A \(k\)-almost prime number is defined as a positive integer with exactly \(k\) prime factors that are not necessarily

[VJesus12]

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

[spoiler]OA=C[/spoiler]

Source: Manhattan GMAT

[Scott@TargetTestPrep]

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

[spoiler]OA=C[/spoiler]

Solution:

Since the smallest 4-almost prime number is 2^4, the second smallest 4-almost prime number is 2^3 x 3 and the third smallest 4-almost prime number is 2^2 x 3^2 = 36.

Since the smallest 3-almost prime number is 2^3, the second smallest 3-almost prime number is 2^2 x 3, the third smallest 3-almost prime number is 2 x 3^2 and the fourth smallest 3-almost prime number is 2^2 x 5 = 20.

Therefore, the difference between the third smallest 4-almost prime number and the fourth smallest 3-almost prime number is 36 - 20 = 16.

Answer: C