2023 · Q71
Item contains a Question followed by two Statements. Answer each item using the following instructions : A number 277XY5 (where X, Y are digits) is divisible by 25.Question : What is the value of X?
Statement IThe given number is divisible by 9.
Statement IIX > 5.
Elementary MathematicsNumber System
- AChoose this option if the Question can be answered by one of the Statements alone but not by the other.
- BChoose this option if the Question can be answered by either Statement alone.
- CChoose this option if the Question can be answered by using both the Statements together, but cannot be answered by using either Statement alone.
- DChoose this option if the Question cannot be answered even by using both Statements together.
Explanation
Divisibility by 25 forces the last two digits Y5 to be 25 or 75, so Y ∈ {2, 7}. Statement I (divisible by 9): the digit sum 21 + X + Y ≡ 0 (mod 9) gives X = 4 (if Y = 2) or X = 8 (if Y = 7) — not unique. Statement II (X > 5) alone leaves many possibilities. Together they pin X = 8. Both statements are needed (C).