Attached is a question from GMAT Prep Test 2.
Please advise how to achieve the result.
Answer: C
Thanks,
K
GMAT Test 2_PS Primes #25
This topic has expert replies
- Attachments
-
- GMAT Test 2_PS Primes #25.docx
- (56.28 KiB) Downloaded 76 times
GMAT/MBA Expert
- Anurag@Gurome
- GMAT Instructor
- Posts: 3835
- Joined: Fri Apr 02, 2010 10:00 pm
- Location: Milpitas, CA
- Thanked: 1854 times
- Followed by:523 members
- GMAT Score:770
Length of an integer is the sum of the powers of its prime factors.kwah wrote:Attached is a question from GMAT Prep Test 2.
Please advise how to achieve the result.
Answer: C
Thanks,
K
Length of 6 implies that the sum of the powers of primes of two-digit integer must be 6.
Now 5 can not be a factor of this integer because the smallest integer with the length of 6 that has 5 as prime factor is 2^5 * 5 = 160, which is not a two-digit integer.
So, the primes of the two-digit integers are 2 and 3, which implies n = 2^a * 3^b, so that a + b = 6
If a = 6, b = 0, then n = 2^6 = 64 (length = 6 + 0 = 6)
If a = 5, b = 1, then n = 2^5 * 3^1 = 32 * 3 = 96 (length = 5 + 1 = 6)
If a = 4, b = 2, then n = 2^4 * 3^2 = 16 * 9 = 144 (length = 5 + 1 = 6) but 144 is not a two-digit integer.
The correct answer is C.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)
Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)
Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
- Bill@VeritasPrep
- GMAT Instructor
- Posts: 1248
- Joined: Thu Mar 29, 2012 2:57 pm
- Location: Everywhere
- Thanked: 503 times
- Followed by:192 members
- GMAT Score:780
We're looking for two-digit numbers that can be expressed as product of 6 primes. This tells us that we're going to be using small primes:
2^6 = 64
2^5 * 3 = 96
2^6 = 64
2^5 * 3 = 96
Join Veritas Prep's 2010 Instructor of the Year, Matt Douglas for GMATT Mondays
Visit the Veritas Prep Blog
Try the FREE Veritas Prep Practice Test
Visit the Veritas Prep Blog
Try the FREE Veritas Prep Practice Test