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A rope 40 feet long is cut into two pieces. If one piece is

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Bunuel
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A rope 40 feet long is cut into two pieces. If one piece is [#permalink] New post   26 Aug 2012, 03:05
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A rope 40 feet long is cut into two pieces. If one piece is 18 feet longer than the other, what is the length, in feet, of the shorter piece?

(A) 9
(B) 11
(C) 18
(D) 22
(E) 29
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BrentGMATPrepNow
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Re: A rope 40 feet long is cut into two pieces. If one piece is [#permalink] New post   Updated on: 09 Jun 2020, 10:41
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Bunuel wrote:
A rope 40 feet long is cut into two pieces. If one piece is 18 feet longer than the other, what is the length, in feet, of the shorter piece?

(A) 9
(B) 11
(C) 18
(D) 22
(E) 29


APPROACH #1: Algebra
Let x = the length of the shorter piece
So, x + 18 = the length of the longer piece

Since the lengths of the two pieces must add to 40 feet, we can write: x + (x + 18) = 40
Simplify: 2x + 18 = 40
Subtract 18 from both sides: : 2x = 22
Solve: x = 11

Answer: B
------------------------------------------

APPROACH #2: Test the answer choices

Start with the middle answer choice C

C) 18
If the shorter piece is 18 feet long, then the longer piece is 36 feet long
Sum of lengths = 18 + 36 = 54
NO GOOD. We want a sum of 40 feet (as per the question)
So, we can ELIMINATE C.
Also, since we need the two pieces to be SHORTER, we can also ELIMINATE D and E

Now try answer choice B
B) 11
If the shorter piece is 11 feet long, then the longer piece is 29 feet long
Sum of lengths = 11 + 29 = 40
PERFECT!!!

Answer: B

Cheers,
Brent

Originally posted by BrentGMATPrepNow on 01 Aug 2018, 17:34.
Last edited by BrentGMATPrepNow on 09 Jun 2020, 10:41, edited 2 times in total.
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Bunuel
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Re: A rope 40 feet long is cut into two pieces. If one piece is [#permalink] New post   26 Aug 2012, 03:06
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SOLUTION:

A rope 40 feet long is cut into two pieces. If one piece is 18 feet longer than the other, what is the length, in feet, of the shorter piece?

(A) 9
(B) 11
(C) 18
(D) 22
(E) 29

Say the length of the shorter piece is \(x\) feet, then the length of the longer piece would be \(x+18\) feet. Since the length of the rope is 40 feet, then \(x+(x+18)=40\) --> \(x=11\).

Answer: B.
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Re: A rope 40 feet long is cut into two pieces. If one piece is [#permalink] New post   26 Aug 2012, 08:18
Let x be the length of the shorter one.
The longer one will be x+18
Therefore, x+x+18=40..> x=11
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Re: A rope 40 feet long is cut into two pieces. If one piece is [#permalink] New post   27 Aug 2012, 11:10
x+x+18 = 40.
So x=11 feet.
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Re: A rope 40 feet long is cut into two pieces. If one piece is [#permalink] New post   10 Nov 2012, 03:26
Or
(40-s)-s = 18
s = 11
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Re: A rope 40 feet long is cut into two pieces. If one piece is [#permalink] New post   19 Dec 2012, 03:36
Let s be the shorter piece
Let the longer piece be s + 18

\(s + s + 18 = 40\)
\(2s + 18 = 40\)
\(2s = 40 - 18 = 22\)
\(s = 11\)

Answer: B
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Re: A rope 40 feet long is cut into two pieces. If one piece is [#permalink] New post   26 May 2014, 03:08
A rope 40 feet long is cut into two pieces. If one piece is 18 feet longer than the other, what is the length, in feet, of the shorter piece?

(A) 9
(B) 11
(C) 18
(D) 22
(E) 29


Solution:

Since, 40 is the total length. Smaller is any one from answers.
Try Back solving from Middle answer, i.e. 18. 18+(18+11) = 47 > 40
Hence, Select next smaller no. : 11 +(11+18) =40. So, 11 is the answer
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Re: A rope 40 feet long is cut into two pieces. If one piece is [#permalink] New post   27 May 2014, 03:21
Longer piece: x+18
Shorter piece: x

x+18 + x = 40
2x+18 = 40
x = 11
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Re: A rope 40 feet long is cut into two pieces. If one piece is [#permalink] New post   10 Sep 2014, 03:37
Bunuel wrote:
A rope 40 feet long is cut into two pieces. If one piece is 18 feet longer than the other, what is the length, in feet, of the shorter piece?

