If k is a positive integer, how many unique prime factors do

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hazelnut01: Master | Next Rank: 500 Posts; Posts: 157; Joined: Sat Nov 19, 2016 5:34 am; Thanked: 2 times; Followed by:4 members

If k is a positive integer, how many unique prime factors do

by hazelnut01 » Thu May 11, 2017 11:26 pm

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

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Source: Beat The GMAT — Data Sufficiency | Thu May 11, 2017 11:26 pm

susheelh: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Sat May 06, 2017 10:45 pm

by susheelh » Tue May 23, 2017 1:04 am

Hi @hazelnut01,

I am solving it as follows. Please correct if wrong

Stem rephrased : What is the value of positive integer K?

S1: K^4 is divisible by 100

K could be 10, 100, 1000 or any other multiple of 10. Insufficient

S2: 50*k has 2 prime factors

5^2*2*k has 2 prime factors.
Means - K has prime factors of 5 or 2 or combination of both.
K could be 5, 2, 10, 50... Insufficient

S1+S2: K is a multiple of 10 and has 5 and 2 as its factors.

The possible option is 10. Sufficient

Final anwer : C

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

Last edited by susheelh on Fri Jun 02, 2017 12:43 am, edited 1 time in total.

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 am; Location: Grand Central / New York; Thanked: 470 times; Followed by:34 members

by Jay@ManhattanReview » Mon May 29, 2017 9:35 pm

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
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