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Math Expert
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If d = (c  b)/(a  b), then b =
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15 Mar 2018, 23:03
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84% (01:38) correct 16% (01:32) wrong based on 61 sessions
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If d = (c  b)/(a  b), then b = A. (c  d)/(a  d) B. (c + d)/(a + d) C. (ca  d)/(ca + d) D. (c  ad)/(1  d) E. (c + ad)/(d 1)
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Re: If d = (c  b)/(a  b), then b =
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15 Mar 2018, 23:04
Bunuel wrote: If d = (c  a)/(a  b), then b =
A. (c  d)/(a  d)
B. (c + d)/(a + d)
C. (ca  d)/(ca + d)
D. (c  ad)/(1  d)
E. (c + ad)/(d 1) 7. Algebra Check below for more: ALL YOU NEED FOR QUANT ! ! !Ultimate GMAT Quantitative Megathread
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Re: If d = (c  b)/(a  b), then b =
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16 Mar 2018, 00:53
Bunuel wrote: If d = (c  a)/(a  b), then b =
A. (c  d)/(a  d)
B. (c + d)/(a + d)
C. (ca  d)/(ca + d)
D. (c  ad)/(1  d)
E. (c + ad)/(d 1) d = (c  a)/(a  b) i.e. (ab) = (ca)/d i.e. b = a  (ca)/d i.e. b = [ad  (ca)]/d Bunuel Are the options correct???
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Joined: 02 Sep 2009
Posts: 58415

Re: If d = (c  b)/(a  b), then b =
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16 Mar 2018, 01:03
GMATinsight wrote: Bunuel wrote: If d = (c  a)/(a  b), then b =
A. (c  d)/(a  d)
B. (c + d)/(a + d)
C. (ca  d)/(ca + d)
D. (c  ad)/(1  d)
E. (c + ad)/(d 1) d = (c  a)/(a  b) i.e. (ab) = (ca)/d i.e. b = a  (ca)/d i.e. b = [ad  (ca)]/d Bunuel Are the options correct??? There was a typo: it's d = (c  b)/(a  b) NOT d = (c  a)/(a  b). Edited. Thank you for noticing!
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If d = (c  b)/(a  b), then b =
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16 Mar 2018, 01:07
Bunuel wrote: If d = (c  b)/(a  b), then b =
A. (c  d)/(a  d)
B. (c + d)/(a + d)
C. (ca  d)/(ca + d)
D. (c  ad)/(1  d)
E. (c + ad)/(d 1) We are given that d = \(\frac{cb}{ab}\) Cross multiplying, da  db = c  b \(db  b = c  ad\) > \(b(d  1) = c  ad\) > \(b = \frac{(c  ad)}{(d  1)}\) Therefore, b = \(\frac{(c  ad)}{(d  1)}\) (Option D)Alternate approach
If c=4,b=1,a=2 then d=41/21 = 3 Now substutiting in the available answer options, A. (c  d)/(a  d) = (43)/(23) = ive
B. (c + d)/(a + d) = (4+3)/(2+3) = 7/5
C. (ca  d)/(ca + d) = (83)/(8+3) = 5/11D. (c  ad)/(1  d) = (46)/(13) = 2/2 = 1 E. (c + ad)/(d 1) = (4+6)/2 = 10/2 = 5 (Option D)
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Re: If d = (c  b)/(a  b), then b =
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16 Mar 2018, 01:09
Bunuel wrote: If d = (c  b)/(a  b), then b =
A. (c  d)/(a  d)
B. (c + d)/(a + d)
C. (ca  d)/(ca + d)
D. (c  ad)/(1  d)
E. (c + ad)/(d 1) d = (c  b)/(a  b) i.e. da  bd = cb i.e. bd  b = da  c i.e. b (d1) = dac i.e. b = (da  c) / (d1) or b = (c  ad)/(1  d) Answer: option D
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Re: If d = (c  b)/(a  b), then b =
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19 Mar 2018, 16:14
Bunuel wrote: If d = (c  b)/(a  b), then b =
A. (c  d)/(a  d)
B. (c + d)/(a + d)
C. (ca  d)/(ca + d)
D. (c  ad)/(1  d)
E. (c + ad)/(d 1) First, we multiply both sides by (a  b) and expand the left side: d(a  b) = c  b da  db = c  b Now, since our goal is to solve for b, we put all terms containing b on the left side of the equation and all other terms on the right side: b  db = c  da On the left side of the equation, factor out the common factor b from both terms: b(1  d) = c  da Divide both sides by (1  d), and now b is by itself on the left side of the equation: b = (c  da)/(1  d) Answer: D
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If d = (c  b)/(a  b), then b =
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19 Mar 2018, 19:32
pushpitkc wrote: Bunuel wrote: If d = (c  b)/(a  b), then b =
A. (c  d)/(a  d)
B. (c + d)/(a + d)
C. (ca  d)/(ca + d)
D. (c  ad)/(1  d)
E. (c + ad)/(d 1) We are given that d = \(\frac{cb}{ab}\) Cross multiplying, da  db = c  b \(db  b = c  ad\) > \(b(d  1) = c  ad\) > \(b = \frac{(c  ad)}{(d  1)}\) Therefore, b = \(\frac{(c  ad)}{(d  1)}\) (Option D)Alternate approach
If c=4,b=1,a=2 then d=41/21 = 3 Now substutiting in the available answer options, A. (c  d)/(a  d) = (43)/(23) = ive
B. (c + d)/(a + d) = (4+3)/(2+3) = 7/5
C. (ca  d)/(ca + d) = (83)/(8+3) = 5/11D. (c  ad)/(1  d) = (46)/(13) = 2/2 = 1 E. (c + ad)/(d 1) = (4+6)/2 = 10/2 = 5 (Option D)I understand the algebraic approach, but I can not get alternative approach. Using your variables I arrived at the correct answer, but when I use the variables a=1 , b=2, c=3, and d=1, I get answer A and D equal to 2. Why can I not use this set of variables?