(A) 9
(B) 11
(C) 18
(D) 22
(E) 29

Practice Questions
Question: 29
Page: 156
Difficulty: 550


let one piece be x feet long then the other piece will be x+18 .

total =40

x+x+18 = 40
2x=22
x=11.
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Re: A rope 40 feet long is cut into two pieces. If one piece is [#permalink] New post   03 Oct 2014, 03:43
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Here's another solution hope it helps.

Let x be the length of the longer piece. Therefore (40-x) is the length of the shorter piece.

Also given that the longer piece is 18 feet greater than the shorter one

--> x=(40-x) +18
--> 2x=58
--> x =29

Therefore shorter piece = 40-29 =11
there's you answer :)
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Re: A rope 40 feet long is cut into two pieces. If one piece is [#permalink] New post   16 Nov 2014, 08:32
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I eliminated immediatly answers D & E since they're impossible, any smaller lenght can't be larger than half the rope.
Then I took the middle choice/value of the three (A,B,C) left (So B) if the side is elven does that match. Even if it doesn't match you get the answer right away since it then must be either bigger or smaller than the number you plug in, which is exactly what options A and C are. In this case option B matched.
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Re: A rope 40 feet long is cut into two pieces. If one piece is [#permalink] New post   20 Nov 2014, 01:55
Twice of the "correct OA" + 18 = 40 should be the length of the shorter piece

Options C, D, E can be ignored as they compute > 40

Only 11 fits in

Answer = B
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Re: A rope 40 feet long is cut into two pieces. If one piece is [#permalink] New post   25 May 2016, 07:17
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Bunuel wrote:
A rope 40 feet long is cut into two pieces. If one piece is 18 feet longer than the other, what is the length, in feet, of the shorter piece?

(A) 9
(B) 11
(C) 18
(D) 22
(E) 29


To solve this problem, we start by setting up two variables for the lengths of the long and short pieces of rope.

L = the length of the longer piece of rope

S = the length of the shorter piece of rope

We are given that the rope is 40 feet long. Translating this into an equation we have:

L + S = 40

Next we are given that one piece is 18 feet longer than the other. Translating this into an equation we have:

L = 18 + S

We can now substitute 18 + S from the second equation for L in the first equation. We have:

18 + S + S = 40

2S = 22

S = 11

The shorter piece of rope is 11 feet.

The answer is B.
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Re: A rope 40 feet long is cut into two pieces. If one piece is [#permalink] New post   25 May 2016, 08:48
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Bunuel wrote:
A rope 40 feet long is cut into two pieces. If one piece is 18 feet longer than the other, what is the length, in feet, of the shorter piece?

(A) 9
(B) 11
(C) 18
(D) 22
(E) 29

Practice Questions
Question: 29
Page: 156
Difficulty: 550


x+x+18= 40
2x= 22
x= 11

B is the answer
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Re: A rope 40 feet long is cut into two pieces. If one piece is [#permalink] New post   12 Feb 2018, 12:11
A rope 40 feet long is cut into two pieces. If one piece is 18 feet longer than the other, what is the length, in feet, of the shorter piece?

(A) 9
(B) 11
(C) 18
(D) 22
(E) 29

Answer:
The first rope cut = x, and the second rope cut = x+18,
x+(x+18) =40
2x = 40 - 18
2x =22
x=11
Answer = 11
B
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Re: A rope 40 feet long is cut into two pieces. If one piece is [#permalink] New post   16 Sep 2019, 08:55
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Bunuel wrote:
A rope 40 feet long is cut into two pieces. If one piece is 18 feet longer than the other, what is the length, in feet, of the shorter piece?

(A) 9
(B) 11
(C) 18
(D) 22
(E) 29

Practice Questions
Question: 29
Page: 156
Difficulty: 550


A rope 40 feet long is cut into two pieces. If one piece is 18 feet longer than the other, what is the length, in feet, of the shorter piece?
l + s = 40
l - s = 18
s = (40 - 18)/2 = 22/2 = 11 feet

IMO B
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A rope 40 feet long is cut into two pieces. If one piece is [#permalink] New post   04 Jul 2023, 07:55
Bunuel wrote:
A rope 40 feet long is cut into two pieces. If one piece is 18 feet longer than the other, what is the length, in feet, of the shorter piece?

(A) 9
(B) 11
(C) 18
(D) 22
(E) 29

\(a + 18 + a = 40\)

\(2a = 22\)

So, \(a = 11 \), Answer must be (B)
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A rope 40 feet long is cut into two pieces. If one piece is [#permalink]
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