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# PS: m = root of 4 + cubeth root of 4 + (Gmat prep)

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PS: m = root of 4 + cubeth root of 4 + (Gmat prep) [#permalink]

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16 Jul 2006, 12:37
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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

Thanks
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16 Jul 2006, 13:42
(E)

4 ^ 1/2 = 2
4 ^ 1/4 = sqrt (2) = 1.41
4 ^ 1/3 = somewhere between 1.41 and 2

add them, we get greater than 4.
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16 Jul 2006, 20:43
4^1/2 = 2

4^1/4 = 1.414

so 3.414 already and 4^1/3 > 4^1/4 3.414 + a value > 1.414 so E
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16 Jul 2006, 23:09
4^1/2 = 2
4^1/4 = 2^1/2 = slightly above 1
4^1/3 = slightly above 1

So the answer should be greater than 4.

Ans E
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17 Jul 2006, 05:32
4^1/2=2
4^1/3=some number slightly more than 1
4^1/4=some number slightly more than 1 but less than 4^1/3

Answer is slighly more than 4

(E)
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17 Jul 2006, 08:36
Thanks Guys. The answer is 'E'.

The way I solved it was

a. Square root of 4 is 2
b. cubeth root and 4th root of 4 should be greater than 1. So we have alteast 4.

However, I was wondering if there is any formula that I can use, because it were not 4 say 9 or 13 or something, then I may not be able to do the cubeth root or fourth root.
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17 Jul 2006, 09:30
e. greater than 4

m = 2 + 1.414 + 4^1/3
m = 3.414 + 1.xxx > 4
17 Jul 2006, 09:30
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# PS: m = root of 4 + cubeth root of 4 + (Gmat prep)

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