Given below is a question followed by two statements. Decide whether the…
2025
Given below is a question followed by two statements. Decide whether the question can be answered using the given statements.
Question: Is (a - b) greater than (a + b)?
Statement I: a and b are negative fractions.
Statement II: a and b are positive fractions.
- A.
Both statements together are necessary; neither statement alone is sufficient.
- B.
Statement II alone is sufficient, but statement I alone is not sufficient.
- C.
Statement I alone is sufficient, but statement II alone is not sufficient.
- D.
Either statement I alone or statement II alone is sufficient.
Attempted by 1014 students.
Show answer & explanation
Correct answer: D
Key point: This is a data-sufficiency question. A statement is sufficient if it gives a definite Yes or No answer; it does not have to make the inequality true.
Simplify the inequality:
(a - b) > (a + b)
-b > b, so 0 > 2b, hence b < 0.
Statement I: a and b are negative fractions, so b < 0. The answer is Yes. Statement I alone is sufficient.
Statement II: a and b are positive fractions, so b > 0. The answer is No. For example, a = 1/2 and b = 1/3 makes the inequality false, but that is still a definite answer. Statement II alone is sufficient.
Correct answer: Either statement I alone or statement II alone is sufficient.