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# If p, q, r and s are positive integers, and q × s < 130, what is the

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Math Expert
Joined: 02 Sep 2009
Posts: 55668
If p, q, r and s are positive integers, and q × s < 130, what is the  [#permalink]

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30 Jul 2017, 22:44
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Difficulty:

25% (medium)

Question Stats:

81% (01:52) correct 19% (01:55) wrong based on 96 sessions

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If p, q, r and s are positive integers, and q × s < 130, what is the value of (q + s)?

(1) p, when divided by q, leaves remainder 9.
(2) r , when divided by s, leaves remainder 10.

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Director
Joined: 21 Mar 2016
Posts: 518
Re: If p, q, r and s are positive integers, and q × s < 130, what is the  [#permalink]

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31 Jul 2017, 10:19
1
Bunuel wrote:
If p, q, r and s are positive integers, and q × s < 130, what is the value of (q + s)?

(1) p, when divided by q, leaves remainder 9.
(2) r , when divided by s, leaves remainder 10.

12 x 10 < 130
13 x 9 < 127... with this lets analyze the stats..

stat1 : q shud be more than 9... 10,11,12... no info on s...
not suff

stat2 : s shud be more than 10... 11,12,13,14..... no info on q,,
not suff

both combined....q * s
10 *11
10 *12...diff answers for ( q+ s)

ans E
Current Student
Joined: 11 May 2015
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Location: United States
Concentration: Strategy, Operations
GPA: 3.44
Re: If p, q, r and s are positive integers, and q × s < 130, what is the  [#permalink]

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31 Jul 2017, 12:09
Bunuel wrote:
If p, q, r and s are positive integers, and q × s < 130, what is the value of (q + s)?

(1) p, when divided by q, leaves remainder 9.
(2) r , when divided by s, leaves remainder 10.

I thought the answer was C considering q*s =130 in error.
But after reading the above explanation I am thinking E. What's the OA
Senior Manager
Joined: 09 Aug 2017
Posts: 340
Re: If p, q, r and s are positive integers, and q × s < 130, what is the  [#permalink]

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28 Oct 2018, 10:40
How I did this question is below.
Statement1:
P= Qn+9 so Q ranges from 0 to 9
but we have no value of S.
Insufficient.

Statement 2:
R= Sn+10 so S ranges from 0 to 10
But no values of Q.
Insufficient.

St1+2
0<=Q<9
0<=S<10

various values satisfying q*s<130

Re: If p, q, r and s are positive integers, and q × s < 130, what is the   [#permalink] 28 Oct 2018, 10:40
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