If r and s are positive integers and rs = 16, what is the value of r ?

Question

(1)  \frac{s}{8}  is an integer.
(2) r is odd.

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Archit3110 · Answer

possible pairs of r*s = 16
(1,16) ; ( 2,8) ; ( 4,4) ; ( 8,2) ; ( 16,1)

#1
 \frac{s}{8}  is an integer.
s can be 16,8 so r is 1 or 2
insufficient
#2
r is odd
r is 1
sufficient
option B

Bunuel · Answer

Similar question: https://gmatclub.com/forum/if-r-and-s-a ... 27232.html (Kaplan)

av1901 · Answer

r and s are both integers and rs = 16
Possible values for r and s are:
(r=1,s=16), (r=2,s=8), (r=4,s=4), (r=8,s=2), & (r=16,s=1)

(1)  \frac{s}{8}  is an integer.

\frac{s}{8}  = Integer 
So, it means that s has to be multiple of 8

From the list of possible values, s can either be 8 or 16
If s=8, r=2
If s=16, r=1
Different values

NOT SUFFICIENT

(2) r is odd.

The factors of 16 are: 1, 2, 4, 8, 16
There is only one odd factor of 16 and that is the value 1. So if r is odd, then r can only be 1

SUFFICIENT

Answer - B

If r and s are positive integers and rs = 16, what is the value of r ?

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If r and s are positive integers and rs = 16, what is the value of r ?

Prep Toolkit

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