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Re: If d = (c  b)/(a  b), then b =
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20 Mar 2018, 00:52
ScottTargetTestPrep wrote: Bunuel wrote: If d = (c  b)/(a  b), then b =
A. (c  d)/(a  d)
B. (c + d)/(a + d)
C. (ca  d)/(ca + d)
D. (c  ad)/(1  d)
E. (c + ad)/(d 1) First, we multiply both sides by (a  b) and expand the left side: d(a  b) = c  b da  db = c  b Now, since our goal is to solve for b, we put all terms containing b on the left side of the equation and all other terms on the right side: b  db = c  da On the left side of the equation, factor out the common factor b from both terms: b(1  d) = c  da Divide both sides by (1  d), and now b is by itself on the left side of the equation: b = (c  da)/(1  d) Answer: D I can follow your manipulations once I see the solution but how did you know  in two minutes  those were the right manipulations to get to the answer choices?.. I got stuck with b=cda+db (which is correct but does not correspond to any answer choices...).



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Joined: 28 Jan 2018
Posts: 50
Location: Netherlands
Concentration: Finance
GPA: 3

If d = (c  b)/(a  b), then b =
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20 Mar 2018, 10:25
Bunuel wrote: If d = (c  b)/(a  b), then b =
A. (c  d)/(a  d)
B. (c + d)/(a + d)
C. (ca  d)/(ca + d)
D. (c  ad)/(1  d)
E. (c + ad)/(d 1) \(d\) = \(\frac{(cb)}{(ab)}\) => \(d(a  b) = c  b\) => \(ad  bd = c  b\) => \(b  bd = c  ad\) => \(b(1  d) = c  ad\) => \(b\) = \(\frac{(cad)}{(1d)}\) Answer (D)



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GPA: 3

Re: If d = (c  b)/(a  b), then b =
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20 Mar 2018, 10:27
grgsky wrote: ScottTargetTestPrep wrote: Bunuel wrote: If d = (c  b)/(a  b), then b =
A. (c  d)/(a  d)
B. (c + d)/(a + d)
C. (ca  d)/(ca + d)
D. (c  ad)/(1  d)
E. (c + ad)/(d 1) First, we multiply both sides by (a  b) and expand the left side: d(a  b) = c  b da  db = c  b Now, since our goal is to solve for b, we put all terms containing b on the left side of the equation and all other terms on the right side: b  db = c  da On the left side of the equation, factor out the common factor b from both terms: b(1  d) = c  da Divide both sides by (1  d), and now b is by itself on the left side of the equation: b = (c  da)/(1  d) Answer: D I can follow your manipulations once I see the solution but how did you know  in two minutes  those were the right manipulations to get to the answer choices?.. I got stuck with b=cda+db (which is correct but does not correspond to any answer choices...). hi, ideally in these kind of questions, you'll want to concentrate all the value that related to b on one side of the equation and the rest on the other side. Check my solution above for details




Re: If d = (c  b)/(a  b), then b =
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20 Mar 2018, 10:27






