What is the two-digit number whose first digit is a and the second digit is b?…
2024
What is the two-digit number whose first digit is a and the second digit is b? The number is greater than 9.
(I) The number is a multiple of 51.
(II) The sum of the digits a and b is 6.
- A.
I alone sufficient while II alone not sufficient to answer
- B.
II alone sufficient while I alone not sufficient to answer
- C.
Either I or II alone sufficient to answer
- D.
Both I and II are not sufficient to answer
Attempted by 5 students.
Show answer & explanation
Correct answer: A
Concept: In a data-sufficiency question, a statement is sufficient on its own only if the given information fixes the unknown quantity to exactly one possible value. Each statement is tested independently first; only if neither one works alone do you consider combining them.
Application:
Statement I says the number is a multiple of 51. Checking two-digit multiples of 51: 51 × 1 = 51 (two digits, valid); 51 × 2 = 102 (three digits, out of range). So exactly one two-digit multiple of 51 exists, and statement I fixes the number uniquely — it is sufficient on its own.
Statement II says the digit sum a + b = 6. Listing two-digit numbers whose digits add to 6: 15, 24, 33, 42, 51, 60 — six different numbers satisfy this condition. Statement II does not fix a single number, so it is not sufficient on its own.
Cross-check: Since statement I alone already fixes a unique number, there is no need to combine the statements. Re-scanning the two-digit range (10 to 99) confirms no other multiple of 51 exists there, so statement I's sufficiency holds up.
Result: Statement I alone is sufficient to answer the question, while Statement II alone is not.