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Is R/S an integer, if R and S are non-zero

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Math Expert
Joined: 02 Aug 2009
Posts: 7197
Is R/S an integer, if R and S are non-zero  [#permalink]

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12 Apr 2016, 20:05
2
2
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Difficulty:

65% (hard)

Question Stats:

45% (01:37) correct 55% (01:17) wrong based on 67 sessions

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Is $$\frac{R}{S}$$ an integer, if R and S are non-zero integers..

(1) $$R>S$$
(2) $$\frac{S}{R}$$ is an integer

OA in two days..

_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: Is R/S an integer, if R and S are non-zero  [#permalink]

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12 Apr 2016, 20:46
1
St1: R > S
If R = 3; S = 1 --> R/S = integer
If R = 3; S = 2 --> R/S is not an integer
Not sufficient

St2: S/R is an integer
If |S| = |R| then R/S is an integer

If S > R,
say S = 3; R = 1 then R/S is not an integer
say S = 3; R = -3 then R/S is an integer

If S < R,
say S = -3; R = 1 then R/S is not an integer
say S = -3; R = 3 then R/S is an integer
St2 is not Sufficient

Combining St1 and St2 --> R > S and S/R is an integer
As we have seen above if R = 3 and S = -3 then R/S is an integer
but, if R = 1 and S = -3 then R/S is not an integer
Not Sufficient

Intern
Joined: 21 Feb 2015
Posts: 6
Re: Is R/S an integer, if R and S are non-zero  [#permalink]

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12 Apr 2016, 20:51
1
ST1: R > S
R & S can hold the value of +ve and –ve integer.
Case 1: R =0, S =-1, R/S = 0 (Integer)
Case 2: R =1, S =-2, R/S = -.5 (Non Integer)
ST1 -Not sufficient

ST2: S/R is an integer
Case 1: R=10, S=20 , R/S =.5 ( Non Integer)
Case 2: R=1, S= -1, R/S = -1 (Integer)
ST2 -Not Sufficient

Combining ST1 & ST2: R>S & S/R is an integer
Case 1: R=10, S=-50, R/S=-.2 (Not integer)
Case 2: R=1, S=-1, R/S =-1 (Integer)
Hence Insufficient.

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Joined: 09 Sep 2013
Posts: 9416
Re: Is R/S an integer, if R and S are non-zero  [#permalink]

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07 Jan 2018, 00:58
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Re: Is R/S an integer, if R and S are non-zero &nbs [#permalink] 07 Jan 2018, 00:58
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