Manhattan GMAT Challenge Problem of the Week - 6 Sept 2011

by Manhattan Prep, Sep 6, 2011

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Question

A k-almost prime number is defined as a positive integer with exactly k prime factors that are not necessarily distinct. The third smallest 4-almost prime number, less the fourth smallest 3-almost prime number is

A. 6

B. 8

C. 16

D. 24

E. 28

Answer

The term k-almost prime is defined: the number has exactly k prime factors (including repeats).

Lets try making some of these numbers out of small primes: the smallest 3-almost prime, for instance, would be 2 2 2 = 8. Keep going by increasing the primes: the second smallest 3-almost prime is 2 2 3 = 12.

The third smallest 3-almost prime is 2 3 3 = 18. The fourth smallest is 2 2 5 = 20. Thats one of the numbers we want.

Now find the pattern with 4-almost primes. The smallest is 2 2 2 2 = 16. The second smallest is 2 2 2 3 = 24, and the third smallest is 2 2 3 3 = 36.

36 20 = 16.

The correct answer is C.

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