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In the formula above, a, b, c, and d are positive numbers.
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Updated on: 12 Sep 2013, 09:37
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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
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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.




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Re: In the formula above, a, b, c, and d are positive numbers.
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12 Sep 2013, 09:44
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. Answer: D.
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Re: In the formula above, a, b, c, and d are positive numbers.
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12 Sep 2013, 09:45
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. Answer: D. 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: ifxyandkarepositivenumberssuchthatxxy128231.html
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Re: In the formula above, a, b, c, and d are positive numbers.
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08 Sep 2014, 03:50
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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In the formula above, a, b, c, and d are positive numbers.
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13 Sep 2014, 01:09
Can anyone explain this in detail?



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



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Re: In the formula above, a, b, c, and d are positive numbers.
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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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Re: In the formula above, a, b, c, and d are positive numbers.
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27 May 2019, 14:45
CounterSniper wrote: 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. I did exactly the same way! Can someone clarify if this method is OK to use for future such questions? Feels like guess work and lucked out with this one.



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Re: In the formula above, a, b, c, and d are positive numbers.
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28 May 2019, 18:06
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 Simplifying, we have: x = (8a + 16b)/c x = (8a + 16b)/(a + b) We see that we have a weighted average, and since b is greater than a, then x must be closer to 16 and also between 8 and 16, so x could be 15. Answer: D
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Re: In the formula above, a, b, c, and d are positive numbers.
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28 May 2019, 18:06






