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If p and q are positive integers, p/9 is an integer and q/8 is an integer, is pq/360 an integer?
(1) p/12 is an integer.
(2) q/25 is an integer.
(1) p/12 is an integer.
(2) q/25 is an integer.
25 Apr 2016, 07:42
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Bunuel
If p and q are positive integers, p/9 is an integer and q/8 is an integer, is pq/360 an integer?
(1) p/12 is an integer.
(2) q/25 is an integer.
(1) p/12 is an integer.
(2) q/25 is an integer.
hi
if p/9 is an integer , p is a multiple of 9
and if q/8 is an integer, q is a multiple of 8..
so pq will be multiple of 9*8=72..
Q is - IS pq/360 an integer...
since pq is a multiple of 72 say pq= 72x, where x is an integer..
so Q becomes IS 72x/360 is an integer or is x or pq a multiple of 360/72= 5..
lets see the staements-
(1) p/12 is an integer.
nothing about pq being multiple of 5..
Insuff
(2) q/25 is an integer.
q is a multiple of 25 so pq will also be multiple of 25..
Suff
B
lets see the statements..
17 Feb 2020, 08:14
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Bunuel
If p and q are positive integers, p/9 is an integer and q/8 is an integer, is pq/360 an integer?
(1) p/12 is an integer.
(2) q/25 is an integer.
(1) p/12 is an integer.
(2) q/25 is an integer.
So, given 360=3^2 * 2^3 * 5
p has highest power of 3 as 9....i
q has highest power of 2 as 8....ii
#1. p*q might or might not have power of 5. Insufficient
#2. q is definitely divided by 5 and from i and ii we can easily see that p is divisible by 3^2 and q is divisible by 8. B
