If m and n are positive integers, each of the following coul

Question

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. \(20\sqrt{2m}\)

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

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Official Answer

D

PareshGmat · Accepted Answer

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

m3equals333 · Answer

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)

PerfectScores · Answer

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.

arpitkansal · Answer

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.

GMATGuruNY · Answer

(\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}

D

siddharthsamant · Answer

\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
Sid

Archit3110 · Answer

\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

happypuppy · Answer

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.

Kinshook · Answer

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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