[b][m][fraction](a/b)/c [/fraction][/m][/b] In the expressio

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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 » Tue Jun 06, 2017 12:29 am

(a/b)/c
In the expression above, a, b, and c are different numbers and each is one of the numbers 3, 4, or 7. What is the least possible value of the expression?
(A) 21/4
(B) 3/28
(C) 4/21
(D) 7/12
(E) 3/7

Source: www.GMATinsight.com

Answer: Option B

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Source: Beat The GMAT — Problem Solving | Tue Jun 06, 2017 12:29 am

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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 » Tue Jun 06, 2017 12:40 am

GMATinsight wrote:(a/b)/c
In the expression above, a, b, and c are different numbers and each is one of the numbers 3, 4, or 7. What is the least possible value of the expression?
(A) 21/4
(B) 3/28
(C) 4/21
(D) 7/12
(E) 3/7

Source: www.GMATinsight.com

Answer: Option B

If I could read this correctly, then you ask for the least possible value of (a/b)/c.

(a/b)/c = (a/b)*(1/c) = a/(bc)

Since the given numbers are all positive and greater than 1, to get the least value of a/(bc), we must have the least value for the numerator and the greater value for the denominator.

Thus, a must be 3 and b and c each must be one between 4 and 7.

Thus, a/(bc) = 3/(4*7) = 3/28 (Least possible value)

The correct answer: B

Hope this helps!

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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 » Tue Jun 06, 2017 2:42 pm

GMATinsight wrote:(a/b)/c
In the expression above, a, b, and c are different numbers and each is one of the numbers 3, 4, or 7. What is the least possible value of the expression?
(A) 21/4
(B) 3/28
(C) 4/21
(D) 7/12
(E) 3/7

Source: www.GMATinsight.com

Answer: Option B

(a/b)/c = (a/b)/(c/1)
= (a/b)(1/c)
= a/(bc)

So, we want to minimize the value of a/(bc)
To do so, we must MINIMIZE the numerator (a) and MAXIMIZE the denominator (bc)
So, let a = 3, and let b = 4 and c = 7

So, (a/b)/c = a/(bc) = 3/(4 x 7)
= 3/28

Answer: B

Brent Hanneson - Creator of GMATPrepNow.com

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Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Thu Jun 08, 2017 5:06 pm

(a/b)/c =>

a/(b * c)

Since we're restricted to positive integers, we want a to be as small as possible and b*c to be as large as possible. This is easily done by making a the smallest option (3) and b and c the other options (4 and 7), leaving us with 3 / (4*7), or 3/28.

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