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Posts: 26
Updated on: 13 May 2017, 04:56
Originally posted by gmatacequants on 23 May 2014, 11:38.
Last edited by Bunuel on 13 May 2017, 04:56, edited 2 times in total.
Last edited by Bunuel on 13 May 2017, 04:56, edited 2 times in total.
Edited the question and added the OA.
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
76% (02:46) correct
24%
(02:55)
wrong
based on 887
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History
Date
Time
Result
Not Attempted Yet
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
(A) 27/4
(B) 27/8
(C) 3/4
(D) 3/8
(E) 1/4
gmatacequants
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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Posts: 26
gmatacequants
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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10-straight-lines-no-two-of-which-are-parallel-and-no-three-171525.html
Posts: 6,727
gmatacequants
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
General Discussion
Posts: 103
gmatacequants
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
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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
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
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
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gmatacequants
Attachment:
Capture.PNG [ 4.08 KiB | Viewed 80195 times ]
Hence, answer will be (D) \(\frac{3}{8}\)
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PareshGmat
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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Enjoying the journey 
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
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
\(\frac{a}{b}\) = \(\frac{1}{3}\), => 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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