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OG2015 PS A rope 40 feet

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by lionsshare » Fri Sep 08, 2017 3:51 pm
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

OA: B

Anyone please, explain the POE. Thanks.
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by Jay@ManhattanReview » Fri Sep 08, 2017 10:12 pm
lionsshare 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

OA: B

Anyone please, explain the POE. Thanks.
Hi lionsshare,

This can certainly be solved through plug-in option values, but the algebraic approach is easier and a time-saver.

Say the length of the longer piece = x feet, the length of the shorter piece = x - 18.

=> Length of longer piece + Length of shorter piece = 40

Thus, x + (x - 18) = 40
2x = 58
So, x = 29

Thus the length of shorter piece = x - 18 = 29 - 18 = 11 feet.

The correct answer: B

Hope this helps!

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by GMATGuruNY » Sat Sep 09, 2017 2:48 am
lionsshare 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
We can PLUG IN THE ANSWERS, which represent the length of the shorter piece.
Since the length of the shorter piece must be less than half of the total length of 40 feet, the shorter piece must be less than 20 feet long.
Eliminate D and E.
When the correct answer choice is plugged in, shorter + longer = 40.

B: shorter = 11 feet
Since the longer piece is 18 feet longer than the shorter piece, longer = 11+18 = 29.
shorter + longer = 11+29 = 40.
Success!

The correct answer is B.

Algebraic solution:
Let L = the longer piece and S = the shorter piece.
Since the total length is 40, we get:
L+S = 40.
Since the difference between the two lengths is 18, we get:
L-S = 18.
Adding together the two equations, we get:
(L+S) + (L-S) = 40+18
2L = 58
L = 29.

Since L is 18 feet longer than S, we get:
S = 29-18 = 11.

The correct answer is B.
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by Scott@TargetTestPrep » Wed Apr 04, 2018 4:54 pm
lionsshare 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
We can let L = the length of the longer piece of rope and 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.

Answer: B

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