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

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Intern
Joined: 12 Aug 2010
Posts: 14

Kudos [?]: 47 [0], given: 0

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

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26 Nov 2010, 10:57
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55% (hard)

Question Stats:

60% (01:26) correct 40% (01:33) wrong based on 104 sessions

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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
[Reveal] Spoiler: OA

Kudos [?]: 47 [0], given: 0

Math Expert
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132631 [0], given: 12326

Re: Is it a hard question [#permalink]

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26 Nov 2010, 11:18
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.

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Kudos [?]: 132631 [0], given: 12326

Senior Manager
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Joined: 05 Sep 2016
Posts: 408

Kudos [?]: 25 [0], given: 283

Re: If each of a, b and c is positive, and a = 5b + 7c, what is [#permalink]

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18 Sep 2016, 20:31
B is correct. Here's why:

(1) 2b +5c = 50

NOT SUFFICIENT - we don't have any way to get a/b

(2) c = 3b - 5c --> Simplifies to 6c = 3b --> b = 2c

We know from the beginning of the question that a = 5b+7c --> Plug b = 2c and you arrive at a = 17c

Thus a/b = 17/2

Kudos [?]: 25 [0], given: 283

Re: If each of a, b and c is positive, and a = 5b + 7c, what is   [#permalink] 18 Sep 2016, 20:31
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