Data Sufficiency

hazelnut01 wrote:If k is a positive integer, how many unique prime factors does 14k have ?

(1) k^4 is divisible by 100
(2) 50*k has 2 prime factors

OA=C

Statement 1: k^4 is divisible by 100

We know that 100 = 2^2*5^2, thus k has two (2 and 5) or more numbers of prime factors. We cannot uniquely determine how many unique prime factors 14k has. Insufficient.

Statement 2: 50*k has 2 prime factors

50k = 2*5^2*k; thus k may have none, one (either 2 or 5), or two (2 and 5) prime factors. Since 14k has two (2 and 7) or more prime factors, we uniquely determine how many unique prime factors 14k has. Insufficient. 14k may have two (2 and 7) or three prime factors (2, 5, and 7). Insufficient.

Statement 1 and 2:

Since from Statement 1, we know that k is a prime factor of 5, we can conclude that 14k has three prime factors (2, 5, and 7). Sufficient.

The correct answer: C

Hope this helps!

Relevant book: Manhattan Review GMAT Data Sufficiency Guide

-Jay
_________________
Manhattan Review GMAT Prep

Locations: New York | Singapore | Doha | Lausanne | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

I posted a solution here: https://www.beatthegmat.com/if-k-is-a-po ... tml#793304