If 0

Question

If 0 < P*Q < 100, where P and Q are both prime numbers, and P < Q, how many combinations of P and Q are there?

A. 27
B. 28
C. 29
D. 30
E. 31

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sumit99kr · Answer

P*Q<100 , let P=2(smallest prime) then Q=47 (max prime). 
So, we need a combination of all primes between 2 and 47 such that the product is less than hundred and Q>P.
Prime number set:
(2,3,5,7,11,13,17,19,23,29,31,37, 41,43,47) 
P=2 Q can be chosen in 14 ways
P=3 Q,9ways
P=5 Q,5ways
P=7 Q,2ways
Total = 14+9+5+2 = 30

Choice D should be correct.

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gmatophobia · Answer

2 is the smallest prime number, so the maximum prime number that we need to consider should be less than 50.

Primes less than 50

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and 47

P = 2, Q can be any of the above numbers. So 14 combinations.

P = 3, Q needs to be under 33 (as 33 * 3 = 99). So 9 combinations.

P = 5, Q needs to be under 20 (as 20*5 = 100). So 5 combinations.

P = 7, Q needs to be under 14 (as 14 * 7 = 98). So 2 combinations.

So total combinations = 14 + 9 + 5 + 2 = 30

Option D

_ankitchawla_ · Answer

I think there is no way that this question can be solved in under 2 mins if it comes on the actual exam

AllisonBell · Answer

I think that’s a fair point! As a 99th percentile GMAT scorer, I timed myself on this and it took about 3:30. That said, I don’t think it’s an unrealistic to expect something similar to this on the official test.

It’s worth remembering that the 2 minute mark is the  average  amount of time that’s recommended for problems. Some question will take less, some will take a little more, and some would take so long that they aren’t worth doing at all.

A good time management strategy can really mitigate the stressful feeling that you have to answer Every. Single. Problem. in under two minutes in order to score well. I used the one outlined in this article  Everything You Need to Know About Time Management on the GMAT , and it was clutch for helping me achieve my GMAT Focus score of 725.

A strong benchmark time management system would guide your choice on whether to invest time in this problem. If you’re doing fine for time, and you know you have a path to solve, it’s totally okay to spend up to 3:30 on it (but not much more!). If you don’t know how to approach this, or you’re behind on time, make a strategic skip or an educated guess.

Best,

If 0 < P*Q < 100, where P and Q are both prime numbers, and P < Q, how

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