UPSC Prelims 2021 · CSAT
Question 79: Basic Numeracy
When a certain number is multiplied by 7, the product entirely comprises ones only (1111...). What is the smallest such number ?
AnswerUPSC’s answer is (d).
A number whose product with 7 is 111...1 is a string of ones divided by 7. Check the strings in turn: 11 leaves remainder 4 on division by 7, 111 leaves 6, 1111 leaves 5, 11111 leaves 2, and 111111 ÷ 7 = 15873 exactly. So the smallest number is 15873. Check: 15873 × 7 = 111111. Remember: for 'ones only' multiples, test 11, 111, 1111 and so on for divisibility, or simply multiply each option by 7.
Why each option is right or wrong
- (a) 15713 × 7 = 109,991, which is not all ones.
- (b) 15723 × 7 = 110,061, not all ones.
- (c) 15783 × 7 = 110,481, not all ones.
- (d) Right: 15873 × 7 = 111,111.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2021, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.