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If the ratio of integers a, b, and c is 1 : 2 : 3, what is

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If the ratio of integers a, b, and c is 1 : 2 : 3, what is  [#permalink]

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New post Updated on: 05 Sep 2013, 04:03
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If the ratio of integers a, b, and c is 1 : 2 : 3, what is the value of a + b + c?

(1) c – a = 8
(2) b – a = 4

Originally posted by mike8c on 01 Dec 2004, 00:12.
Last edited by Bunuel on 05 Sep 2013, 04:03, edited 3 times in total.
Edited the question, added the OA and moved to DS forum.
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New post 01 Dec 2004, 02:30
I guess it is D

statement 1 : c/a = 3 id est a = 4, c=12, b=8 a+b+c = 24

statement 2 : b/a = 2 id est a = 4, b=8, c=12...
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Re: if the ratio of integers a, b, and c is 1:2:3, what is the  [#permalink]

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New post 05 Sep 2013, 03:33
can someone help me with this problem? I don't understand the necessary passages to find the value of a,b and c
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Re: if the ratio of integers a, b, and c is 1:2:3, what is the  [#permalink]

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New post 05 Sep 2013, 04:08
2
lucasITA wrote:
can someone help me with this problem? I don't understand the necessary passages to find the value of a,b and c


If the ratio of integers a, b, and c is 1 : 2 : 3, what is the value of a + b + c?

Given that a:b:c=1:2:3, find the value of a + b + c.

(1) c – a = 8. From above we have that a/c=1/3 and from the statement that c-a=8. We can solve for a and c, and then get the value of b from a:b:c=1:2:3. Sufficient.

Just to illustrate: a/c=1/3 and c-a=8 --> a=4 and c=12 --> a/b=1/2 --> b=8 --> a+b+c=24.

(2) b – a = 4. The same here. We have two distinct linear equation: a/b=1/2 and b-a=4. We can solve for a and b, and then get the value of c from a:b:c=1:2:3. Sufficient.

Answer: D.

Hope it's clear.
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Re: If the ratio of integers a, b, and c is 1 : 2 : 3, what is  [#permalink]

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New post 25 Jan 2016, 17:17
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 independent equations ensures a solution.

If the ratio of integers a, b, and c is 1 : 2 : 3, what is the value of a + b + c?

(1) c – a = 8
(2) b – a = 4


When you modify the original condition and the question, they become a=k,, b=2k, c=3k. Therefore 4 variables(a,b,c,k) and 3 equations(a=k,, b=2k, c=3k), which should match with the number of equations. So you need 1 more equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.
For 1), k=4 is derived from 3k-k=2k=8, which is unique and sufficient.
For 2), k=4 is derived from 2k-k=4, which is unique and sufficient.
Therefore, the answer is D.


-> For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
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Re: If the ratio of integers a, b, and c is 1 : 2 : 3, what is &nbs [#permalink] 25 Jan 2016, 17:17
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