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Updated on: 22 Jul 2014, 02:52
Originally posted by WoundedTiger on 22 Jul 2014, 02:03.
Last edited by Bunuel on 22 Jul 2014, 02:52, edited 1 time in total.
Last edited by Bunuel on 22 Jul 2014, 02:52, edited 1 time in total.
Edited the question.
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A repunit is a positive integer that contains only the digit 1. If the integer r is a repunit, is r prime?
(1) The number of digits in r is a multiple of 3.
(2) 0 < r < 1200
(1) The number of digits in r is a multiple of 3.
(2) 0 < r < 1200
22 Jul 2014, 02:55
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A repunit is a positive integer that contains only the digit 1. If the integer r is a repunit, is r prime?
As defined repunit numbers are 1, 11, 111, 1111, ....
(1) The number of digits in r is a multiple of 3. This implies that the sum of the digits is 3*1 (for 111), 6*1 (for 111,111), 9*1 (for 111,111,111), ... So in any case the sum of the digits is a multiple of 3, hence the number is divisible by 3, which means that it cannot be a prime. Sufficient.
(2) 0 < r < 1200. If r = 11, then it's a rpime but if r = 111, then it's not a prime. Not sufficient.
Answer: A.
As defined repunit numbers are 1, 11, 111, 1111, ....
(1) The number of digits in r is a multiple of 3. This implies that the sum of the digits is 3*1 (for 111), 6*1 (for 111,111), 9*1 (for 111,111,111), ... So in any case the sum of the digits is a multiple of 3, hence the number is divisible by 3, which means that it cannot be a prime. Sufficient.
(2) 0 < r < 1200. If r = 11, then it's a rpime but if r = 111, then it's not a prime. Not sufficient.
Answer: A.
General Discussion
22 Jul 2014, 02:59
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Bunuel
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