-applied/
If y is anything less than 6, you can make one more group!

When a is divided by b, the remainder is 9.
Now I say, "b must be greater than 9 and a is either 9 or at least 9 greater than y."

Which of the following is NOT a possible value for y + b
I already know that y must be greater than 6 and b must be greater than 9. So (y+b) must be greater than 15. Now I will just look for an option <= 15
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Karishma
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews GMAT Club Legend Joined: 09 Sep 2013 Posts: 13435 Followers: 575 Kudos [?]: 163 [0], given: 0 Re: x, y, a, and b are positive integers. When x is divided by y [#permalink] ### Show Tags 26 Jul 2014, 21:00 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Manager Joined: 26 Feb 2015 Posts: 127 Followers: 0 Kudos [?]: 9 [0], given: 43 Re: x, y, a, and b are positive integers. When x is divided by y [#permalink] ### Show Tags 16 May 2015, 10:37 VeritasPrepKarishma wrote: enigma123 wrote: x, y, a, and b are positive integers. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 9. Which of the following is NOT a possible value for y + b? a)24 b)21 c)20 d)17 e)15 My answer is A as I can get other values. But the OA is not given. What I am keen on asking is "I have solved this question by picking the values for x,y,a and b. Is there any shortcut and do you guys agree with my answer? I would suggest you to analyze each statement as you read it. Often, you will find that you are very close to the answer by the time you read the last sentence of the question. "When x is divided by y, the remainder is 6." Here, I say to myself, "Ok, so y must be greater than 6 and x is either 6 or at least 6 greater than y." If you are not sure how I deduced this, check out these posts: http://www.veritasprep.com/blog/2011/04 ... unraveled/ http://www.veritasprep.com/blog/2011/04 ... y-applied/ If y is anything less than 6, you can make one more group! When a is divided by b, the remainder is 9. Now I say, "b must be greater than 9 and a is either 9 or at least 9 greater than y." Which of the following is NOT a possible value for y + b I already know that y must be greater than 6 and b must be greater than 9. So (y+b) must be greater than 15. Now I will just look for an option <= 15 Question: If 15 is not in the answer choice, is the answer to this question "any number that is not a multiple of 10 + multiple of 7"? So, 37 and 38 would be okay, but 39 no, correct? Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7119 Location: Pune, India Followers: 2132 Kudos [?]: 13631 [0], given: 222 Re: x, y, a, and b are positive integers. When x is divided by y [#permalink] ### Show Tags 18 May 2015, 03:53 erikvm wrote: VeritasPrepKarishma wrote: enigma123 wrote: x, y, a, and b are positive integers. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 9. Which of the following is NOT a possible value for y + b? a)24 b)21 c)20 d)17 e)15 My answer is A as I can get other values. But the OA is not given. What I am keen on asking is "I have solved this question by picking the values for x,y,a and b. Is there any shortcut and do you guys agree with my answer? I would suggest you to analyze each statement as you read it. Often, you will find that you are very close to the answer by the time you read the last sentence of the question. "When x is divided by y, the remainder is 6." Here, I say to myself, "Ok, so y must be greater than 6 and x is either 6 or at least 6 greater than y." If you are not sure how I deduced this, check out these posts: http://www.veritasprep.com/blog/2011/04 ... unraveled/ http://www.veritasprep.com/blog/2011/04 ... y-applied/ If y is anything less than 6, you can make one more group! When a is divided by b, the remainder is 9. Now I say, "b must be greater than 9 and a is either 9 or at least 9 greater than y." Which of the following is NOT a possible value for y + b I already know that y must be greater than 6 and b must be greater than 9. So (y+b) must be greater than 15. Now I will just look for an option <= 15 Question: If 15 is not in the answer choice, is the answer to this question "any number that is not a multiple of 10 + multiple of 7"? So, 37 and 38 would be okay, but 39 no, correct? I am not sure what you mean by "37 and 38 would be okay, but 39 no" y should be at least 7 and b should be at least 10. So their sum should be at least 17. The sum could be 18 (y is 8 and b is 10 or y is 7 and b is 11) or it could be 19 or 20 or 37 or 38 or 39. If it is 39, y could be 9 and b could be 30. There are no constraints except that the sum should be at least 17 and y should be at least 7 and b should be at least 10. So a case such as x = 15, y = 9 will give remainder 6 and a = 39 and b = 30 will give remainder 9. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Kudos [?]: 9 [0], given: 43

x, y, a, and b are positive integers. When x is divided by y [#permalink]

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18 May 2015, 03:56
VeritasPrepKarishma wrote:
.

