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rxs0005
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Bunuel
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From (2) \(a\) and \(b\) are not necessarily prime numbers they are co-prime numbers (numbers which don't share ANY common factor but 1), so each can be non-prime as well for example: \(a=8\) and \(b=9\).

Stupid me. Overlooked the word "common". Thanks Bunuel.
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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and equations ensures a solution.


For integers a, b, c, a/(b - c)=1 what is the value of (b-c)/b ?

(1) a/b=3/5
(2) a and b have no common factors greater than 1

Transforming the original condition and the question we have a=b-c, and the question is (b-c)/b=(b/b)-(c/b)=1-(c/b)=?. We need to know the relation between c and b, and in order to do that from a=b-c we need to know relation between a and b or a and c. In case of 1), 5a=3b thus we know the relation between a and b. Therefore A is the answer.
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A is correct. Here's why:

(1) a/b = 3/5
=b = (5/3)a

plug this into c = b -a (eq from the beginning manipulated) --> c = (2/3)a

1 - (c/b) = 1 - [(2/3)a]/[(5/3)a] = (5/5) - (2/5) = 3/5

SUFFICIENT

(2) NOT SUFFICIENT - We can't gather any values from this statement
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Basically Question is asking us , what is the value of a/b=?

Condition 1: This condition is providing a/b. so, it is sufficient

Condition 2: This condition is telling us that a and b are co-prime. Hence, it can take multiple value and not sufficient to answer the question
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