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

Question

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

BrushMyQuant · Accepted Answer

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

So, Answer will be E

hope it helps!

Donnie84 · Answer

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.

Answer (E).

Answer (E).

PareshGmat · Answer

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

Answer = E

GGMU · Answer

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

srihad · Answer

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

And hence answer choice E

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards