Question:
What is the two-digit number?
Statement I: The sum of its digits is 9.
Statement II: The number is divisible by 9 and its tens digit is 4.
What is the two-digit number?
Statement I: The sum of its digits is 9.
Statement II: The number is divisible by 9 and its tens digit is 4.
Show Hint
Write the number as 10a + b and turn the divisibility-by-9 condition into a modular equation for b once the tens digit a is fixed - see if it pins down a unique digit.
Updated On: Jul 8, 2026
- Statement I alone is sufficient, but Statement II alone is not sufficient.
- Statement II alone is sufficient, but Statement I alone is not sufficient.
- Both statements together are sufficient, but neither statement alone is sufficient.
- Each statement alone is sufficient.
Show Solution
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The Correct Option is B
Solution and Explanation
Statement I: many two-digit numbers have digit sum 9 (18, 27, 36, 45, ...), not unique. Statement II: two-digit multiples of 9 are 18, 27, 36, 45, 54, 63, 72, 81, 90, 99; only 45 has tens digit 4, so the number is uniquely 45. Statement II alone is sufficient. Correct option: Statement II alone is sufficient, but Statement I alone is not sufficient.
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