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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 ]
23 May 2014, 11:38

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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

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 ]
23 May 2014, 11:48
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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 ]
24 May 2014, 00:36
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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

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

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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 ]
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 ]
16 Jul 2014, 23:16

\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
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