Is pq divisible by 168?

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Is pq divisible by 168?

by melguy » Tue Nov 01, 2016 1:06 am
Hello

This is a slightly different question to what i posted earlier
https://www.beatthegmat.com/is-p-divisib ... 93231.html

Is pq divisible by 168?
(1) p is divisible by 14
(2) q is divisible by 12

Statement 1
p is divisible by 2 x 7
Not Sufficient

Statement 2
q is divisible by 2 x 2 x 3
Not Sufficient

Combine
LCM of p and q is 2 x 2 x 3 x 7 = 84.

Testing numbers

84 is not divisible by 168
168 is divisible by 168.

So the solution should be E and not C
Source: — Data Sufficiency |

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by fiza gupta » Tue Nov 01, 2016 6:06 am
in earlier question we were only dealing with variable p
in this case we have two variables p and q
we will not take the LCM

in earlier question we have p divisible by 14 and 12
14 = 2*7
12 = 2*2*3
why we need the LCM because the 2 is common in both
84 = is divisible by 14 and 12

example we have number x= 30
30 = > 2*3*5
30 is divisible by 6
30 is also divisible by 10
so we cannot say x is divisible by 6*10 = 60
2 is common in both we are writing it twice but in factors its just one term
Fiza Gupta

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by fiza gupta » Tue Nov 01, 2016 6:10 am
pq in this case are two separate numbers will not take the LCM
p is divisible by 14 and q= 12
pq will be at least divisible by 14*12 = 168

example p = 2 and q = 6(2*3)
pq will be divisible by 2*6 = 12 or 2*2 = 4 or 2*3 = 6
Fiza Gupta

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by melguy » Tue Nov 01, 2016 9:38 pm
Thanks Fiza