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Intern  Joined: 13 May 2014
Posts: 33
Concentration: General Management, Strategy
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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Difficulty:   55% (hard)

Question Stats: 71% (02:48) correct 29% (02:46) wrong based on 359 sessions

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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

Originally posted by gmatacequants on 23 May 2014, 12:38.
Last edited by Bunuel on 13 May 2017, 05:56, edited 2 times in total.
Edited the question and added the OA.
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Math Expert V
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Posts: 57095
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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Intern  Joined: 13 May 2014
Posts: 33
Concentration: General Management, Strategy
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 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
(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

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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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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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 [ 4.08 KiB | Viewed 19206 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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Location: Canada
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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Top Contributor
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gmatacequants 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

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: A
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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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PareshGmat wrote:
$$\frac{a}{b} = \frac{1}{3}, \frac{b}{c} = 2, \frac{c}{d} = \frac{1}{2}, \frac{d}{e} = 3 and \frac{e}{f} = \frac{1}{4}$$

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

This is the best approach to solve the problem in minimum time. Plugging in different values takes lot of time...Thanks for the short cut method...
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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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I actually got the question wrong because I wasn't that focused, then this is what i found:
So the question asks about the value of abc/def
and a/b=1/3, b/c=2, c/d = 1/2, d/e=3 and last e/f=1/4
based on that , a=1 ,d=2 , b=3, e=1, c=1 and f=4
=(1*3*1)/(2*1*4)= 3/8

See ya Re: If a/b = 1/3, b/c = 2, c/d = 1/2, d/e = 3 and e/f = 1/4, the   [#permalink] 18 Feb 2019, 07:08
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