Is the positive integer r a multiple of the positive integer s?

Question

(1) r + 2s is a multiple of s.
(2) 2r + s is a multiple of s.

Kinshook · Answer

Q:Is the positive integer r a multiple of the positive integer s?

#1: r + 2s is a multiple of s.
Since 2s is a multiple of s => r is a multiple of s
SUFFICIENT

#2: 2r + s is a multiple of s.
Since s is a multiple of s => 2r is a multiple of s
Take for example 24(2*12) is a multiple of 24 but 12 is not a multiple of 24.
It is not necessary that r is a multiple of s
NOT SUFFICIENT.

IMO A

MariemeDieng · Answer

Did you say 12 is not a multiple of 24?? How come it isn't?

LfcLegend · Answer

Using 1 only
 (r+2s)/s  should be an integer
this can only be possible if  r/s  is an integer. Hence r is a multiple of the positive integer s. Remove C and E.

Using 2 only

(2r+s)/s  should be an integer
this can be possible even if  2r/s  even if  r=3 and s=2  or if r is a multiple of the positive integer s. Insufficient.

Answer is  A

sathik63 · Answer

Multiples of 24 are 24,48,72 etc.. 24 is a multiple of 12 but 12 is not a multiple of 24

Posted from my mobile device

auradediligodo · Answer

Hi everyone,

Is the positive integer r a multiple of the positive integer s?

(1) r + 2s is a multiple of s.
 Can be written as: r+2s=sk where k is a positive integer
r=sk-2s=s*(k-2)
Since k-2 is an integer r is a multiple of s 
Statement 1 is sufficient

(2) 2r + s is a multiple of s.
 Can be written as 2r+s=ks where k is a positive integer
r=s*(k-s)/2
Now r is a multiple of s if s or (k-s) can be divided by 2.
Since we cannot verify this information statement 2 is insufficient.

Statement a only is sufficient to answer this question

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Is the positive integer r a multiple of the positive integer s?

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Is the positive integer r a multiple of the positive integer s?

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