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If M= √4 + ¼4 + ³√ 4

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by baalok88 » Sun Oct 09, 2016 8:05 am
Please tell me the trick to find the answer in the quickest of the ways... I am missing some logic somewhere and depending on the calculations of 'sqrt of 2 = 1.414'
Options for above question-
1. less than 3
2. equal to 3
3. between 3 and 4
4. equal to 4
5. greater than 4
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by Brent@GMATPrepNow » Sun Oct 09, 2016 9:08 am
If M = √4 + ∛4 + ∜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
√4
√4 = 2

∛4
∛1 = 1
∛8 = 2
So, ∛4 is BETWEEN 1 and 2.
In other words, ∛4 = 1.something

∜4
∜1 = 1
∜16 = 2
So, ∜4 is BETWEEN 1 and 2.
In other words, ∜4 = 1.something

So, √4 + ∛4 + ∜4 = 2 + 1.something + 1.something
= more than 4
= E

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Brent
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by [email protected] » Sun Oct 09, 2016 12:17 pm
Hi baalok88,

Brent's already explained the math behind this question, so I won't rehash any of that here. Instead, I want to point out a pattern that sometimes appears in the answer choices of GMAT questions that you can take advantage of. Notice that the 5 answer choices to this question are 'ranges'; GMAT questions almost never require heavy calculations to be solved, so when the answers are written in the way that these answers are written then chances are really good that you can use logic/estimation/comparisons/etc. to get to the correct answer (without having to actually calculate something crazy, such as the cube-root of 4).

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