if a/b = 1/3, b/c=2, c/d = 1/2, d/e=3, and e/f=1/4 then find

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GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Sat May 20, 2017 7:19 pm

if a/b = 1/3, b/c=2, c/d = 1/2, d/e=3, and e/f=1/4 then find the value of abc/def?

A) 3/8
B) 27/8
C) 3/4
D) 27/4
E) 1/4

ans: A

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Source: Beat The GMAT — Problem Solving | Sat May 20, 2017 7:19 pm

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sun May 21, 2017 4:40 am

GMATinsight wrote:if a/b = 1/3, b/c=2, c/d = 1/2, d/e = 3, and e/f = 1/4 then find the value of abc/def?

A) 3/8
B) 27/8
C) 3/4
D) 27/4
E) 1/4

ans: A

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

Brent Hanneson - Creator of GMATPrepNow.com

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gary391: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Tue Nov 09, 2010 7:23 pm; Thanked: 1 times

by gary391 » Thu Jun 15, 2017 10:20 am

By looking at what is being asked we can see - abc/def = a/d*b/e*c/f

a/d = a/b*b/c*c/d = 1/3*2*1/2 = 1/3
b/e = b/c*c/d*d/e = 2*1/2*3= 3
c/f = c/d*d/e*e/f = 1/2*3*1/4 =3/8

abc/def = 1/3*3*3/8 = 3/8

Answer: A

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

by Jay@ManhattanReview » Thu Jun 15, 2017 8:53 pm

GMATinsight wrote:if a/b = 1/3, b/c=2, c/d = 1/2, d/e=3, and e/f=1/4 then find the value of abc/def?

A) 3/8
B) 27/8
C) 3/4
D) 27/4
E) 1/4

ans: A

We have

a/b = 1/3 ---(1),
b/c = 2/1 ---(2),
c/d = 1/2 ---(3),
d/e = 3/1 ---(4),
e/f = 1/4 ---(5)

We have to find out the value of abc/def.

abc/def = (a/f)*(b/e)*(c/d)

a/f = (1)*(2)*(3)*(4)*(5) = 1/3 * 2/1 * 1/2 * 3/1 * 1/4 = 1/4;
b/e = (2)*(3)*(4) = 2/1 * 1/2 * 3/1 = 3/1

=> abc/def = (a/f)*(b/e)*(c/d) = 1/4 * 3/1 * 1/2 = [spoiler]3/8[/spoiler].

The correct answer: A

Hope this helps!

Relevant book: Manhattan Review GMAT Math Essentials Guide

-Jay
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Pritish7805: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Tue Jul 12, 2016 6:59 pm

by Pritish7805 » Wed Aug 09, 2017 6:04 pm

Let's see how we can modify the expression.
As we have one abc in the denominator and both the terms with b per the given data can be cancelled out.
Let's square the term where we have it in the denominator.
Squaring b/c we have a c^2 in the denominator, so multiply the cube of c/d...

Following this we see the following expression.

abc/def=a/b*b^2/c^2*c^3/d^3*/d^2/e^2*e/f

Now, we can just put the values.
abc/def=1/3*4*1/8*9*1/4=3/8.(A)

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Balla: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Fri Jul 28, 2017 7:21 pm

by Balla » Wed Aug 09, 2017 6:20 pm

a/b=1/3

since we obtain an exact answer, we can suppose a=1 and b=3

so c must =1.5 since b/c=2

d= 3 using same reasoning
e=1
f=4
We have easy values to work with and have satisfied the ratio conditions.

abc= 1(3)(1.5)=4.5
def=3(1)(4)=12
we obtain 4.5/12
=9/24 and dividing numerator and denominator by 3 we obtain 3/8

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

if a/b = 1/3, b/c=2, c/d = 1/2, d/e=3, and e/f=1/4 then find

by Brent@GMATPrepNow » Wed Jan 10, 2018 8:23 am

GMATinsight wrote:if a/b = 1/3, b/c=2, c/d = 1/2, d/e=3, and e/f=1/4 then find the value of abc/def?

A) 3/8
B) 27/8
C) 3/4
D) 27/4
E) 1/4

ans: A

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

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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