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

Question

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

Bunuel · Accepted Answer

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.

gmatacequants · Answer

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 (D) Kudo me if you are getting help from my posts

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BrentGMATPrepNow · Answer

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

PerfectScores · Answer

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

PareshGmat · Answer

\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

MHI · Answer

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

Abhishek009 · Answer

Capture.PNG So, \frac{abc}{def} = \frac{2*6*3}{6*2*8} = \frac{3}{8} Hence, answer will be (D) \frac{3}{8}

buan15 · Answer

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...

ams3212 · Answer

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

sm1510 · Answer

Can someone pls confirm if the below working is legit?

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

from the above, b = 3a = 2c = d = 3e and 4e=f

Question is  \frac{abc }{ def}  = ? 
Capturing all values in terms of d: (simply because d stood out as a common digit, any digit can be chosen) 
a =  \frac{d}{3} 
b = d
c =  \frac{d}{2} 
d = d 
e =  \frac{d}{3} 
f =  4(\frac{d}{3})  =  \frac{4d}{3}

>>  \frac{abc }{ def}  = (\frac{d}{3} * d * \frac{d}{2} ) / (d * \frac{d}{3} * \frac{4d}{3})  
 \frac{d^3}{6}  /  \frac{4d^3}{9} 
( d^3  cancels out) 
left with  \frac{3}{8}

Answer = D

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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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