If P is a positive integer and Q = 120P 60, which of the following

Question

If P is a positive integer and Q = 120P – 60, which of the following MUST be a divisor of Q?

A. 7
B. 11
C. 13
D. 17
E. 30

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vasu1104 · Answer

P>0 
 Q = 120p -60 
 60(2p-1) 
 so 60 must be factor of divisor.

from choices only E divides Q

Dereno · Answer

Given that P>0 as it’s a positive integer.

Q = 120P – 60

taking 60 as common, we get

Q = 60*(2P-1)

for Q to be divisible, any factor of 60 will be good enough.

factors of 60 = 2*3*2*5= 2^2*3*5, we get 12 factors.

Say: 1,2,3,4,5,6,10,12,15,20,30,60.

Among the options given,  30  matches.

Option E

AbhishekP220108 · Answer

Since P is +ve Integer i.e P has value from set (1,2,3.....,n)

Q=120P-60=60(2P-1), Among all the options 30 is a factor of 60. So, E.

007Phoenix007 · Answer

Taking out the greatest common factor, we get
Q= 60(2P-1)
P is an integer so (2P-1) is always an integer
So no matter what values we take as P, 60 will always be multiplied.
So factor of 60 must be a divisor.

Therefore 30 ie option E is the answer

ExpertsGlobal5 · Answer

Video explanation:

https://www.youtube.com/watch?v=BdmHVvh7TdI

If P is a positive integer and Q = 120P 60, which of the following

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GMAT Problem Solving (PS) Questions

If P is a positive integer and Q = 120P 60, which of the following

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