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The Quest for 700: Weekly GMAT Challenge (Answer)

Yesterday, Manhattan GMAT posted a GMAT question on our blog. Today, they have followed up with the answer:

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

Let’s try making some of these numbers out of small integers, starting low: 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. The fourth smallest is 2 × 2 × 5 = 20. That’s 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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