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

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rxs0005
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m/n = 1/2 , what is the value of m + n ? [#permalink] New post   17 Dec 2010, 11:24
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m/n = 1/2 , what is the value of m + n ?

(1) mn = 2
(2) n > 0
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C
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m/n = 1/2 , what is the value of m + n ? [#permalink] New post   17 Dec 2010, 11:34
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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.
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Re: m/n = 1/2 , what is the value of m + n ? [#permalink] New post   16 Mar 2016, 07:22
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.
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Re: m/n = 1/2 , what is the value of m + n ? [#permalink] New post   18 Jun 2016, 04:50
rxs0005 wrote:
m / n = 1 / 2 , what is the value of m + n


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


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
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Re: If m/n = 1/2, what is the value of m + n ? [#permalink] New post   27 Jun 2022, 06:57
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)
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Re: If m/n = 1/2, what is the value of m + n ? [#permalink] New post   27 Jun 2022, 09:41
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System of equations. Be careful with incomplete quadratic equations that produces two value as answers.
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Re: If m/n = 1/2, what is the value of m + n ? [#permalink]
27 Jun 2022, 09:41
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