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Math Expert V
Joined: 02 Sep 2009
Posts: 57290
Is j/m + k/n = 2 ? (1) jk/(mn) = 1 (2) jn/(mk) = 1  [#permalink]

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Difficulty:   65% (hard)

Question Stats: 49% (02:03) correct 51% (02:04) wrong based on 39 sessions

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Is $$\frac{j}{m} + \frac{k}{n} = 2$$ ?

(1) $$\frac{jk}{mn} = 1$$

(2) $$\frac{jn}{mk} = 1$$

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Manager  S
Joined: 18 Apr 2019
Posts: 66
Re: Is j/m + k/n = 2 ? (1) jk/(mn) = 1 (2) jn/(mk) = 1  [#permalink]

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Bunuel wrote:
Is $$\frac{j}{m} + \frac{k}{n} = 2$$ ?

(1) $$\frac{jk}{mn} = 1$$

(2) $$\frac{jn}{mk} = 1$$

S1:
jk/mn can be split and written as k/n * j/m = 1.
which means k/n = m/j .

Putting it in simpler terms let a=k/n and b=j/m. Then,
ab=1 or a=1/b
Now, a+b can only be equal to 2 if a=b, but do we know this for sure? NO. Therefore, INSUFF

S2:
Similarly, we get a/b=1 or a=b. Again, do we know if a&b equal 1? they can be anything. Therefore, INSUFF

1+2
ab=1 and a=b
The question does not say if j/m and k/n are positive or negative.
Therefore they can be either 1 or -1.
Adding upto 2 or -2
Hence, INSUFF.
IMO E
Intern  B
Joined: 09 Jul 2014
Posts: 9
Re: Is j/m + k/n = 2 ? (1) jk/(mn) = 1 (2) jn/(mk) = 1  [#permalink]

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is j/m + k/n = 2?

Let's assume j/m = p ; k/n = q => p + q = 2

Statement 1: jk/mn = 1 => j/m = n/k => p = 1/q

p + 1/p => p^2 +1....in order to be 2; p^2 has to be 1 But it's not given. Hence INSUFFICIENT

Statement 2: jn/mk =1 => j/m = k/n => p = q => p + q = 2p ...in order to be 2, p has to be 1 But it's not given. Hence INSUFFICIENT

Taking both the statements together => p = 1/q & p = q => gives us two values of (p,q) = (1,1) and (-1, -1).
From (-1,-1) => p+q = -2 whereas from (1,1) => p+q = 2.........no clear answer......Hence INSUFFICIENT

so, OA should be E.
Let's say j = 1 then m =1 Re: Is j/m + k/n = 2 ? (1) jk/(mn) = 1 (2) jn/(mk) = 1   [#permalink] 09 Aug 2019, 10:31
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