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lukaswelker: Senior | Next Rank: 100 Posts; Posts: 65; Joined: Wed Mar 26, 2014 6:56 amFollowed by: 1 member

by lukaswelker » Tue Apr 01, 2014 1:41 am

here is the question;

If M=âˆš4+âˆ›4+âˆœ4, 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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Source: Beat The GMAT — Problem Solving | Tue Apr 01, 2014 1:41 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue Apr 01, 2014 2:06 am

If M=âˆš4+âˆ›4+âˆœ4, 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:

âˆš4 = 2.
4^(1/3) > 1.
4^(1/4) = âˆš2 â‰ˆ 1.4.

So M > 4.4.

The correct answer is E.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Tue Apr 01, 2014 6:36 am

lukaswelker wrote:here is the question;

If M = âˆš4 + âˆ›4 + âˆœ4, 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

âˆš4
âˆš4 = 2

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

âˆœ4
âˆœ1 = 1
âˆœ16 = 2
So, âˆœ is BETWEEN 1 and 2.
In other words, âˆœ = 1.something

So, âˆš4 + âˆ›4 + âˆœ4 = 2 + 1.something + 1.something
= more than 4
= E

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Abhishek009: Master | Next Rank: 500 Posts; Posts: 359; Joined: Wed Mar 11, 2009 4:37 amFollowed by: 2 members; Location: Kolkata, India; Thanked: 50 times

by Abhishek009 » Wed Apr 02, 2014 11:22 am

lukaswelker wrote:here is the question;

If M=âˆš4+âˆ›4+âˆœ4, 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=âˆš4+âˆ›4+âˆœ4, then the value of M is-

M = 2 + 2âˆš2 + âˆš2

We know that âˆš2 = 1.41

So, 2 + 2âˆš2 + âˆš2 => 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]

Abhishek

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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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