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

Redeem

exponents

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Junior | Next Rank: 30 Posts
Posts: 24
Joined: Sat Nov 05, 2011 10:01 am
Thanked: 1 times
Followed by:1 members

exponents

by arpitad » Tue Dec 20, 2011 2:40 pm
If x is the product of the positive integers from 1 to 8, inclusive, and if i, k, m, and p are
positive integers such that x = 2^i 3^k 5^m 7^p, then i + k + m + p =

A.4
B.7
C.8
D.11
E.12
Top
Source: — Problem Solving |
User avatar
Community Manager
Posts: 1060
Joined: Fri May 13, 2011 6:46 am
Location: Utrecht, The Netherlands
Thanked: 318 times
Followed by:52 members

by neelgandham » Tue Dec 20, 2011 3:09 pm
n = 1*2*3*4*5*6*7*8
n = 2^7 * 3^2 * 5^1 * 7^1 = 2^i * 3^k * 5^m * 7^p
Equating the exponents
i+k+m+p = 7+ 2+ 1+ 1= 11
D it is !

Already solved here:https://www.beatthegmat.com/if-x-is-the- ... 13395.html
Anil Gandham
Welcome to BEATtheGMAT | Photography | Getting Started | BTG Community rules | MBA Watch
Check out GMAT Prep Now's online course at https://www.gmatprepnow.com/
Top

GMAT/MBA Expert

User avatar
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

by Anurag@Gurome » Tue Dec 20, 2011 7:45 pm
arpitad wrote:If x is the product of the positive integers from 1 to 8, inclusive, and if i, k, m, and p are positive integers such that x = 2^i 3^k 5^m 7^p, then i + k + m + p =

A.4
B.7
C.8
D.11
E.12
x = 2^i 3^k 5^m 7^p
x = 8! = 1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 = 2^7 * 3^2 * 5^1 * 7^1
So, 2^7 * 3^2 * 5^1 * 7^1 = 2^i * 3^k * 5^m * 7^p
Equating the exponents on both sides,
i = 7, k = 2, m = 1, and p = 1
Therefore, i + k + m + p = 7 + 2 + 1 + 1 = 11

The correct answer is D.
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/
Top
Master | Next Rank: 500 Posts
Posts: 382
Joined: Thu Mar 31, 2011 5:47 pm
Thanked: 15 times

by ArunangsuSahu » Fri Dec 30, 2011 8:27 am
11. Convert to the terms as said in the question
Top
Post new topic Post Reply
• Page 1 of 1