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

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

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New post 25 Feb 2018, 11:21
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E

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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
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Re: A piece of fabric is cut into three sections so that the first is thre  [#permalink]

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New post 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
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Re: A piece of fabric is cut into three sections so that the first is thre  [#permalink]

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New post 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)= \(\frac{x}{13x}\)= \(\frac{1}{13}\)

Answer: E.
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Re: A piece of fabric is cut into three sections so that the first is thre  [#permalink]

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New post 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, \(\frac{C}{A+B+C} = \frac{1}{9+3+1} = \frac{1}{13}\)

Answer is E
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Re: A piece of fabric is cut into three sections so that the first is thre  [#permalink]

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New post 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.

Answer: E
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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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