anudeep133 wrote:

Bunuel wrote:

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

Kudos for a correct solution.

Solution: 3-almost prime numbers : 8(as 8 = 2*2*2) , 12 (2*2*3) , 18 (2*3*3) , 20 (2*2*5)....

4-almost prime numbers : 16(as 8 = 2*2*2*2) , 24 (2*2*2*3) , 36 (2*2*3*3)...

The third smallest 4-almost prime number, less the fourth smallest 3-almost prime number = 36-20 = 16.

Option C.

Bunuel I almost took 5 min to solve this. Is there a easier method?

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.

answer C.

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Please award kudos if you like my explanation.

Thanks