Question

If K is an integer such that 50 < K < 60 , what is the value of K? Statement 1:- The sum of digits in K has exactly two divisors. Statement 2:- The sum of the sum of digits of K is not a prime number. question can be answered by using one of the statements alone, but cannot be answered by using the other statements alone. question can be answered by using either statement alone. question can be answered by using both statements together, but cannot be answered by using the either statement alone. question cannot be answered even by using both the statements together.

Answer 1

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GMAT Club Forum Index Data Sufficiency (DS)

The positive integer k has exactly two positive prime factors, 3 and 7 : Data Sufficiency (DS)

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gmatnub

Updated on: Jan 4, 2018

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DIFFICULTY: 65% (hard) QUESTION STATS: based on 1289 sessions

57% (01:42) correct

43% (02:08) wrong

The positive integer k has exactly two positive prime factors, 3 and 7. If k has a total of 6 positive factors, including 1 and k, what is the value of K?

(1) 3^2 is a factor of k

(2) 7^2 is NOT a factor of k

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Spoiler: OA

Last edited by Bunuel on 04 Jan 2018, 06:54, edited 3 times in total.

Renamed the topic, edited the question and added the OA.

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Most Helpful Expert Reply

Bunuel

EXPERT'S

POST

Dec 31, 2013

jjack0310 wrote:

samiam7 wrote:

From the stem, we know that K's factors are 1, 3, 7, 21 (3*7), __, and K.

1) This tells us there are two factors of 3, so 9 is also a factor of K. K's factors are 1, 3, 7, 9, 21, and K. Since there are two 3's and a 7 in K's factors, then 3*3*7 = 63 is also a factor.

Therefore K's factors are 1, 3, 7, 9, 21, 63.

SUFFICIENT

2) If there are not 2 7's in K's factors, and there are exactly 6 factors total, there must be two factors of 3. Otherwise, if we were to use a non-prime factor, then K would have