The question below is followed by two statements numbered I and II. Choose the option that describes whether the statements are sufficient to answer the question.
Four friends A, B, C and D took a test. What is the difference between the marks obtained by A and D?
I. The difference between the marks obtained by A and C is 20, and that between the marks obtained by B and D is 15.
II. The difference between the marks obtained by B and C is 18, and B got the highest marks.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → The question can be answered by using both statements together, but not by using either statement alone.
A difference only says how far apart two scores are, not which is higher; the second fact in II, that B is the highest, fixes the directions. Let the marks be A, B, C and D.
Statement I alone:
A and C are 20 apart, B and D are 15 apart, but the two pairs are not linked: not sufficient
Statement II alone:
C = B − 18, but A and D are not mentioned: not sufficient
Both together:
B is the highest, so D = B − 15 and C = B − 18
A = C + 20 = B + 2 would put A above B, which is not allowed, so A = C − 20 = B − 38
Difference between D and A = (B − 15) − (B − 38) = 23: sufficient