UPSC Prelims 2023 · CSAT

Question 59: Data Interpretation

Consider a 3-digit number. Question : What is the number ?

Statement-1The sum of the digits of the number is equal to the product of the digits.
Statement-2The number is divisible by the sum of the digits of the number.

Which one of the following is correct in respect of the above Question and the Statements ?

aThe Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone.

bThe Question can be answered by using either Statement alone.

cThe Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.

dThe Question cannot be answered even by using both the Statements together.

AnswerUPSC’s answer is (d).

Statement 1: the digit sum equals the digit product only for the digits 1, 2, 3, giving 123, 132, 213, 231, 312, 321 (a zero digit makes the product zero but the sum positive). Statement 2 allows many numbers. Together, divisibility by 6 holds only for 132 and 312 (123, 213, 231, 321 are not multiples of 6). Two numbers remain, so the number cannot be fixed even using both.

Why each option is right or wrong

(a) Wrong: statement 1 alone leaves six numbers and statement 2 alone leaves many more.
(b) Wrong: neither statement alone fixes the number.
(c) Wrong: together they still leave 132 and 312.
(d) Right: even both statements leave two possible numbers.

Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.

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Source: UPSC, Civil Services (Preliminary) Examination 2023, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.