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

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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Try the following problem :
10-straight-lines-no-two-of-which-are-parallel-and-no-three-171525.html

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

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

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

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

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

Hence, answer will be (D) \(\frac{3}{8}\)

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...

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

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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