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If a/b = 1/3, b/c = 2, c/d = 1/2, d/e = 3 and e/f = 1/4, the

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If a/b = 1/3, b/c = 2, c/d = 1/2, d/e = 3 and e/f = 1/4, the [#permalink]

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If a/b = 1/3, b/c = 2, c/d = 1/2, d/e = 3 and e/f = 1/4, then what is the value of abc/def ?

(A) 27/4
(B) 27/8
(C) 3/4
(D) 3/8
(E) 1/4
[Reveal] Spoiler: OA

Last edited by Bunuel on 23 May 2014, 11:42, edited 1 time in total.
Edited the question and added the OA.
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Re: If a/b = 1/3, b/c = 2, c/d = 1/2, d/e = 3 and e/f = 1/4, the [#permalink]

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gmatacequants wrote:
If a/b = 1/3, b/c = 2, c/d = 1/2, d/e = 3 and e/f = 1/4, then what is the value of abc/def ?

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


Say a = 2. Then:

a/b = 1/3 --> b = 6;
b/c = 2 --> c = 3;
c/d = 1/2 --> d = 6;
d/e = 3 --> e = 2;
e/f = 1/4 --> f = 8.

abc/def = (2*6*3)/(6*2*8) = 3/8.

Answer: D.
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Re: If a/b = 1/3, b/c = 2, c/d = 1/2, d/e = 3 and e/f = 1/4, the [#permalink]

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gmatacequants wrote:
If a/b = 1/3, b/c = 2, c/d = 1/2, d/e = 3 and e/f = 1/4, then what is the value of abc/def ?

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



Solving the equation:
As a/b = 1/3, b/c = 2, c/d = 1/2, d/e = 3 and e/f = 1/4
:idea: then,
a/b*b/c*c/d = \frac{a}{d} = (1/3)*2*(1/2) = 1/3
b/c*c/d*d/e = \frac{b}{e}= 2*(1/2)*3 = 3
c/d*d/e*e/f = \frac{c}{f} = (1/2)*3*(1/4) = 3/8

(a/d)*(b/e)*(c/f) = a*b*c/(d*e*f )= (1/3)*3*(3/8) = 3/8
Hence
[Reveal] Spoiler:
(D)


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Re: If a/b = 1/3, b/c = 2, c/d = 1/2, d/e = 3 and e/f = 1/4, the [#permalink]

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New post 24 May 2014, 05:05
gmatacequants wrote:
If a/b = 1/3, b/c = 2, c/d = 1/2, d/e = 3 and e/f = 1/4, then what is the value of abc/def ?

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


Let us say that a = 4 then b = 12, c = 6, d = 12, e = 4, f = 16

then abc = (4)(12)(6) and def = (12) (4) (16)

(abc)/(def) = 6/16 = 3/8
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Re: If a/b = 1/3, b/c = 2, c/d = 1/2, d/e = 3 and e/f = 1/4, the [#permalink]

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\(\frac{a}{b} = \frac{1}{3}, \frac{b}{c} = 2, \frac{c}{d} = \frac{1}{2}, \frac{d}{e} = 3 and \frac{e}{f} = \frac{1}{4}\)

Multiple all with each other:

\(\frac{abcde}{bcdef} = \frac{1*2*3*1}{3*2*4}\)

\(\frac{a}{f} = \frac{1}{4}\) ............ (1)

\(\frac{b}{c} * \frac{c}{d} = 2*\frac{1}{2}\)

\(\frac{b}{d} = 2\) .......... (2)

\(\frac{c}{d} * \frac{d}{e} = \frac{1}{2} * 3\)

\(\frac{c}{e} = \frac{3}{2}\) .............. (3)

Mulitply (1) (2) & (3)

\(\frac{abc}{def} = \frac{1}{4} * 2 * \frac{3}{2} = \frac{3}{8}\)

Answer = D
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Re: If a/b = 1/3, b/c = 2, c/d = 1/2, d/e = 3 and e/f = 1/4, the [#permalink]

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Re: If a/b = 1/3, b/c = 2, c/d = 1/2, d/e = 3 and e/f = 1/4, the [#permalink]

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Re: If a/b = 1/3, b/c = 2, c/d = 1/2, d/e = 3 and e/f = 1/4, the [#permalink]

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New post 14 Nov 2016, 08:36
Answer:D
Best thing to do is to pick up a number. If not we can minimize abc/def to be fraction of just 2 variables.
1- Starting with def. We know that d=3e and f=4e ⇒ def=12e^3
2- As long as the denominator is formed of e, we need d in the numerator as long as d/e=3 is a constant. For abc, we have c=d/2, b=2c=d, a=b/3=d/3 ⇒ abc=(d^3)/6.
Finally, abc/def= ((d^3)/6) / 12e^3 = (d/e)^3 x (1/(6x12)) = 3^3/6x12 = 3/8
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Re: If a/b = 1/3, b/c = 2, c/d = 1/2, d/e = 3 and e/f = 1/4, the [#permalink]

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New post 14 Nov 2016, 09:02
gmatacequants wrote:
If a/b = 1/3, b/c = 2, c/d = 1/2, d/e = 3 and e/f = 1/4, then what is the value of abc/def ?

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

Attachment:
Capture.PNG
Capture.PNG [ 4.08 KiB | Viewed 412 times ]

So, \(\frac{abc}{def} = \frac{2*6*3}{6*2*8} = \frac{3}{8}\)

Hence, answer will be (D) \(\frac{3}{8}\)
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Re: If a/b = 1/3, b/c = 2, c/d = 1/2, d/e = 3 and e/f = 1/4, the   [#permalink] 14 Nov 2016, 09:02
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