What I meant was that the result cannot be something that is a multiple of 10x + 7y. 37 is the same as 30(3) + 7(1). 38 = 7(4) + 10(1). But there is no way to arrive at 39 with a multiple of 10 + multiple of 7. In other words, my question is: Would the answer to this question be "anything that is not "10x + 7y" or is it simply "x + y must be more than 16?"

Doesnt this question have anything to do with multiples of x and y?
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Re: x, y, a, and b are positive integers. When x is divided by y [#permalink]

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18 May 2015, 04:05
erikvm wrote:
VeritasPrepKarishma wrote:
.

What I meant was that the result cannot be something that is a multiple of 10x + 7y. 37 is the same as 30(3) + 7(1). 38 = 7(4) + 10(1). But there is no way to arrive at 39 with a multiple of 10 + multiple of 7. In other words, my question is: Would the answer to this question be "anything that is not "10x + 7y" or is it simply "x + y must be more than 16?"

Doesnt this question have anything to do with multiples of x and y?

Why not? Sum can be 17 or 37 or 38.

It is possible that y = 7 and b = 10.
x = 13, y = 7, remainder of x/y = 6
a = 19, b = 10, remainder of a/b = 9
y + b = 17

Sum 37 is also possible:
It is possible that y = 7 and b = 30.
x = 13, y = 7, remainder of x/y = 6
a = 39, b = 30, remainder of a/b = 9
y + b = 37

etc
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Manager Joined: 26 Feb 2015 Posts: 127 Followers: 0 Kudos [?]: 9 [0], given: 43 x, y, a, and b are positive integers. When x is divided by y [#permalink] ### Show Tags 18 May 2015, 04:25 VeritasPrepKarishma wrote: erikvm wrote: VeritasPrepKarishma wrote: . What I meant was that the result cannot be something that is a multiple of 10x + 7y. 37 is the same as 30(3) + 7(1). 38 = 7(4) + 10(1). But there is no way to arrive at 39 with a multiple of 10 + multiple of 7. In other words, my question is: Would the answer to this question be "anything that is not "10x + 7y" or is it simply "x + y must be more than 16?" Doesnt this question have anything to do with multiples of x and y? Why not? Sum can be 17 or 37 or 38. It is possible that y = 7 and b = 10. x = 13, y = 7, remainder of x/y = 6 a = 19, b = 10, remainder of a/b = 9 y + b = 17 Sum 37 is also possible: It is possible that y = 7 and b = 30. x = 13, y = 7, remainder of x/y = 6 a = 39, b = 30, remainder of a/b = 9 y + b = 37 etc Well that kinda enforces my question. All of those options are actually a multiple of 10 + multiple of 7? 37 is the same as 10*3 + 7*1. 17 is the same as 10*1 + 7*1 38 is the same as 10*1 + 7*4 My question remains; Is anything that is not a multiple of 10x + 7y the correct answer? All the options except 15 is actually a multiple of 10x + 7y a)24 - same as 7*2 + 10*1 b)21 - same as 7*3 + 10*0 c)20 - same as 7*0 + 10*2 d)17 - same as 10*1 + 7*1 e)15 - No combination of 10x + 7y can give us 15. So: Is this just a coincidence here, or is the "pattern" to this question? i.e: Could the question stem just as well say "Which of the following answer choices is not a multiple of 10 + multiple of 7? Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7119 Location: Pune, India Followers: 2132 Kudos [?]: 13631 [0], given: 222 Re: x, y, a, and b are positive integers. When x is divided by y [#permalink] ### Show Tags 18 May 2015, 05:18 erikvm wrote: All the options except 15 is actually a multiple of 10x + 7y a)24 - same as 7*2 + 10*1 b)21 - same as 7*3 + 10*0 c)20 - same as 7*0 + 10*2 d)17 - same as 10*1 + 7*1 e)15 - No combination of 10x + 7y can give us 15. So: Is this just a coincidence here, or is the "pattern" to this question? i.e: Could the question stem just as well say "Which of the following answer choices is not a multiple of 10 + multiple of 7? I did show above that a sum of 18 is also possible. 39 is also possible. ANY sum is possible as long as it is more than 16. So no, the question is not the same as "Which of the following answer choices is not a multiple of 10 + multiple of 7?" It is the same as "Which of the following is less than 17?" Every number which is 17 or more can be written as y + b where y is more than 6 and b is more than 9. That is the ONLY constraint. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: x, y, a, and b are positive integers. When x is divided by y [#permalink]

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26 May 2016, 02:27
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Re: x, y, a, and b are positive integers. When x is divided by y   [#permalink] 26 May 2016, 02:27
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