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A board of length L feet is cut into two pieces such that th [#permalink]
Expert's post 00:00

Question Stats: 74% (02:00) correct 24% (01:28) wrong based on 28 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

_________________ Director Joined: 20 Apr 2016
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WE: Engineering (Energy and Utilities)
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Re: A board of length L feet is cut into two pieces such that th [#permalink]
1
KUDOS
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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Manager Joined: 02 Dec 2018
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Re: A board of length L feet is cut into two pieces such that th [#permalink]
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 Target Test Prep Representative Joined: 12 Sep 2018
Posts: 149
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Re: A board of length L feet is cut into two pieces such that th [#permalink]
1
KUDOS
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

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

See why Target Test Prep is the top rated GRE quant course on GRE Prep Club. Read Our Reviews 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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