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Rational Sum (Posted on 2016-02-15)

Find the sum of all possible values of a rational number R of the form N/30, where N is a positive integer with gcd (N, 30) = 1 and, R < 10.

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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Very rational (spoiler)

Comment 1 of 1

1) If N/30 < 10, then N < 300

2) 30 = 2*3*5, so N is not a multiple of 2 or 3 or 5

3) Between 1 and 30, N can only be 1,7,11,13,17,19,23 and 29. Sum = 120.

So sum(R) where R < 1 = 120/30 = 4

4) There are 8 terms, so sum(R) where 1 < R < 2 is 4 + 8 = 12

5) Desired sum = 4 * (1+3+5+...+19) = 4*10*20/2 = 400

Posted by Steve Herman on 2016-02-15 09:49:30

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