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GMATPrep Test 1 - Surds problem

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by anirban_lax » Tue Aug 10, 2010 8:13 am
Hi,

I encountered this surds related problem while writing the Test 1 of GMATPrep. During the test I got the answer by process of elimination but I'm sure there is a better and more accurate way of solving this. Here is the problem:

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: e
Many thanks in advance.


-Anirban
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by Rahul@gurome » Tue Aug 10, 2010 8:34 am
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

M = (4^1/2) + (4^1/3) + (4^1/4)
4^1/2 = √4 = 2
4^1/4 = (2^2)^1/4 = 2^(1/2) = √2 = 1.414
4^1/3 lies between 1 and 2.
So, (4^1/2) + (4^1/3) + (4^1/4) = 2 + value between 1 and 2 + 1.414 = 3.414 + value greater than 1, which means M will be a value greater than 4.

The correct answer is [spoiler](E)[/spoiler].
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by anirban_lax » Tue Aug 10, 2010 8:41 am
Thanks Rahul!

That's an elegant solution!

I was wondering if there is a way to solve this if I do not know the value of 2^1/3, or for that matter if we have a number whose cube root is not well known.
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by Rahul@gurome » Tue Aug 10, 2010 8:49 am
anirban_lax wrote:Thanks Rahul!

That's an elegant solution!

I was wondering if there is a way to solve this if I do not know the value of 2^1/3, or for that matter if we have a number whose cube root is not well known.
We don't need to find the exact value if we don't know the cube root of a number. Just find the approximate value in that case as done in this question.
1^(1/3) = 1 and 8^(1/3) = 2. So, definitely 2^(1/3) will have a value between 1 and 2.

Does that help?
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by anirban_lax » Tue Aug 10, 2010 9:03 am
Ah! I see it now! Awesome!

Can't help but click the Thanks button twice for your 2 replies on this post :) Thanks a lot!
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by Rahul@gurome » Tue Aug 10, 2010 2:50 pm
anirban_lax wrote:Ah! I see it now! Awesome!

Can't help but click the Thanks button twice for your 2 replies on this post :) Thanks a lot!
U r welcome!
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