gmat prep question

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mathew.tony: Newbie | Next Rank: 10 Posts; Posts: 5; Joined: Wed Jun 16, 2010 7:20 pm

by mathew.tony » Fri Aug 05, 2011 5:04 am

Hi All,

I faced the following question in the GmatPrep software

Q) If M = (4)^1/2 + (4)^1/3 + (4)^1/4, then the value of M is
a) less than 3
b) equal to 3
c) between 3 and 4
d) equal to 4
e) greater than 4(OA)

Is there an easy way to solve this question ?
The official answer is E[/img][/list]

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Source: Beat The GMAT — Problem Solving | Fri Aug 05, 2011 5:04 am

Frankenstein: Legendary Member; Posts: 1448; Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members; Location: India; Thanked: 375 times

by Frankenstein » Fri Aug 05, 2011 5:09 am

Hi,
(4)^1/2 = 2
(4)^1/3 > 1
(4)^1/4 > 1
So, sum will be greater than 2+1+1 = 4

Hence, E

Cheers!

Things are not what they appear to be... nor are they otherwise

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tpr-becky: GMAT Instructor; Posts: 509; Joined: Wed Apr 21, 2010 1:08 pmFollowed by: 85 members; Location: Irvine, CA; Thanked: 199 times; GMAT Score:750

by tpr-becky » Fri Aug 05, 2011 1:49 pm

the fractional exponents tell you to use the denominator of the fracton as a root

The square root of 4 = 2

and 4^1/4 = [(4)^1/2]^1/2 - which is equal to the square root of 2. you should have GMAT values for the square root of 2 and 3 memorized. Sqrt2 = 1.4 for approximation purposes on the GMAT.

Thus the sum of the first term and the second term = 3.14

The third term is harder but you can see that it will be between 2 and 1.4 - thus the sum of all three will be greater than 4.

Becky
Master GMAT Instructor
The Princeton Review
Irvine, CA

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Fri Aug 05, 2011 9:18 pm

mathew.tony wrote:If M = (4)^1/2 + (4)^1/3 + (4)^1/4, then the value of M is
a) less than 3
b) equal to 3
c) between 3 and 4
d) equal to 4
e) greater than 4

The key point to remember while solving this problem is any number greater than 1 raised to any positive power is also greater than 1.

Hence, 4^(1/3) and 4^(1/4) both are greater than 1.

Therefore, M = [(4)^1/2 + (4)^1/3 + (4)^1/4] > (2 + 1 + 1) > 4

The correct answer is E.

Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

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