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# If a:b=b:c=c:d=d:e=3:1,then what is the value of (c+e)/(b+d)?

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Manager
Joined: 15 Dec 2015
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If a:b=b:c=c:d=d:e=3:1,then what is the value of (c+e)/(b+d)?  [#permalink]

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31 Jul 2017, 11:57
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84% (01:48) correct 16% (02:52) wrong based on 49 sessions

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If a:b=b:c=c:d=d:e=3:1,then what is the value of (c+e)/(b+d)?

A. 2:3
B. 3:1
C. 1:3
D. 4:1
E. 1:4
Manager
Joined: 15 Dec 2015
Posts: 115
GMAT 1: 660 Q46 V35
GPA: 4
WE: Information Technology (Computer Software)
Re: If a:b=b:c=c:d=d:e=3:1,then what is the value of (c+e)/(b+d)?  [#permalink]

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31 Jul 2017, 12:01
DH99 wrote:
If a:b=b:c=c:d=d:e=3:1,then what is the value of (c+e)/(b+d)?

A. 2:3
B. 3:1
C. 1:3
D. 4:1
E. 1:4

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If a:b=b:c=c:d=d:e=3:1,then what is the value of (c+e)/(b+d)?  [#permalink]

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31 Jul 2017, 15:16
DH99 wrote:
If a:b=b:c=c:d=d:e=3:1,then what is the value of (c+e)/(b+d)?

A. 2:3
B. 3:1
C. 1:3
D. 4:1
E. 1:4

Method I - brute force, which I think is easier. It's quick, too. Find the pattern.

$$\frac{a}{b}$$ = $$\frac{3}{1}$$ --> $$\frac{b}{c}$$ = $$\frac{3}{1}$$-->$$\frac{c}{d}$$ = $$\frac{3}{1}$$ --> $$\frac{d}{e}$$ = $$\frac{3}{1}$$
****

$$\frac{a}{b}$$ = $$\frac{3}{1}$$
3b = a ---> b = $$\frac{a}{3}$$

$$\frac{b}{c}$$ = $$\frac{3}{1}$$
3c = b ---> c = $$\frac{b}{3}$$ ...
d = $$\frac{c}{3}$$
e = $$\frac{d}{3}$$

Each term gets divided by 3 to yield the next term. So the greatest term is a and the smallest term is e. Because there is division by 3 a few times, pick a semi-large power of 3 for a. Or be precise:

We have $$\frac{1}{3}$$*$$\frac{1}{3}$$*$$\frac{1}{3}$$*$$\frac{1}{3}$$= $$\frac{1}{81}$$

Let a = 81. Then b = 27, c = 9, d = 3, and e = 1

(c + e)/(b + d) =

(9 + 1)/(27 + 3) =

10/30 = 1/3

Method II - sequence

Find the ratio:
$$\frac{a}{b}$$ = $$\frac{3}{1}$$
a = 3b

$$\frac{b}{c}$$ = $$\frac{3}{1}$$
b = 3c . . .

This is a geometric sequence, with common ratio of 3 (if $$A_1$$ is e). Let e = $$A_1$$, and call it x

$$A_{n}$$ = $$A_1$$ * $$r^{n-1}$$, where n is the nth term and r is the common ratio.

$$A_{n}$$ = $$A_1 * 3^{n-1}$$

$$A_1$$ = e = x
$$A_2$$ = d = x * 3 = 3x
$$A_3$$ = c = x * $$3^2$$ = 9x
$$A_4$$ = b = x * $$3^3$$ = 27x
$$A_5$$ = a = x * $$3^4$$ = 81x

Value of (c+e)/(b+d)?

(9x + x)/(27x + 3x) =

$$\frac{10x}{30x}$$ = $$\frac{1}{3}$$

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Joined: 15 Feb 2018
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Re: If a:b=b:c=c:d=d:e=3:1,then what is the value of (c+e)/(b+d)?  [#permalink]

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01 Mar 2019, 20:58
I am new to the concept of componendo and dividendo. Is there a quick way to solve this question using it?
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Joined: 25 Feb 2019
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Re: If a:b=b:c=c:d=d:e=3:1,then what is the value of (c+e)/(b+d)?  [#permalink]

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01 Mar 2019, 21:50
philipssonicare wrote:
I am new to the concept of componendo and dividendo. Is there a quick way to solve this question using it?

You can find the value of c and e in terms of D = 10d/3

similarly find the value of b and d in terms of C = 10c/3

now c+e/b+d = (10d/3)/(10c/3) = d /c = 1:3

it is derived using our traditional method.

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Re: If a:b=b:c=c:d=d:e=3:1,then what is the value of (c+e)/(b+d)?   [#permalink] 01 Mar 2019, 21:50
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