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A board of length L feet is cut into two pieces such that the length

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Joined: 02 Sep 2009
Posts: 46291
A board of length L feet is cut into two pieces such that the length [#permalink]

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22 Sep 2017, 00:44
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Difficulty:

45% (medium)

Question Stats:

75% (01:35) correct 25% (00:46) wrong based on 24 sessions

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A board of length L feet is cut into two pieces such that the length of one piece is 1 foot more than twice the length of the other piece. Which of the following is the length, in feet, of the longer piece?

(A) (L + 2)/2
(B) (2L + 1)/2
(C) (L – 1)/2
(D) (2L + 3)/3
(E) (2L + 1)/3

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Joined: 02 Jul 2017
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Re: A board of length L feet is cut into two pieces such that the length [#permalink]

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22 Sep 2017, 01:26
let two piece length be x and y
=> x+y =L

Given x=2y+1 <= longer piece
=> y=$$\frac{x-1}{2}$$

x+y = L => $$x+\frac{x-1}{2} = L$$ => $$\frac{3x-1}{2}= L$$ => $$3x-1= 2L$$ => $$x= \frac{2L+1}{3}$$

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Re: A board of length L feet is cut into two pieces such that the length [#permalink]

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23 Sep 2017, 08:47
Bunuel wrote:
A board of length L feet is cut into two pieces such that the length of one piece is 1 foot more than twice the length of the other piece. Which of the following is the length, in feet,
of the longer piece?

(A) (L + 2)/2
(B) (2L + 1)/2
(C) (L – 1)/2
(D) (2L + 3)/3
(E) (2L + 1)/3

Choosing numbers here works well: the answer choices do not require lengthy calculation. The algebra here can be time-consuming.

It's probably easiest to pick the length of the short piece first.

Short piece = 2
Long piece, ((2*short)+1) = 5
L = (2 + 5) = 7

Using L = 7, go through the answer choices until one of them yields the answer 5, the length of the longer piece.

(A) (L + 2)/2 is (7+2)/2 = 4.5, not an integer, NOT a match

(B) (2L + 1)/2 is (14+1)/2 = not an integer, NOT a match

(C) (L – 1)/2 is (7-1)/2 = 3: NOT a match

(D) (2L + 3)/3 is (14+3)/3: not an integer, NOT a match

(E) (2L + 1)/3 is (14+1)/3 = 5. This IS a match.

Sidenote: If the short piece = anything from 1 to 10, in all but one case, the result is three non-integer answers, one integer answer that does not match, and E as the correct answer.

The one exception: if the shorter piece = 1. The longer piece is 3, and L = 4. In that case alone, answers A and E both work. But assigning any other single-digit length to the short piece will quickly distinguish A as incorrect and E as correct.

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Re: A board of length L feet is cut into two pieces such that the length   [#permalink] 23 Sep 2017, 08:47
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