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# A piece of fabric is cut into three sections so that the first is thre

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Math Expert
Joined: 02 Sep 2009
Posts: 59561
A piece of fabric is cut into three sections so that the first is thre  [#permalink]

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25 Feb 2018, 11:21
00:00

Difficulty:

15% (low)

Question Stats:

88% (01:08) correct 12% (01:36) wrong based on 43 sessions

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A piece of fabric is cut into three sections so that the first is three times as long as the second and the second section is three times as long as the third. What part of the entire piece is the smallest section?

(A) 1/12
(B) 1/9
(C) 1/3
(D) 1/7
(E) 1/13
Current Student
Joined: 07 Jan 2016
Posts: 1081
Location: India
GMAT 1: 710 Q49 V36
Re: A piece of fabric is cut into three sections so that the first is thre  [#permalink]

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25 Feb 2018, 11:36
Bunuel wrote:
A piece of fabric is cut into three sections so that the first is three times as long as the second and the second section is three times as long as the third. What part of the entire piece is the smallest section?

(A) 1/12
(B) 1/9
(C) 1/3
(D) 1/7
(E) 1/13

start from the smallest and let the size = 1

3rd part= 1
2nd part = 3 ( thrice of 3rd part)
1st = 9

total = 9+3+1= 13

smallest = 1/13

(E) imo
Senior Manager
Joined: 07 Jul 2012
Posts: 365
Location: India
Concentration: Finance, Accounting
GPA: 3.5
Re: A piece of fabric is cut into three sections so that the first is thre  [#permalink]

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26 Feb 2018, 01:03
Let third part= x

Second part= 3x

First part= 3*3x= 9x

Total= 9x+3x+x= 13x

Third part (Smallest)= $$\frac{x}{13x}$$= $$\frac{1}{13}$$

Intern
Joined: 20 Dec 2017
Posts: 35
Location: Singapore
Re: A piece of fabric is cut into three sections so that the first is thre  [#permalink]

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26 Feb 2018, 02:43
For these type of ratio questions, I would usually go for table method:

Name the 3 pieces of fabrics as A, B & C

A B C
3 1 -
- 3 1

Make B the same value, i.e. 3

A B C
9 3 -
- 3 1

Therefore, $$\frac{C}{A+B+C} = \frac{1}{9+3+1} = \frac{1}{13}$$

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Location: United States (CA)
Re: A piece of fabric is cut into three sections so that the first is thre  [#permalink]

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27 Feb 2018, 10:25
Bunuel wrote:
A piece of fabric is cut into three sections so that the first is three times as long as the second and the second section is three times as long as the third. What part of the entire piece is the smallest section?

(A) 1/12
(B) 1/9
(C) 1/3
(D) 1/7
(E) 1/13

We can let f = the longest piece, s = the second longest piece, and t = the shortest piece and create the equations:

f = 3s

and

s = 3t

Thus, f = 3(3t) = 9t

The total piece of fabric is:

9t + 3t + t = 13t

Thus, the shortest piece is t/(13t) = 1/13 of the entire piece.

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Re: A piece of fabric is cut into three sections so that the first is thre   [#permalink] 27 Feb 2018, 10:25
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