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In the expression above, a, b, and c are different numbers and each is

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In the expression above, a, b, and c are different numbers and each is  [#permalink]

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New post Updated on: 06 Jun 2017, 08:39
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(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

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Originally posted by GMATinsight on 06 Jun 2017, 01:29.
Last edited by Bunuel on 06 Jun 2017, 08:39, edited 1 time in total.
Renamed the topic and edited the question.
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Re: In the expression above, a, b, and c are different numbers and each is  [#permalink]

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New post 06 Jun 2017, 02:41
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: http://www.GMATinsight.com


A is improper fraction hence it is bigger than all other options.
Check all other options.
B) 3/28 = 0.107
C) 4/21 = 0.190
D) 7/12 = 0.583
E) 3/7 = 0.428

Least possible value of (a/b)/c is \(\frac{3}{28}\) = 0.107. Answer B...
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Re: In the expression above, a, b, and c are different numbers and each is  [#permalink]

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New post 06 Jun 2017, 05:37
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: http://www.GMATinsight.com
(a/b)/c = a/(bc).

The fraction with the least value will have the smallest possible numerator and the largest possible denominator - i.e., the fewest parts of many.

The two larger values, 4 and 7 multiplied, make the largest denominator. Choice (B), 3/28 is the smallest.

The only close answer is 4/21. Lots of ways to check that it isn't the smaller value; one is that 4/21 is close to 1/5 and 3/28 is close to 1/9.

Answer (B)
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Re: In the expression above, a, b, and c are different numbers and each is  [#permalink]

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New post 06 Jun 2017, 09:51
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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: http://www.GMATinsight.com


(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:

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Re: In the expression above, a, b, and c are different numbers and each is  [#permalink]

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New post 08 Jun 2017, 16:44
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


We can simplify the given expression:

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

To make a fraction’s value as small as possible, we need to make the numerator as small as possible and the denominator as large as possible.

Thus, we can let a = 3, b = 4, and c = 7, and we have:

3/28

Answer: B
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Re: In the expression above, a, b, and c are different numbers and each is  [#permalink]

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New post 12 Jun 2017, 20:05
Working from answer choices.
A = 21/4. Not possible as the numerator can only be 3, 4 or 7.

B=3/28. Possible, if a=3, and either b is 4 and c is 7 or vice versa.

Question asks for least possible value. All other choices are bigger than 3/28, so B
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Re: In the expression above, a, b, and c are different numbers and each is  [#permalink]

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New post 18 Jun 2017, 21:25
a/b/c, Just substitute the given values in the following fraction.
3/4/7
i.e, 3/4/7/1, which is nothing but,
3/4 * 1/7= 3/28
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Re: In the expression above, a, b, and c are different numbers and each is  [#permalink]

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New post 24 Jun 2017, 16:40
\((a/b)/c\)

a, b and c can be any of these three different numbers. - 3, 4 & 7.

We have to find the least possible value of the equation.

So, we must increase the denominator - means we will take bigger numbers to the denominator and smaller ones to numerator.

after simplying above quation we get

\(\frac{a}{bc}\)

a - minimum value \(= 3\), b and c can take remaining values = \(4 * 7\) (or vice a versa) \(= 28\)

We get \(\frac{3}{28}\)

Hence, Answer is B

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Re: In the expression above, a, b, and c are different numbers and each is  [#permalink]

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New post 27 Jan 2019, 22:31
Maximize the denominator in order to get the least value of the fraction. Hence, choose the largest of the three numbers i.e. 7 as the value of the overall denominator (c), and next largest value as the value of b.

(3/4)/7 = 3/28 (Option B)
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Re: In the expression above, a, b, and c are different numbers and each is   [#permalink] 27 Jan 2019, 22:31
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