a small doubt

[nayasnayas]

There is an apparent simple DS question:

Is n < 0 ?

a) m < n
b) -n < m


My answer says, it would be C, although some expert says it will be E.

Could anyone please advice !

Thanks in advance.

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Hi nayasnayas,

This DS question asks is N < 0? This is a YES/NO question. We are told nothing about N to start.

Fact 1: M < N

This is perfect for TESTing VALUES.

If M = 1, N = 2 then the answer to the question is NO.
If M = -2, N = -1 then the answer to the question is YES.
Fact 1 is INSUFFICIENT

Fact 2: -N < M

This is also perfect for TESTing Values.

If N = 0, M = 1 then the answer to the question is NO.
If N = -1, M = 2 then the answer to the question is YES.
Fact 2 is INSUFFICIENT

Combined, we know:
M < N
-N < M

The second inequality can be "multiplied by -1" and becomes....

N > -M

So we know....
M < N
-M < N

With these two in equations, there are only 2 options...
1) M = 0 and N = positive
2) M = pos or neg and N = positive that is greater than both possibilities.

In both situations, the answer to the question is the SAME: the answer is ALWAYS NO.
Combined, SUFFICIENT

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

[ProGMAT]

Statement a) n can be +ve and -ve.
Statement b) n can be +ve and -ve.

Combining both: n can only have +ve values.

Ans : C. What is OA:?

[Brent@GMATPrepNow]

Is n < 0 ?

a) m < n
b) -n < m

Here's another approach:

Target question: Is n < 0 ?

Statement 1: m < n
There are several values of m and n that satisfy this condition. Here are two:
Case a: m = -2 and n = -1, in which case n < 0
Case b: m = 0 and n = 1, in which case n > 0
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: -n < m
There are several values of m and n that satisfy this condition. Here are two:
Case a: m = 2 and n = -1, in which case n < 0
Case b: m = 2 and n = 1, in which case n > 0
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that m < n
Statement 2 tells us that -n < m
IMPORTANT: Since the inequality signs are FACING IN THE SAME DIRECTION, we can add the inequalities to get...
m + (-n) < n + m
Now subtract m from both sides to get: -n < n
Add n to both sides to get: 0 < 2n
Divide both sides by 2 to get: 0 < n
In other words, n is definitely not less than 0
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent