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02 Jul 2012, 03:47
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
74% (01:03) correct
26%
(01:09)
wrong
based on 1068
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If a and b are positive integers, what is the value of a + b?
(1) \(\frac{a}{b} = \frac{5}{8}\)
(2) The greatest common divisor of a and b is 1.
(1) \(\frac{a}{b} = \frac{5}{8}\)
(2) The greatest common divisor of a and b is 1.
02 Jul 2012, 06:13
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If a and b are positive integers, what is the value of a + b?
(1) \(\frac{a}{b} = \frac{5}{8}\) --> \(a\) and \(b\) could be: (5, 8), (10, 16), (15, 24), ... Not sufficient.
(2) The greatest common divisor of a and b is 1. Clearly insufficient: \(a\) and \(b\) could be any co-prime numbers.
(1)+(2) Since from (2) \(a\) and \(b\) do not share any common factor but 1, then from (1) \(a=5\) and \(b=8\) --> \(a+b=13\). Sufficient.
Answer: C.
(1) \(\frac{a}{b} = \frac{5}{8}\) --> \(a\) and \(b\) could be: (5, 8), (10, 16), (15, 24), ... Not sufficient.
(2) The greatest common divisor of a and b is 1. Clearly insufficient: \(a\) and \(b\) could be any co-prime numbers.
(1)+(2) Since from (2) \(a\) and \(b\) do not share any common factor but 1, then from (1) \(a=5\) and \(b=8\) --> \(a+b=13\). Sufficient.
Answer: C.
General Discussion
02 Jul 2012, 04:01
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Stiv
Hi,
Using (1),
a/b=5/8
or a=5k & b=8k
thus, a+b = 5k+8k = 13k
k is any integer, Insufficient.
Using (2),
GCD of a & b is 1, of a & b are co-prime. (a,b) = (7, 15) (5, 8) (45, 77). Insufficient,
Combining (1) & (2),
(a,b) = (5, 8), thus, a+b = 13. Sufficient.
Answer is (C),
Regards,
