Another inequalities question

[Troika]

If m and n are negative, is m/n less than 1 ?

1. mn < 1
2. m - n > n

Answer E

[pemdas]

st(1) implies mn is positive but less than 1, which is possible only if both m and n are greater than -1. Hence -1<m<0 and -1<n<0. This is Not Sufficient to answer this question, as m=-1/4 and n=-1/2 satisfy condition with m/n=1/2<1. Whereas m=-1/2 and n=-1/4 also fit the condition but m/n=2>1.

st(2) implies m > 2n and m/n translates into m/n < 2n/n because n is negative. We obtain m/n < 2 which is Not Sufficient to answer the question, as m/n can be less than 1 or 1.5 or some other value.

Combining st(1&2) we get no new information and both statements can be valid with multiple answers. Not Sufficient

e

If m and n are negative, is m/n less than 1 ?

1. mn < 1
2. m - n > n

Answer E

[Anurag@Gurome]

If m and n are negative, is m/n less than 1 ?

1. mn < 1
2. m - n > n

Answer E

Question: Is m/n < 1? or m > n?

(1) mn < 1
Since m < 0 and n < 0, so 0 < mn < 1. But we cannot say if m > n or m < n; NOT sufficient.

(2) m - n > n
m > 2n
We can pick some numbers.
If m = -3, n = -4, then 2n = -8, and m > 2n. Here m > n.
If m = -3, n = -2, then 2n = -4, and m > 2n. Here m < n.
No definite answer; NOT sufficient.

Combining (1) and (2), if m = -1/4, n = -2, then 2n = -4, m > 2n. Here m > n.
If m = -3/4, n = -1/2, then 2n = -1, m > 2n. Here m < n.
No definite answer; NOT sufficient.

The correct answer is E.

[Troika]

@pemdas and anurag

Thank you for the explanations!