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GMAT Diagnostic Test Question 2

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GMAT Diagnostic Test Question 2 [#permalink]

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06 Jun 2009, 19:03
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GMAT Diagnostic Test Question 2
Field: Arithmetic, Square Roots
Difficulty: 600

$$\sqrt{36+64+5^2} + \sqrt{20} = ?$$

A. $$19 + \sqrt{20}$$
B. $$19\sqrt{20}$$
C. $$\sqrt{145}$$
D. $$5\sqrt{100}+\sqrt{20}$$
E. $$7\sqrt{5}$$
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Last edited by Bunuel on 07 Oct 2013, 00:02, edited 1 time in total.
Edited the difficulty.

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Re: GMAT Diagnostic Test Question 2 [#permalink]

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24 May 2011, 14:52
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l0rrie wrote:
I feel so stupid among you guys lol.. Was I really the only one that picked A?

Why is that wrong anyways.. I mean if you square root everything under it it just becomes the number itself right.. * Huge sigh *

$$\sqrt{1+2-3+5-5+9} \ne \sqrt{1}+\sqrt{2}-\sqrt{3}+\sqrt{5}-\sqrt{5}+\sqrt{9}$$

If you see multiple addition or subtraction under the root, make sure you simplify that first and take square root of the total.

$$\sqrt{1+2-3+5-5+9} = \sqrt{9} = 3$$

However,
$$\sqrt{mn} = \sqrt{m}*\sqrt{n}$$

For addition and subtraction, one can't split the terms as individual root term. And also the vice versa is not allowed(two split root terms can't be combined under one root)

For multiplication and division, one can split the terms as individual root term. Vice versa is also true.

$$\sqrt{36+64+5^2}+\sqrt{20}=\sqrt{125}+\sqrt{20}=\sqrt{5^2*5}+\sqrt{2^2*5}=5\sqrt{5}+2\sqrt{5}=7\sqrt{5}$$

Ans: "E"
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Re: GMAT Diagnostic Test Question 2 [#permalink]

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25 May 2011, 01:39
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MitDavidDv wrote:
I actually didn't get why you eliminated A, B, D. I think this method would be dangerous. Solving it entirely is better. Shouldn't take you more than 45 seconds if you practice a bit.

What if the question was:
\sqrt{9^2+5^3+10^2+55}+\sqrt{20}

Shalom. I eliminated A, B, and D because they contain the sqrt{20} unsimplified. I am sure that solving it would be better I agree. I am only pointing out that I noticed A, B, and D could possibly be done away with using the process of elimination. The remaining two answers have the sqrt{20} broken down. If the question was \sqrt{9^2+5^3+10^2+55}+\sqrt{20} then I would consider the answer choices with the sqrt{20} simplified.

$$\sqrt{9^2+5^3+10^2+55}+\sqrt{20} = 19+\sqrt{20}$$

I wouldn't advocate to guess in these simplify type of questions. Save the guessing and POE for relatively difficult questions.

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Re: GMAT Diagnostic Test Question 2 [#permalink]

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06 Jun 2009, 19:16
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Explanation:
 Rating:

$$\sqrt{36+64+5^2} + \sqrt{20} =$$

$$\sqrt{125} + \sqrt{20} =$$

$$\sqrt{25*5} + \sqrt{4*5} =$$

$$5\sqrt{5} + 2\sqrt{5} =$$

$$7\sqrt{5}$$
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Re: GMAT Diagnostic Test Question 2 [#permalink]

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26 Nov 2009, 08:15
Made a stupid mistake and really shouldn't have since I factored 20 right away! Figured that 5 under the radical would matter and it did. Will go w/ my gut next time.
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11 Jan 2010, 21:46
gottabwise wrote:
Made a stupid mistake and really shouldn't have since I factored 20 right away! Figured that 5 under the radical would matter and it did. Will go w/ my gut next time.

Just reworked problem. Remembered that I had to add the numbers under the radical before I could simplify anything.
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Re: GMAT Diagnostic Test Question 2 [#permalink]

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23 Jan 2010, 02:42
This one was pretty easy.....

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Re: GMAT Diagnostic Test Question 2 [#permalink]

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02 Feb 2010, 12:01
Good question, but really simple. Good practice anyway..

