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by lukaswelker » Tue Apr 01, 2014 1:41 am
here is the question;

If M=√4+∛4+∜4, then the value of M is:

Less than 3
equal to 3
between 3 and 4
equal to 4
greater than 4

Is there an easy way to simplify this equation?

Let me know
Many thanks
Lukas
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by GMATGuruNY » Tue Apr 01, 2014 2:06 am
If M=√4+∛4+∜4, then the value of M is:

Less than 3
equal to 3
between 3 and 4
equal to 4
greater than 4


Since the problem above asks only for an estimation, we can ballpark:

√4 = 2.
4^(1/3) > 1.
4^(1/4) = √2 ≈ 1.4.

So M > 4.4.

The correct answer is E.
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by Brent@GMATPrepNow » Tue Apr 01, 2014 6:36 am
lukaswelker wrote:here is the question;

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

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

Cheers,
Brent
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by Abhishek009 » Wed Apr 02, 2014 11:22 am
lukaswelker wrote:here is the question;

If M=√4+∛4+∜4, then the value of M is:

Less than 3
equal to 3
between 3 and 4
equal to 4
greater than 4

Is there an easy way to simplify this equation?

Let me know
Many thanks
Lukas
M=√4+∛4+∜4, then the value of M is-

M = 2 + 2√2 + √2

We know that √2 = 1.41

So, 2 + 2√2 + √2 => 2 + 2(1.41) + (1.41)

Or, 2 + 2.82 + 1.41

Or, 6.23

[spoiler]So the answer is greater than 4 ( E )[/spoiler]
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by [email protected] » Wed Apr 02, 2014 1:34 pm
Hi Abhishek009,

While it would not have hurt you on this question, you did make a math mistake in your calculation.

The second term, "the cube root of 4" does NOT = 2.82; it's about 1.6

As it stands, the GMAT would NEVER ask you to do that calculation, so as long as you realize that the "cube root of 4" is greater than 1, that's all that matters.

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