MAH-CET 2026 — Reasoning PYQ
MAH-CET | Reasoning | 2026Data sufficiency: Is x > y?

Data sufficiency: Is x > y?
I: x+y=10
II: x−y=2
I alone sufficient
II alone sufficient
(Correct Answer)Both needed
Neither sufficient
II alone sufficient
The objective of a data sufficiency problem is to determine whether the given statements provide enough information to definitively answer the question: "Is x > y?"
Let us analyze each statement individually:
The equation given is x+y=10.
If x=6 and y=4, then x+y=10, and here x > y is True.
If x=4 and y=6, then x+y=10, and here x > y is False.
Since we can get both a "Yes" and a "No" answer, Statement I alone is not sufficient.
The equation given is x−y=2.
We can rewrite this equation by moving y to the right side:
x=y+2
Since adding a positive number (2) to y gives us x, it mathematically guarantees that x will always be greater than y (regardless of whether they are positive, negative, or fractional numbers).
Let's test with examples:
If y=3, then x = 5 \implies 5 > 3 (Yes)
If y=−5, then x = -3 \implies -3 > -5 (Yes)
Since we get a definitive "Yes" in every case, Statement II alone is sufficient.
Therefore, Statement II alone is sufficient to answer the question, while Statement I alone is not.
The correct option is (b) II alone sufficient.
The objective of a data sufficiency problem is to determine whether the given statements provide enough information to definitively answer the question: "Is x > y?"
Let us analyze each statement individually:
The equation given is x+y=10.
If x=6 and y=4, then x+y=10, and here x > y is True.
If x=4 and y=6, then x+y=10, and here x > y is False.
Since we can get both a "Yes" and a "No" answer, Statement I alone is not sufficient.
The equation given is x−y=2.
We can rewrite this equation by moving y to the right side:
x=y+2
Since adding a positive number (2) to y gives us x, it mathematically guarantees that x will always be greater than y (regardless of whether they are positive, negative, or fractional numbers).
Let's test with examples:
If y=3, then x = 5 \implies 5 > 3 (Yes)
If y=−5, then x = -3 \implies -3 > -5 (Yes)
Since we get a definitive "Yes" in every case, Statement II alone is sufficient.
Therefore, Statement II alone is sufficient to answer the question, while Statement I alone is not.
The correct option is (b) II alone sufficient.