BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Positive Factors

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Data Sufficiency |
User avatar
Legendary Member
Posts: 1100
Joined: Sat May 10, 2014 11:34 pm
Location: New Delhi, India
Thanked: 205 times
Followed by:24 members

by GMATinsight » Mon Nov 30, 2015 8:03 am
vrn2vw wrote: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

May I receive some help with this problem? It's from the official GMAT Prep application.


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

Statement 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

Statement 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 more than 6 factors. (Remember 'K' has exactly two positive prime factors)

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

Answer: Option D
"GMATinsight"Bhoopendra Singh & Sushma Jha
Most Comprehensive and Affordable Video Course 2000+ CONCEPT Videos and Video Solutions
Whatsapp/Mobile: +91-9999687183 l [email protected]
Contact for One-on-One FREE ONLINE DEMO Class Call/e-mail
Most Efficient and affordable One-On-One Private tutoring fee - US$40-50 per hour
Top
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 am
Location: Las Vegas, USA
Thanked: 19 times
Followed by:37 members

by Max@Math Revolution » Thu Dec 03, 2015 7:42 am
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

The positive integer k has eactly two positive prime factors, 3 and 7. If k has a total of 6 positive factors, incuding 1 and k, what is the vlaue of k?
1) 3^2 is a factor of k
2) 7^2 is not a factor of k

We get k=(3^2)7 or (7^2)3 so that the number of factors becomes 6[=(2+1)(1+1)]
There is one variable (k) and 2 equations are given by the 2 conditions, so there is high chance (D) will be the answer.
For condition 1, we get k=(3^2)7 , an unique answer making the condition sufficient.
For condition 2, we get k=(3^2)7, an unique answer making the condition sufficient as well
Therefore the answer becomes (D)

For cases where we need 1 more equation, such as original conditions with "1 variable", or "2 variables and 1 equation", or "3 variables and 2 equations", we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
Top
Post new topic Post Reply
• Page 1 of 1