UPSC Prelims 2021·CSAT·Quantitative Aptitude·Number System

When a certain number is multiplied by 7, the product entirely comprises ones only (1111...). What is the smallest such number?

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Last updated 23 May 2026, 3:31 pm IST
  1. A15713
  2. B15723
  3. C15783
  4. D15873Correct

Explanation

To find the smallest number, we need to find the smallest number consisting entirely of ones (1111...) that is divisible by 7. We can test numbers made of ones by dividing them by 7: 1 / 7 = not an integer 11 / 7 = not an integer 111 / 7 = 15 with a remainder 1111 / 7 = 158 with a remainder 11111 / 7 = 1587 with a remainder 111111 / 7 = 15873 Since 111111 is the first number made entirely of ones that is perfectly divisible by 7, the quotient, 15873, is the smallest such number. Let's verify the options: A) 15713 * 7 = 109991 (not all ones) B) 15723 * 7 = 109061 (not all ones) C) 15783 * 7 = 110481 (not all ones) D) 15873 * 7 = 111111 (all ones) Thus, 15873 is the smallest number that satisfies the condition. The final answer is D.
Quantitative Aptitude: When a certain number is multiplied by 7, the product entirely comprises ones only (1111...). What is the smallest such
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