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Bunuel
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Bunuel Can you please validate the both Statement? the statements seem to be inconsistent!!! Agree with IanStewart
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Bunuel
If m/n = 7/4, what is the value of m + n ?

(1) n < 0
(2) 3m + 7n = 7

If m/n is positive, then m and n are both positive or both negative. If, as Statement 1 tells us, n is negative, then m must also be negative. But in that case, 3m + 7n would be negative, so could not equal 7, so Statement 2 could not be true. So unless I'm missing something (a bit early in the morning for me! :) ) the statements seem to be inconsistent. I wonder if perhaps a negative sign is missing somewhere?

Copy/paste error. Edited. Thank you.
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Bunuel
If m/n = 7/4, what is the value of m + n ?

(1) n < 0
(2) 3m + 7n = -7

the ratio of \(m:n = 7:4\). so let \(m = 7x\) & \(n = 4x\). we need to find \(m+n = 7x+4x = 11x\). we need the value of \(x\)

Statement 1: provides \(n\) is negative so \(m\) also has to be negative for the ratio to be positive. but we don't have any information to calculate the value of \(m\) or \(n\). Hence insufficient

Statement 2: substituting the value of \(m\) & \(n\) in the equation
\(3*7x +7*4x = -7\) or \(49x = -7\) or \(x = \frac{-1}{7}\) . hence sufficient

Option B
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