Is AB < 0? Statement 1: A/B < 0 Statement 2: A + B < 0
2023
Is AB < 0?
Statement 1: A/B < 0
Statement 2: A + B < 0
- A.
Statement 1 alone is sufficient, but Statement 2 alone is not sufficient to answer the question.
- B.
Each statement alone is sufficient to answer the question.
- C.
Statements 1 and 2 together are not sufficient, and additional data is needed to answer the question.
- D.
Statement 2 alone is sufficient, but Statement 1 alone is not sufficient to answer the question.
Attempted by 1 students.
Show answer & explanation
Correct answer: A
Concept: For any nonzero numbers A and B, the ratio A/B and the product A × B always share the same sign, because A/B equals (A × B) divided by B2, and B2 is always positive — dividing by a positive quantity never flips a sign. So a strict inequality on the ratio is just as informative about the sign of the product as an inequality on the product itself.
Statement 1 alone: A/B < 0. Since the ratio and the product always share the same sign, A/B < 0 directly gives A × B < 0 — the question is answered with a firm ‘yes’. So Statement 1 alone is sufficient.
Statement 2 alone: A + B < 0 only restricts how the two numbers add up. Take A = -5, B = -3: the sum is -8 (satisfies A + B < 0), but the product is 15 (positive). Now take A = -10, B = 2: the sum is again -8 (satisfies A + B < 0), but the product is -20 (negative). Two pairs that both satisfy Statement 2 give opposite answers to the question, so Statement 2 alone is not sufficient.
Cross-check: Checking Statement 1 a second way, without the ratio-product identity: A/B < 0 means the numerator and denominator have opposite signs — one positive and one negative. A product of two oppositely-signed numbers is always negative, so A × B < 0 either way. This confirms Statement 1 is sufficient on its own.
Result: Statement 1 alone answers the question; Statement 2 alone does not.