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Re: If m and n are positive integers, each of the following coul [#permalink]
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goodyear2013 wrote:
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. \(20\sqrt{2m}\)

OE
Attachment:
OE.png


Hi, I want to know if this OE is the best way to solve this question, please.


Take all the numbers inside the root

(A) 6400m which can be written as 800m(8)
(B) 16000m can be written as 800m(20)
(C) 8000m(m) can be written as 800m(10m)
(D) 2000m cannot be written as 800m x integer as 2000 is not divisible by 800
(E) 800m can be written as 800m(1)

Hence the answer is D.
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Re: If m and n are positive integers, each of the following coul [#permalink]
m,n are positive integers

sqrt(800mn)= 20*sqrt(2*m*n)

Equate this to 20*sqrt(5*m) which gives n=5/2 which is incorrect as m,n are positive integers.
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Re: If m and n are positive integers, each of the following coul [#permalink]
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goodyear2013 wrote:
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. \(20\sqrt{2m}\)


\((\sqrt{800mn})^2 = 800mn\)
Test whether the SQUARE of each answer choice can be equal to \(800mn\) such that m and n are positive integers.
The correct answer will yield a NONINTEGER value for m or n.

When the question stem includes the phrase which of the following, the correct answer is often D or E.

E: \(800mn = (20\sqrt{2m})^2\)
\(800mn = 400*2m\)
\(n=1\)
Since n is a positive integer, eliminate E.

D: \(800mn = (20\sqrt{5m})^2\)
\(800mn = 400*5m\)
\(n=\frac{5}{2}\)

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Re: If m and n are positive integers, each of the following coul [#permalink]
\(\sqrt{ 800 mn } \)can be simplified to \(20\sqrt{2 m n}\)

Now the easiest way would be to square our options and our simplified question stem on both sides and check for m or n to not be integers.
i.e the equation will not hold true if either n or m is an integer.

So when we do that

In option D

on squaring 20\(\sqrt{5m}\) we get 20 x 20 x 5 x m .....(1)

and on squaring 20\(\sqrt{2 m n }\) we get 20 x 20 x 2 x m x n .....(2)

For the eqn to hold true (1) and (2) must be equal.

20 x 20 x 5 x m = 20 x 20 x 2 x m x n

we get n = 5/2 which is not an integer.

therefore option D is the correct choice

Hope this Helps
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Re: If m and n are positive integers, each of the following coul [#permalink]
\(\sqrt{800mn}\)
10*2√2mn
20√2mn
A. \(80\sqrt{m}\)
possible when n=8

B .\(40\sqrt{10m}\)
possible when n=20

C. \(40m\sqrt{5}\)
possible when m = square value and n=10

E. \(20\sqrt{2m}\)
possible when n=1

D \(20\sqrt{5m}\)
not possible as n cannot be a fraction i.e. 5/2 as m & n are integers ; option D is correct

goodyear2013 wrote:
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. \(20\sqrt{2m}\)

OE
Attachment:
OE.png


Hi, I want to know if this OE is the best way to solve this question, please.
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Re: If m and n are positive integers, each of the following coul [#permalink]
goodyear2013 wrote:
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. \(20\sqrt{2m}\)

OE
Attachment:
OE.png


Hi, I want to know if this OE is the best way to solve this question, please.


The best way is to take the outer number inside the root and see if it is of form 800mn.

D. 20_/5m = /400*5m = We don't see a 800 factor here. Hence, wrong.
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Re: If m and n are positive integers, each of the following coul [#permalink]
Asked: If m and n are positive integers, each of the following could be equivalent to \(\sqrt{800mn}\) EXCEPT


A. \(80\sqrt{m}\): n = 8; Possible
B. \(40\sqrt{10m}\): n=20: Possible
C. \(40m\sqrt{5}\): \(n=10\sqrt{m}\): Possible when m is a square of a positive integer
D. \(20\sqrt{5m}\): \(n=2\sqrt{5}\): Not possible since n is a positive integer
E. \(20\sqrt{2m}\) : n=1: Possible

IMO D
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Re: If m and n are positive integers, each of the following coul [#permalink]
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