If \((A+B)=(C+D)\) and \((A+D)\gt(B+C)\), then which of the following is definitely wrong?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(B\gt D\)
Note: The given answer is as per the official NTA Answer Key. However, the question has two possible answers, i.e. both Option (2) and Option (4), as explained below.
An equation and an inequality can be subtracted side by side: taking equal amounts from both sides of an inequality keeps it true. Subtracting the given equation from the inequality leaves only B and D.
\(A+B=C+D\) (1)
\(A+D\gt B+C\) (2)
Subtracting (1) from (2), A and C cancel: \(D-B\gt B-D\)
\(2D\gt2B\), so \(D\gt B\)
D is always greater than B, so the statement \(B\gt D\) is definitely wrong.
Adding (1) and (2) instead, B and D cancel:
\(2A+B+D\gt B+D+2C\), so \(2A\gt2C\)
\(A\gt C\) always, so the statement \(C\gt A\) is also definitely wrong
The other two statements, \(A\gt B\) and \(C\gt D\), can be true or false, depending on the values.
Tip for students: When a question has two possible answers, mark the one you worked out yourself. If NTA’s answer key gives a different answer, challenge it when NTA opens the window for challenges.