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# If p and q are positive integers each greater than 1, and 17

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Intern
Joined: 06 Oct 2011
Posts: 10
If p and q are positive integers each greater than 1, and 17  [#permalink]

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Updated on: 12 Jul 2014, 17:30
3
7
00:00

Difficulty:

65% (hard)

Question Stats:

61% (01:57) correct 39% (02:32) wrong based on 103 sessions

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If p and q are positive integers each greater than 1, and 17(p+1)=29(q+1), what is the least possible value of p+q?

A) 36
B) 42
C) 44
D) 46
E) none

Originally posted by arifaisal on 12 Jul 2014, 17:24.
Last edited by Bunuel on 12 Jul 2014, 17:30, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
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Joined: 02 Sep 2009
Posts: 58449
Re: If p and q are positive integers each greater than 1, and 17  [#permalink]

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12 Jul 2014, 17:35
3
arifaisal wrote:
If p and q are positive integers each greater than 1, and 17(p+1)=29(q+1), what is the least possible value of p+q?

A) 36
B) 42
C) 44
D) 46
E) none

17(p+1)=29(q+1) --> (p+1)/(q+1) = 29/17 --> the least positive value of p+1 is 29, so the least value of p is 28 and the least positive value of q+1 is 17, so the least value of q is 16 --> the least value of p+q is 28+16=44.

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Re: If p and q are positive integers each greater than 1, and 17  [#permalink]

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12 Jul 2014, 17:40
thanks Bunuel..u r a life saver xD
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Re: If p and q are positive integers each greater than 1, and 17  [#permalink]

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15 Jul 2014, 21:37
1
17(p+1)=29(q+1)

$$\frac{p+1}{q+1} = \frac{29}{17}$$

$$\frac{29}{17}$$ cannot be simplified further as both are prime numbers

Equating numerator & denominator respectively

p+1 = 29; p = 28

q+1 = 17; q = 16

p+q = 44

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Re: If p and q are positive integers each greater than 1, and 17  [#permalink]

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08 Mar 2019, 02:50
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).

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Re: If p and q are positive integers each greater than 1, and 17   [#permalink] 08 Mar 2019, 02:50
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