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

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A board of length L feet is cut into two pieces such that th [#permalink]  20 Jun 2018, 09:42
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70% (01:30) correct 29% (01:33) wrong based on 68 sessions
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) $$\frac{L + 2}{2}$$

(B) $$\frac{2L +1}{2}$$

(C) $$\frac{L-1}{3}$$

(D) $$\frac{2L+ 3}{3}$$

(E) $$\frac{2L+1}{3}$$
[Reveal] Spoiler: OA

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Re: A board of length L feet is cut into two pieces such that th [#permalink]  23 Jun 2018, 06:40
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Carcass 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) $$\frac{L + 2}{2}$$

(B) $$\frac{2L +1}{2}$$

(C) $$\frac{L-1}{3}$$

(D) $$\frac{2L+ 3}{3}$$

(E) $$\frac{2L+1}{3}$$

In this type I prefer to use number; however there are other ways to solve it -

Let
B = smaller side = 3

A = Larger side = 1 + (2*3) = 7

So the total length = 10.

Put the value of L in the option and we need 7 as an answer. Only option E yields the correct answer.

It is also advisable to start substituting the number L from option C as we will come to know whether we need to proceed towards option A or to option E.
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Re: A board of length L feet is cut into two pieces such that th [#permalink]  13 Dec 2018, 17:37
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I was able to solve this using numbers, but it didn't work out using algebraic expressions. Can someone find out why? [quantity][/quantity]

Let's split up a line and translate the sentence given into an equation. Then the line can be broken up to a piece of length 2x+1 and a piece of length x. Then 3x+1 = L. Solving for L we get

x = (L-1)/3

Therefore, the length of the longer piece by substitution is 2x+1 = 2(l-1)/3

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Re: A board of length L feet is cut into two pieces such that th [#permalink]  21 Jan 2019, 17:41
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Expert's post
Carcass 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) $$\frac{L + 2}{2}$$

(B) $$\frac{2L +1}{2}$$

(C) $$\frac{L-1}{3}$$

(D) $$\frac{2L+ 3}{3}$$

(E) $$\frac{2L+1}{3}$$

We can let b= the length of piece B and (2b - 1) = the length of piece A and create the equation:

b + 2b - 1 = L

3b - 1 = L

3b = L + 1

b = (L + 1)/3

So the length of piece A is:

2(L + 1)/3 - 1

(2L + 2)/3 - 1

(2L + 2)/3 - 3/3 = (2L - 1)/3

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Re: A board of length L feet is cut into two pieces such that th [#permalink]  17 Apr 2020, 01:20
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My approach for this exercise would be to draw it out.

L/3.........L/3................L/3
..........I...............I....................I

now I imagine we divide it into 3 pieces, since we are given the information that the length of one piece is twice the other.

Following this it gets really easy.-->we know that the longer one is twice the other, thereby 2*(L/3)-->2L/3 and since we know that we have +1-->(2L+1)/3
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Re: A board of length L feet is cut into two pieces such that th [#permalink]  11 May 2020, 03:27
This problem can be solved algebraically.

The length of the board = L

It is cut into two pieces, one smaller and another larger.

Lets call the smaller piece S.

Now we know that the length of the longer piece is 2.S + 1.

But the choices are all representing the length of the longer piece in terms of L, the total length of the board.

So we need an equation relating S to L so that 2.S + 1 can be represented in terms of L, the total length, instead of the smaller piece S.

Since Length of the board = Length of the Smaller Piece + Length of the Larger Piece

L = S + 2.S + 1

L = 3.S + 1

3.S + 1 = L

3.S = L - 1

S = (L - 1)/3

Now we substitute the above equation into 2.S + 1, which is the length of the longer piece in terms of the shorter piece.

=> 2.[(L - 1)/3] + 1

= 2.[(L-1) + 3]/3

= (2.L - 2 + 3)/3

= (2.L + 1)/3

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Re: A board of length L feet is cut into two pieces such that th   [#permalink] 11 May 2020, 03:27
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