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

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

by VJesus12 » Sat Jul 11, 2020 11:52 pm

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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]

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

by Scott@TargetTestPrep » Sun Jul 19, 2020 11:06 am
VJesus12 wrote: ↑
Sat Jul 11, 2020 11:52 pm
 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

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