किसी 3-अंकों की एक संख्या पर विचार कीजिए ।
प्रश्न : वह संख्या क्या है ?
- कथन-1: उस संख्या के अंकों का योगफल अंकों के गुणनफल के बराबर है ।
- कथन-2: वह संख्या, उस संख्या के अंकों के योगफल से विभाज्य है ।
उपर्युक्त प्रश्न और कथनों के बारे में निम्नलिखित में से कौन-सा एक सही है ?
Read this question in English
Consider a 3-digit number.
Question: What is the number?
Statement-1. The sum of the digits of the number is equal to the product of the digits.
Statement-2. The 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?
(a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone. · (b) The Question can be answered by using either Statement alone. · (c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone. · (d) The Question cannot be answered even by using both the Statements together.
उत्तर और व्याख्या · explanation in English
Answer: (d) इस प्रश्न का उत्तर, दोनों कथनों का एक साथ उपयोग करके भी नहीं दिया जा सकता ।
Digits whose sum equals their product can only be 1, 2 and 3, so Statement 1 leaves six numbers. Adding Statement 2, the number must be divisible by 6, but both 132 and 312 qualify, so the number still cannot be fixed.
- Statement 1: for the digits of a 3-digit number, sum = product only for 1, 2, 3 (1 + 2 + 3 = 6 = 1 × 2 × 3).
- So the number is one of 123, 132, 213, 231, 312, 321 — not unique.
- Statement 2 alone: many numbers are divisible by their digit sum (for example 100, 102, 108) — not sufficient.
- Together: the digit sum is 6, so the number must be even and divisible by 3; both 132 and 312 work.
- Two answers remain, so the Question cannot be answered even with both Statements.
Remember · Data sufficiency needs one unique answer; two cases surviving both statements prove insufficiency.
Question and answer: UPSC's official GS Paper II (2023, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·