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# If each of a, b and c is positive, and a = 5b + 7c, what is

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If each of a, b and c is positive, and a = 5b + 7c, what is [#permalink]  26 Nov 2010, 09:57
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58% (02:05) correct 42% (00:55) wrong based on 33 sessions
If each of a, b and c is positive, and a = 5b + 7c, what is the value of a/b?

1) 2b + 5c = 50
2) 3b - 5c = c
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Re: Is it a hard question [#permalink]  26 Nov 2010, 10:18
Expert's post
chiragatara wrote:
If each of a, b and c is positive, and a = 5b + 7c, what is the value of a/b?

1) 2b + 5c = 50
2) 3b - 5c = c

Given: $$a=5b+7c$$.

Now, as we are asked to get the value of $$\frac{a}{b}$$ then divide both parts of $$a=5b+7c$$ by $$b$$ (to have LHS equal to $$\frac{a}{b}$$): $$\frac{a}{b}=5+7\frac{c}{b}$$. So, basically finding the value of $$\frac{c}{b}$$ will be sufficient.

(1) 2b + 5c = 50 --> we can neither solve for unknowns (2 distinct linear equations, 3 variables) nor get the desired ratio. Not sufficient.
(2) 3b - 5c = c --> $$3b=6c$$ --> $$\frac{c}{b}=\frac{1}{2}$$. Sufficient.

_________________
Re: Is it a hard question   [#permalink] 26 Nov 2010, 10:18
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