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# In the formula above, a, b, c, and d are positive numbers.

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Board of Directors
Joined: 01 Sep 2010
Posts: 3430
In the formula above, a, b, c, and d are positive numbers. [#permalink]

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Updated on: 12 Sep 2013, 09:37
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Question Stats:

52% (01:56) correct 48% (02:12) wrong based on 248 sessions

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x = 8(a/c) + 16(b/c)

In the formula above, a, b, c, and d are positive numbers. If c = a + b and b > a, which of the following could be the value of x?

(A) 8
(B) 10
(C) 12
(D) 15
(E) 21

_________________

Originally posted by carcass on 12 Sep 2013, 09:32.
Last edited by Bunuel on 12 Sep 2013, 09:37, edited 1 time in total.
Moved to PS forum.
Math Expert
Joined: 02 Sep 2009
Posts: 47037
Re: In the formula above, a, b, c, and d are positive numbers. [#permalink]

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12 Sep 2013, 09:44
3
6
carcass wrote:
x = 8(a/c) + 16(b/c)

In the formula above, a, b, c, and d are positive numbers. If c = a + b and b > a, which of the following could be the value of x?

(A) 8
(B) 10
(C) 12
(D) 15
(E) 21

$$\frac{8a}{c} + \frac{16b}{c}=\frac{8a+16b}{c}=\frac{8a+16b}{a+b}$$.

You can notice that it's a weighted average formula for $$a+b$$ items, where the weight of each of the items of $$a$$ is 8 and the weight of each of the items of $$b$$ is 16. Now, since b > a, then the average must be closer to 16, then to 8. Only D fits.

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##### General Discussion
Math Expert
Joined: 02 Sep 2009
Posts: 47037
Re: In the formula above, a, b, c, and d are positive numbers. [#permalink]

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12 Sep 2013, 09:45
1
Bunuel wrote:
carcass wrote:
x = 8(a/c) + 16(b/c)

In the formula above, a, b, c, and d are positive numbers. If c = a + b and b > a, which of the following could be the value of x?

(A) 8
(B) 10
(C) 12
(D) 15
(E) 21

$$\frac{8a}{c} + \frac{16b}{c}=\frac{8a+16b}{c}=\frac{8a+16b}{a+b}$$.

You can notice that it's a weighted average formula for $$a+b$$ items, where the weight of each of the items of $$a$$ is 8 and the weight of each of the items of $$b$$ is 16. Now, since b > a, then the average must be closer to 16, then to 8. Only D fits.

Similar question to practice from OG:
Quote:
If x, y, and k are positive numbers such that (x/(x+y))(10) + (y/(x+y))(20) = k and if x < y, which of the following could be the value of k?

A. 10
B. 12
C. 15
D. 18
E. 30

Discussed here: if-x-y-and-k-are-positive-numbers-such-that-x-x-y-128231.html
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Joined: 15 Sep 2013
Posts: 38
Concentration: Strategy, Entrepreneurship
GMAT 1: 680 Q47 V36
GMAT 2: 740 Q50 V40
GPA: 3.65
Re: In the formula above, a, b, c, and d are positive numbers. [#permalink]

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08 Sep 2014, 03:50
1
1
carcass wrote:
x = 8(a/c) + 16(b/c)

In the formula above, a, b, c, and d are positive numbers. If c = a + b and b > a, which of the following could be the value of x?

(A) 8
(B) 10
(C) 12
(D) 15
(E) 21

x = 8a/c + 16b/c
x= 8(a+b)/c + 8b/c
now substituting c = a + b in the above equation
x = 8 + 8b/(a+b)
The ratio b/(a+b) is smaller than 1 thus answer choice E is eliminated... and as a < b ... thus the ratio b/(a+b) is larger than 1/2 or 0.5... thus
8*b/(a+b) is larger than 4... thus the only answer choice left is D
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Intern
Joined: 02 Jul 2013
Posts: 13
Concentration: General Management, Finance
GMAT Date: 11-08-2013
WE: Programming (Computer Software)
In the formula above, a, b, c, and d are positive numbers. [#permalink]

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13 Sep 2014, 01:09
Can anyone explain this in detail?
Math Expert
Joined: 02 Sep 2009
Posts: 47037
Re: In the formula above, a, b, c, and d are positive numbers. [#permalink]

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13 Sep 2014, 07:18
vijayann wrote:
Can anyone explain this in detail?

Please specify what part in the solutions above is unclear.
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Senior Manager
Joined: 20 Feb 2015
Posts: 421
Concentration: Strategy, General Management
In the formula above, a, b, c, and d are positive numbers. [#permalink]

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15 Sep 2015, 13:30
x = 8(a/c) + 16(b/c)

just by looking at the options .. we should be able to understand that 8 or its multiple i.e 16 should be divisible by C..why ? Because none of the options are in p/q form.

let us say c =4 which gives us a=1 and b=3

the equation thus becomes x=8(1/4) + 16(3/4) =2+12=14 --close enough
the other value c can take is 8
which gives us possible values for (a,b) as (1,7) (2,6) (3,5)

take 1,7

x=8(1/8)+16(7/8)=15

That's how I managed to do.
Board of Directors
Joined: 17 Jul 2014
Posts: 2726
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
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Re: In the formula above, a, b, c, and d are positive numbers. [#permalink]

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11 Jan 2016, 19:17
oh man..I did the long way..
8a+8b/a+b = 8
now, 8b/a+b =??
we can eliminate A right away..
tried several numbers..then got to:
a=1
b=7
a+b=8
8b=56.
56/8=7.
7+8=15.

D
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Joined: 09 Sep 2013
Posts: 7277
Re: In the formula above, a, b, c, and d are positive numbers. [#permalink]

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19 May 2017, 08:50
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Re: In the formula above, a, b, c, and d are positive numbers.   [#permalink] 19 May 2017, 08:50
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# In the formula above, a, b, c, and d are positive numbers.

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