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For how many positive integers n is it true that the sum of
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03 May 2019, 02:04
03 May 2019, 02:04
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Question Stats:
42% (01:32) correct
57% (01:19) wrong based on 19 sessions
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For how many positive integers n is it true that the sum of \(\frac{13}{n}\), \(\frac{18}{n}\), and \(\frac{29}{n}\) is an integer?
(A) 6
(B) 60
(C) Greatest common factor of 13, 18, and 29
(D) Least common multiple of 13, 18, and 29
(E) 12
(A) 6
(B) 60
(C) Greatest common factor of 13, 18, and 29
(D) Least common multiple of 13, 18, and 29
(E) 12
Re: For how many positive integers n is it true that the sum of
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21 Nov 2019, 14:35
21 Nov 2019, 14:35
2
Think about it this way,
the sum of the provided numbers shall be equal to a certain integer k:
13/n + 18/n + 29/n = k -----> 13 + 18 + 29 = k*n = 60
Hence, the number of integers that respect our condition will be equal to the number of factors of 60:
60 = 2^(2) * 3^(1) * 5^(1), the number of divisors is (2+1)(1+1)(1+1) = 3*2*2 = 12
Answer is E.
the sum of the provided numbers shall be equal to a certain integer k:
13/n + 18/n + 29/n = k -----> 13 + 18 + 29 = k*n = 60
Hence, the number of integers that respect our condition will be equal to the number of factors of 60:
60 = 2^(2) * 3^(1) * 5^(1), the number of divisors is (2+1)(1+1)(1+1) = 3*2*2 = 12
Answer is E.
Re: For how many positive integers n is it true that the sum of
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22 Nov 2019, 02:26
22 Nov 2019, 02:26
I am getting better in mathematics with your help. Thanks.
