m/n = 1/2 , what is the value of m + n ?

Question

(1) mn = 2
(2) n > 0

Bunuel · Answer

If m/n = 1/2, what is the value of m + n ?

Given:  \frac{m}{n}=\frac{1}{2}  -->  n=2m . 
Question:  m + n = m + 2m = 3m = ?

(1)  mn = 2 :

Substitute  n = 2m  into the above: 
  m*(2m) = 2 ;
 2m^2 = 2 ; 
 m^2 = 1 ;
 m = -1  or  m=1 .

If  m = -1 , then  3m = -3 ; 
If  m = 1 , then  3m = 3 .

Not sufficient.

(2) n > 0. Not sufficient.

(1)+(2) Since from (2)  n>0 , then  m>0  (as n=3m), thus  3m=3 . Sufficient.

Answer: C.

Vinayprajapati · Answer

m / n = 1 / 2 , what is the value of m + n
m/n=1/2 => n=2m

(1) mn = 2
n=2m => m^2=1 => m=+1 or -1. No single value. INSUFFICIENT
(2) n > 0 
Nothing about m. Insufficient.

Combining 1 and 2
m= +1, n=2
Sufficient
Hence C.

ishan92 · Answer

As per the question, m / n = 1 / 2. 
Let the common factor be x. m=x, n=2x.

(1) mn=2
x*2x=2 (As m=x & n=2x)
2x^2=2
x^2=1
So x=1, -1. Value of m+n=-1-2=-3 OR 1+3=3.
NOT SUFFICIENT

(2) n>0
obviously NOT SUFFICIENT

(1)+(2)
As n>0, n cannot be equal to -2, so it has to be equal to 2.
So m+n=3.

Thanks,
Ishan

aarushi1710 · Answer

What we know from the question

\frac{m}{n}  =  \frac{1}{2}

2m = n ---- Equation 1

Statement 1

mn = 2

n =  \frac{2}{m}  ---- Equation 2

Substituting eq 2 in 1, we get, 
 2m =  \frac{2}{m}

m^2  = 1

m = +/1

Statement 1 alone is insufficient

Statement 2

n > 0

This statement alone is insufficient to answer what m + n is

Using statement 1 and 2 together

From statement 1 we know that m = +/1 and from equation 1 we know that 2m = n
From statement 2, we know that n has to be greater than 0, ie n cannot be negative. For n to be positive, m has to be positive to satisfy equation 1 (i.e. 2m=n)
Thus, m has to be 1

2m = n
m = 1 and n = 2

Sufficient to answer m + n

Answer choice (C)

MBAHOUSE · Answer

System of equations. Be careful with incomplete quadratic equations that produces two value as answers.

m/n = 1/2 , what is the value of m + n ?

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