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If a and b are positive itegers, what is the value of a + b? [#permalink]
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02 Jul 2012, 02:47
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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.
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Re: If a and b are positive itegers, what is the value of a + b? [#permalink]
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02 Jul 2012, 03:01
Stiv wrote: 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. 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 coprime. (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,



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Re: If a and b are positive itegers, what is the value of a + b? [#permalink]
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02 Jul 2012, 05:13
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 coprime 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.
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Re: If a and b are positive itegers, what is the value of a + b? [#permalink]
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14 Jan 2015, 21:49
HI All, This DS question involves a handful of simple math "rules" and can be solved by TESTing VALUES. We're told that A and B are positive integers. We're asked for the value of A+B Fact 1: A/B = 5/8 This gives us the ratio of the two integers, but not the integers themselves. It also means that A is a multiple of 5 and B is the equivalent multiple of 8. IF.... A = 5 B = 8 Then the answer to the question is 13 IF.... A = 10 B = 16 Then the answer to the question is 26 Fact 1 is INSUFFICIENT Fact 2: The greatest common divisor of A and B is 1 IF.... A = 1 B = 2 Then the answer to the question is 3 A = 5 B = 8 Then the answer to the question is 13 Fact 2 is INSUFFICIENT Combined, we know A/B = 5/8; A is a multiple of 5 and B is the equivalent multiple of 8 The greatest common factor of A and B is 1 IF.... A = 5 B = 8 Then the answer to the question is 13 Since A and B are multiples of 5 and 8, respectively, we can stop working. If we take ANY multiple of the two (then those resulting numbers will have a GCF that is GREATER than 1 For Example.... A = 10 B = 16 These numbers have a CGF of 2. This does not match the "restriction" from Fact 2, so it's NOT a useable TEST. None of the possibilities beyond 5 and 8 will "fit" these restrictions, so the answer to the question MUST be 5+8 = 13 Combined, SUFFICIENT. Final Answer: GMAT assassins aren't born, they're made, Rich
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Re: If a and b are positive itegers, what is the value of a + b? [#permalink]
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09 Jun 2015, 02:56
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So was the answer C or E? My reasoning for C is:
Rearranging the first statement gives us A = 5B/8.
Given both A and B are integers, and that 5 is not divisible by 8, then B must be a multiple of 8.
Also, since B=0 would not be a positive integer value, then B must equal 8 (and so A=5), or 16 (which is 8*2, meaning A = 5*2 = 10), or 24 (which is 8*3, A= 5*3 = 15), or 32 (a = 5*4 = 20) etc.
Note that in every case A and B have the multiple of 8 in common (e.g. if B = 16, which is 8*2, then A = 5*[8*2]/8, which means both A and B will have 2 as a factor). Since statement 2 tells us that they only have 1 as a common factor, B must equal 8 and A must equal 5 (5*[8*1]/8). Answer = C.
I'd appreciate further comments and explanation on this question.
Last edited by ElCorazon on 09 Jun 2015, 03:14, edited 1 time in total.



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Re: If a and b are positive itegers, what is the value of a + b? [#permalink]
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09 Jun 2015, 03:13
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ElCorazon wrote: So was the answer C or E? I'd appreciate further explanation if it's C! Hello ElCorazon1) From this statement we can infer that 8a = 5b so more than two variants are possible: a =5 and b = 8 or a = 50 and b = 80 and so on Insufficient 2) GCF (a, b) = 1 Insufficient because we know only that a and b is primes or both or one of them equal to 1 1+2) a and b can only be 5 and 8 because all other variant will share some common factor other than 1 for example GCF(50, 80) = 10 Sufficient Answer is C
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Re: If a and b are positive itegers, what is the value of a + b? [#permalink]
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09 Jun 2015, 03:16
Thank you  I edited my post before I saw your update  glad to see I was on the right track! Harley1980 wrote: ElCorazon wrote: So was the answer C or E? I'd appreciate further explanation if it's C! Hello ElCorazon1) From this statement we can infer that 8a = 5b so more than two variants are possible: a =5 and b = 8 or a = 50 and b = 80 and so on Insufficient 2) GCF (a, b) = 1 Insufficient because we know only that a and b is primes or both or one of them equal to 1 1+2) a and b can only be 5 and 8 because all other variant will share some common factor other than 1 for example GCF(50, 80) = 10 Sufficient Answer is C



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Re: If a and b are positive itegers, what is the value of a + b? [#permalink]
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