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Re: GMAT Diagnostic Test Question 2 [#permalink]

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02 Apr 2010, 04:21
Got this right away. This question -700 difficulty level- appears a little easier
than question1- 650 level.

Buddy, thanks a bunch for your efforts.
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Re: GMAT Diagnostic Test Question 2 [#permalink]

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17 Apr 2010, 17:58
Hey,

Not sure I agree this was easier than Q1, but I must question the difficulty level. How is this "700" level derived...?

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Re: GMAT Diagnostic Test Question 2 [#permalink]

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20 May 2010, 11:03
A lot easier than the first one. I would say 500-600 level?

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Re: GMAT Diagnostic Test Question 2 [#permalink]

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26 May 2010, 11:33
Why can't the answer be D? Is it not factored enough?

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Re: GMAT Diagnostic Test Question 2 [#permalink]

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07 Sep 2010, 12:27
The first part of D, 5 times sqrt of 100, is impossible to get if you factored correctly. If you add up all three terms you should get 125. The sq. root of 125 can be broken down into the square root of (5 x 5 x 5).

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Re: GMAT Diagnostic Test Question 2 [#permalink]

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Shalom
[b]Tell me if I am wrong but if I had to make an educated guess on this question I would chose E. If you breakdown the sqrt(20) that leaves 2*sqrt(5). The only possible answer would be E simply because three of the other four possible answers include the sqrt(20) unsimplified.
[/b]

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Re: GMAT Diagnostic Test Question 2 [#permalink]

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24 May 2011, 14:30
I feel so stupid among you guys lol.. Was I really the only one that picked A?

Why is that wrong anyways.. I mean if you square root everything under it it just becomes the number itself right.. * Huge sigh *

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Re: GMAT Diagnostic Test Question 2 [#permalink]

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24 May 2011, 14:53
Aaah I get it.. Aargh my math basics are still horrible after so many weeks of studying.. Thanks, fluke.. you save the day... AGAIN..

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Re: GMAT Diagnostic Test Question 2 [#permalink]

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24 May 2011, 14:58
Shalom
[b]Tell me if I am wrong but if I had to make an educated guess on this question I would chose E. If you breakdown the sqrt(20) that leaves 2*sqrt(5). By using the process of elimination you can get rid of three of the four possible answers. That would leave C and E. Then if I would have had to make a choice between these two I would chose E because it is the most simplified.

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Re: GMAT Diagnostic Test Question 2 [#permalink]

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24 May 2011, 15:09
MitDavidDv wrote:
Shalom
[b]Tell me if I am wrong but if I had to make an educated guess on this question I would chose E. If you breakdown the sqrt(20) that leaves 2*sqrt(5). By using the process of elimination you can get rid of three of the four possible answers. That would leave C and E. Then if I would have had to make a choice between these two I would chose E because it is the most simplified.

I actually didn't get why you eliminated A, B, D. I think this method would be dangerous. Solving it entirely is better. Shouldn't take you more than 45 seconds if you practice a bit.

What if the question was:
$$\sqrt{9^2+5^3+10^2+55}+\sqrt{20}$$
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Re: GMAT Diagnostic Test Question 2 [#permalink]

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24 May 2011, 21:54
I actually didn't get why you eliminated A, B, D. I think this method would be dangerous. Solving it entirely is better. Shouldn't take you more than 45 seconds if you practice a bit.

What if the question was:
\sqrt{9^2+5^3+10^2+55}+\sqrt{20}

Shalom. I eliminated A, B, and D because they contain the sqrt{20} unsimplified. I am sure that solving it would be better I agree. I am only pointing out that I noticed A, B, and D could possibly be done away with using the process of elimination. The remaining two answers have the sqrt{20} broken down. If the question was \sqrt{9^2+5^3+10^2+55}+\sqrt{20} then I would consider the answer choices with the sqrt{20} simplified.

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Re: GMAT Diagnostic Test Question 2 [#permalink]

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25 May 2011, 06:27
Shalom
Yes I will save the guessing for the harder questions.

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Re: GMAT Diagnostic Test Question 2   [#permalink] 25 May 2011, 06:27

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