Target question: Is n < 1?buoyant wrote:If mn < np < 0, is n < 1?
1) n is an integer.
2) m < p.
Given: mn < np < 0
Statement 1: n is an integer.
There are several values of m, n and p that satisfy this condition. Here are two:
Case a: m = 3, n = -1 and p = 2, in which case n IS less than 1
Case b: m = -2, n = 3 and p = -1, in which case n is NOT less than 1
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: m < p
IMPORTANT: Notice that if we take this inequality, m < p, and multiply both sides, we get the given inequality, mn < np . Notice that the direction of the inequality STAYS THE SAME. This tells us that n is POSITIVE
Aside: This is an often-tested concept on the GMAT. If we multiply both sides of an inequality by a POSITIVE number, the direction of the inequality STAYS THE SAME. If we multiply both sides of an inequality by a NEGATIVE number, the direction of the inequality IS REVERSED.
So, statement 2 tells us that n is a POSITIVE number. Is this enough information to determine whether n < 1? No.
Consider these two conflicting cases:
Case a: m = -4, n = 1/2 and p = -2, in which case n IS less than 1
Case b: m = -2, n = 3 and p = -1, in which case n is NOT less than 1
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 2 tells us that n is POSITIVE
Statement 1 tells us that n is an INTEGER
So, n = 1 or 2 or 3 or 4 or...
This means that n is definitely NOT less than 1
Since we can answer the target question with certainty, the combined statements are SUFFICIENT
Answer = C
Cheers,
Brent
