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What is the value of (7x + 2y + 5z)/(8a + b + 3c) ?

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What is the value of (7x + 2y + 5z)/(8a + b + 3c) ?  [#permalink]

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New post 05 Mar 2019, 16:32
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Difficulty:

  65% (hard)

Question Stats:

47% (02:03) correct 53% (01:36) wrong based on 34 sessions

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What is the value of \(\frac{7x + 2y + 5z}{8a + b + 3c}\)?


(1) x = 10a, y = 3b, z = 7c.

(2) x: y: z = 10: 3: 7.
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Re: What is the value of (7x + 2y + 5z)/(8a + b + 3c) ?  [#permalink]

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New post 05 Mar 2019, 18:21
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selim wrote:
What is the value of \(\frac{7x + 2y + 5z}{8a + b + 3c}\)?

1) x = 10a, y = 3b, z = 7c.

2) x: y: z = 10: 3: 7.



Prompt has a fraction with 6 variables! Chances are won't be able to solve for x, y, z, a, b, & c. Goal is to get all variables in terms of as few variables as possible and hope things cancel out(ie 3x/5x = 3/5)

Statement 1:
- Plugging in gives (70a + 6b + 35c)/(8a + b + 3c).
- Still left with 3 variables. ----> INSUFFICIENT

Statement 2:
- x, y, and z are all in ration of 10:3:7
- If other words, the actual values of x, y, and z can be represented as 10d:3d:7d where d is some multiplier
- plugging in ----> (70d + 6d + 35d)/(8a + b + 3c) ------> (111d/8a + b + 3c)
- still have too many variables ----> INSUFFICIENT

Statements together:
- Now can get EVERYTHING in terms of d. Once you realize this no need to even solve because you know that d will cancel out giving a single value
- x = 10a = 10d -----> a = d
- y = 3b = 3d -------> b = d
- z = 7c = 7d --------> c = d
- Simplified -------> (111d/12d) = 111/12

Answer: C
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Re: What is the value of (7x + 2y + 5z)/(8a + b + 3c) ?   [#permalink] 05 Mar 2019, 18:21
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