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Updated on: 26 Jan 2024, 00:52
Originally posted by goodyear2013 on 12 Jan 2014, 14:13.
Last edited by Bunuel on 26 Jan 2024, 00:52, edited 2 times in total.
Last edited by Bunuel on 26 Jan 2024, 00:52, edited 2 times in total.
Renamed the topic and edited the question.
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
61% (02:18) correct
39%
(02:03)
wrong
based on 901
sessions
History
Date
Time
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Not Attempted Yet
If m and n are positive integers, each of the following could be equivalent to \(\sqrt{800mn}\) EXCEPT
A. \(80\sqrt{m}\)
B. \(40\sqrt{10m}\)
C. \(40m\sqrt{5}\)
D. \(20\sqrt{5m}\)
E. \(20\sqrt{2m}\)
A. \(80\sqrt{m}\)
B. \(40\sqrt{10m}\)
C. \(40m\sqrt{5}\)
D. \(20\sqrt{5m}\)
E. \(20\sqrt{2m}\)
Attachment:
File comment: OE
OE.png [ 46.34 KiB | Viewed 15407 times ]
Hi, I want to know if this OE is the best way to solve this question, please.OE.png [ 46.34 KiB | Viewed 15407 times ]
02 Jun 2014, 00:11
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Consider the options one by one:
A:
\(80\sqrt{m} = \sqrt{6400m}\)
\(\sqrt{6400m} = \sqrt{800mn}\)
If n = 8, then the condition satisfies
B:
\(40\sqrt{10m} = \sqrt{16000m}\)
\(\sqrt{16000m} = \sqrt{800mn}\)
If n = 20, then the condition satisfies
C:
\(40m\sqrt{5} = \sqrt{1600 m^2 * 5} = \sqrt{8000 m^2}\)
\(\sqrt{8000 m^2} = \sqrt{800mn}\)
If m = 1 & n = 10, then the condition satisfies
D:
\(20\sqrt{5m} = \sqrt{2000m}\)
\(\sqrt{2000m} = \sqrt{800mn}\)
2000m = 800mn
2000 = 800n
We will require to make n a fraction to satisfy the condition; m & n are +ve integers, so the condition fails
E:
\(20\sqrt{2m} = \sqrt{800m}\)
\(\sqrt{800m} = \sqrt{800mn}\)
If n = 1, then the condition satisfies
Answer = D
A:
\(80\sqrt{m} = \sqrt{6400m}\)
\(\sqrt{6400m} = \sqrt{800mn}\)
If n = 8, then the condition satisfies
B:
\(40\sqrt{10m} = \sqrt{16000m}\)
\(\sqrt{16000m} = \sqrt{800mn}\)
If n = 20, then the condition satisfies
C:
\(40m\sqrt{5} = \sqrt{1600 m^2 * 5} = \sqrt{8000 m^2}\)
\(\sqrt{8000 m^2} = \sqrt{800mn}\)
If m = 1 & n = 10, then the condition satisfies
D:
\(20\sqrt{5m} = \sqrt{2000m}\)
\(\sqrt{2000m} = \sqrt{800mn}\)
2000m = 800mn
2000 = 800n
We will require to make n a fraction to satisfy the condition; m & n are +ve integers, so the condition fails
E:
\(20\sqrt{2m} = \sqrt{800m}\)
\(\sqrt{800m} = \sqrt{800mn}\)
If n = 1, then the condition satisfies
Answer = D
General Discussion
m3equals333
GMAT 3: 710 Q48 V40
Posts: 142
12 Jan 2014, 17:02
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I think OE solution is quickest method given the constraint that m and n need to be positive integers. Basically, whatever number is outside the square root in the answer choices is a perfect square and needs to be squared and multiplied by whatever is inside the square root....for n to be a positive integer, this number has to be divisible by 800.
Sqrt800mn = Sqrt20^2*2*m*n
solving for n
C
40m*Sqrt5 = Sqrt40^2*m^2*5 = Sqrt20^2*2^2*m^2*5
Sqrt20^2*5*2^2*m^2 = Sqrt20^2*2*m*n
n=5m (m=1, n=5...ok)
D
20sqrt5m = Sqrt5m*20^2
5m = 2*m*n
5=2n (n=(5/2)....not pos int)
Sqrt800mn = Sqrt20^2*2*m*n
solving for n
C
40m*Sqrt5 = Sqrt40^2*m^2*5 = Sqrt20^2*2^2*m^2*5
Sqrt20^2*5*2^2*m^2 = Sqrt20^2*2*m*n
n=5m (m=1, n=5...ok)
D
20sqrt5m = Sqrt5m*20^2
5m = 2*m*n
5=2n (n=(5/2)....not pos int)
