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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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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!

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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.
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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
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Gurome, Inc.
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