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If [m][fraction]a/b[/fraction] = [fraction]1/3[/fraction][/m

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Carcass
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If [m][fraction]a/b[/fraction] = [fraction]1/3[/fraction][/m [#permalink] New post   08 Jan 2021, 07:51
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If \(\frac{a}{b} = \frac{1}{3}\), \(\frac{b}{c} = 2\), \(\frac{c}{d} = \frac{1}{2}\), \(\frac{d}{e} = 3\) and \(\frac{e}{f} = \frac{1}{4}\), then what is the value of \(\frac{abc}{def}\) ?

(A) 27/4
(B) 27/8
(C) 3/4
(D) 3/8
(E) 1/4

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D
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If [m][fraction]a/b[/fraction] = [fraction]1/3[/fraction][/m [#permalink] New post   08 Jan 2021, 07:58
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Carcass wrote:
If \(\frac{a}{b} = \frac{1}{3}\), \(\frac{b}{c} = 2\), \(\frac{c}{d} = \frac{1}{2}\), \(\frac{d}{e} = 3\) and \(\frac{e}{f} = \frac{1}{4}\), then what is the value of \(\frac{abc}{def}\) ?

(A) 27/4
(B) 27/8
(C) 3/4
(D) 3/8
(E) 1/4

Kudos for the right answer and explanation


Assign some values to the given variables.

Given: a/b = 1/3
Let a = 2 and b = 6

Given: b/c = 2
Since b = 6, it must be the case that c = 3

Given: c/d = 1/2
Since c = 3 , it must be the case that d = 6

Given: d/e=3
Since d = 6 , it must be the case that e = 2

Given: e/f = 1/4
Since e = 2 , it must be the case that f = 8

So, abc/def = (2)(6)(3)/(6)(2)(8)
= 36/96
= 3/8

Answer: D
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kushal07
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Re: If [m][fraction]a/b[/fraction] = [fraction]1/3[/fraction][/m [#permalink] New post   13 Jan 2021, 00:04
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Say,
f = 24
e = 24 x 1/4 = 6
d = 6 x 3 = 18
c = 18 x 1/2 = 9
b = 9 x 2 = 18
a = 18 x 1/3 = 6

Therefore,
abc/def
= (6 x 18 x 9)/(18 x 6 x 24)
= 9/24
= 3/8
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Re: If [m][fraction]a/b[/fraction] = [fraction]1/3[/fraction][/m [#permalink] New post   04 Jun 2023, 23:29
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If [m][fraction]a/b[/fraction] = [fraction]1/3[/fraction][/m [#permalink]
04 Jun 2023, 23:29
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