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Math Expert V
Joined: 02 Sep 2009
Posts: 65062
A board of length L feet is cut into two pieces such that the length  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 69% (02:10) correct 31% (02:04) wrong based on 95 sessions

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

A. (L - 1)/2
B. (2L + 1)/3
C. (L + 1)/3
D. (2L + 2)/3
E. (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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Let length of piece A and B be A feet and L-A feet
as per question
A=2(L-A)-1 => 3A=2L -1 => A=(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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1
Let length of piece A= 2x-1
length of piece B= x
2x-1+x = L
=>3x-1 = L
=>x = (L+1)/3

length of piece A=2[(L+1)/3] - 1
= (2L+2 -3)/3 = (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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hi!

i don't understand the solutions given by CounterSniper and Skywalker18.
why is A= 2x-1 when B= x ?

shouldn't it be A= x-1 when B= x ?
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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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whitehalo wrote:
hi!

i don't understand the solutions given by CounterSniper and Skywalker18.
why is A= 2x-1 when B= x ?

shouldn't it be A= x-1 when B= x ?

No. You are not reading the statement properly.

The question is:

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

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

If you look closely at the text in red above, you see that A is 1 foot less than TWICE the length of B. Thus, if B = x , then A = 2*B-1 = 2x-1.

Once you figure this out, you get L=x+2x-1=3x-1. ---> x=(L+1)/3 and A=2x-1 = 2(L+1)/3 -1 = (2L-1)/3. E is the correct answer.

Hope this helps.
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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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1
Engr2012 wrote:
whitehalo wrote:
hi!

i don't understand the solutions given by CounterSniper and Skywalker18.
why is A= 2x-1 when B= x ?

shouldn't it be A= x-1 when B= x ?

No. You are not reading the statement properly.

The question is:

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

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

If you look closely at the text in red above, you see that A is 1 foot less than TWICE the length of B. Thus, if B = x , then A = 2*B-1 = 2x-1.

Once you figure this out, you get L=x+2x-1=3x-1. ---> x=(L+1)/3 and A=2x-1 = 2(L+1)/3 -1 = (2L-1)/3. E is the correct answer.

Hope this helps.

Oh I see. Careless mistake. Thanks for pointing that out, Engr2012!
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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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Hi All,

While this prompt can be approached algebraically, it can be solved rather easily by TESTing VALUES.

We're told that a board of length L feet is cut into two pieces and that Piece A is 1 foot LESS than TWICE the length of Piece B.

IF....
B = 2 feet
A = 2(2) - 1 = 3 feet

L = 2+3 = 5 feet

We're asked for the length of PIECE A, so we're looking for an answer that equals 3 when L=5... There's only one answer that fits:

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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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Bunuel wrote:
A board of length L feet is cut into two pieces such that the length of piece A is 1 foot less than twice the length of piece B. Which of the following is the length, in feet, of piece A ?

A. (L - 1)/2
B. (2L + 1)/3
C. (L + 1)/3
D. (2L + 2)/3
E. (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 the length  [#permalink]

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_________________ Re: A board of length L feet is cut into two pieces such that the length   [#permalink] 30 May 2020, 04:44

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