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# If p = (a + c)/(b+d) = (c+e)/(d + f) = (a + e)/(b + f)

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If p = (a + c)/(b+d) = (c+e)/(d + f) = (a + e)/(b + f)  [#permalink]

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Updated on: 13 Jun 2016, 10:57
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35% (medium)

Question Stats:

75% (02:06) correct 25% (02:37) wrong based on 227 sessions

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If $$p=\frac{(a + c)}{(b+d)} = \frac{(c+e)}{(d + f)} = \frac{(a + e)}{( b + f)}$$ and all variables are positive,then which is true ?

I. p= a/b
II. p= e/f
III. p= c/d

A. I only
B. II only
C. I & I
D. II & III
E. I, II & III

Originally posted by pran21 on 17 Aug 2014, 00:15.
Last edited by Bunuel on 13 Jun 2016, 10:57, edited 1 time in total.
Edited the question.
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Re: If p = (a + c)/(b+d) = (c+e)/(d + f) = (a + e)/(b + f)  [#permalink]

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17 Aug 2014, 01:45
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p =(a+c)/(b+d) => a+c = (b+d)*p ...(1)
p = (c+e) / (d+f) => c+ e = (d+f)*p ....(2)
p = (a+e) / (b+f) => a + e = (b+f)*p ...(3)

(1) - (2) we get
a-e = (b-f)*p ...(4)

(3) + (4) we get
2a = 2bp => p =a/b

(3) - (4) we get
2e = 2fp => p=e/f

(2) - (3) we get
c-a = (d-b)*p ...(5)

(1) + (5) we get
2c = 2dp => p=c/d

hope it helps!
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Re: If p = (a + c)/(b+d) = (c+e)/(d + f) = (a + e)/(b + f)  [#permalink]

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17 Aug 2014, 19:19
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We are told that variables a through f are all positive. However, the question does not say anything about them being same/distinct. So, I assumed a through f to be 1 each. That makes p = 1 and all the three options work.

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Re: If p = (a + c)/(b+d) = (c+e)/(d + f) = (a + e)/(b + f)  [#permalink]

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17 Aug 2014, 22:11
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$$p = \frac{a + c}{b+d} = \frac{c+e}{d + f} = \frac{a + e}{b + f}$$

Let a = b = c = d = e = f = 1

$$p =\frac{1+1}{1+1} = \frac{1+1}{1+1} = \frac{1+1}{1+1} = 1$$

Satisfies all 3 conditions given

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Re: If p = (a + c)/(b+d) = (c+e)/(d + f) = (a + e)/(b + f)  [#permalink]

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03 Nov 2017, 02:05
From the question stem, we can infer that a=b=c=d=e=f. So P will always be equal to 1. So,

I. p= a/b =1
II. p= e/f =1
III. p= c/d= 1

So all are correct. Hence option E
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Re: If p = (a + c)/(b+d) = (c+e)/(d + f) = (a + e)/(b + f)  [#permalink]

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16 Dec 2017, 15:38
Chose a = 1, C=3, B=2, D=6, e=1 and f = 2 to make sure the ratios are equal as mentioned
p = (a + c)/(b+d) = (c+e)/(d + f) = (a + e)/(b + f) = 1/2.

I. p= a/b =1/2
II. p= e/f =4/8 = 1/2
III. p= c/d=4/8 = 1/2

Re: If p = (a + c)/(b+d) = (c+e)/(d + f) = (a + e)/(b + f)   [#permalink] 16 Dec 2017, 15:38
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