If mn ≠ 0, is m/n 0 (1) (m|n| - |mn|)/(|m + n|)

Question

If  mn ≠ 0 , is  \frac{m}{n} > 0  ?

(1)  \frac{m|n| - |mn|}{|m + n|} < 0

(2)  |m + n| = |m| + |n|

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ArunSharma12 · Answer

Given: m,n ≠ 0 m/n >0? basically we need to find the sign of m and n. if m & n have the same sign then m/n will be positive. statement 1: \frac{m|n| - |mn|}{|m + n|} < 0 , multiply both sides by |m + n| m|n| - |mn| < 0 |mn| > m|n| m has to be negative but n can be positive or negative. not sufficient statement 2: |m+n|= |m|+|n| m & n have the same sign or at least one of them is 0. we know m,n ≠ 0 thus m & n have same sign. could be (+,+) or (-,-) doesn't matter because the fraction will be positive in both cases. sufficient Ans: B

chetan2u · Answer

Is \frac{m}{n} > 0 ..Means we are looking for whether m and n have SAME sign. (1) \frac{m|n| - |mn|}{|m + n|} < 0 This means both numerator and denominator have DIFFERENT sign. |m+n|>0, so m|n| - |mn|<0........ If m>0, |mn|=m|n|, so m<0, but n could ne anything + or -. (2) |m + n| = |m| + |n| This means both m and n can never be of opposite sign. Also, none of them is 0, so m and n have SAME sign. Suff B

GMATWhizTeam · Answer

Solution Step 1: Analyse Question Stem • mn ≠ 0 • We need to find if \frac{m}{n} > 0 o m/n will be greater than 0 only if both m and n have same sign (i.e. either both are positive or both are negative). Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE Statement 1: \frac{m|n|−|mn| }{|m+n|}< 0 • According to this statement, \frac{m|n|−|mn| }{|m+n|}< 0 o ⟹ m|n| - |mn| < 0 o ⟹m|n| < |mn| o Since, |n| and |mn| are always positive, so the above equation is true only if m < 0, n may be positive or negative.  Therefore, when n is negative, \frac{m}{n }> 0 and  When n is positive, \frac{m}{n }< 0 • We are getting two contradictory results. Hence, statement 1 is NOT sufficient and we can eliminate answer Options A and D. Statement 2: |m+n|=|m|+|n| • The above statement will be true only if both m and n have same sign. • Hence, \frac{m}{n} > 0 Hence, statement 2 is also sufficient. Thus, the correct answer is Option B.

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If mn ≠ 0, is m/n > 0 (1) (m|n| - |mn|)/(|m + n|) < 0 (2) |m + n| = |m

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