A rectangular piece of cloth 2 feet wide was cut lengthwise

Question

A rectangular piece of cloth 2 feet wide was cut lengthwise into two smaller rectangular pieces. The shorter piece was one-third the length of the longer of the 2 new pieces and had an area of 12 square feet. What was the length in feet of the original piece of cloth before cutting?

A. 6
B. 18
C. 24
D. 36
E. 48

A. 6
B. 18
C. 24
D. 36
E. 48

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KarishmaB · Accepted Answer

A rectangular piece 2 feet wide was cut lengthwise into two pieces. This means the width of the two pieces is still 2 feet each. The total length has got split into two parts. The smaller part has area 12 sq feet so its length must be 6 feet. Since this is 1/3rd of the length of the bigger piece, the length of the bigger piece must be 3 * 6 = 18 feet.
Hence total original length must be 6 + 18 = 24 feet.

PTK · Answer

Second sentence is terrible, how could it be "the shorter part......" if there is a rectangle cut lengthwise, so both parts must have the same length.

aim730 · Answer

answer should be 36 
the rectangular cut lengthwise here suggests that the length is divided and the breadth remains the same

chaoswithin · Answer

I'm getting an answer = 24.

Given: original rect has dimensions 2 by L

Its not cut so there is two smaller rect. with one being bigger than the other.

so dimensions are:

rect_big = 2 by L_b
rect_small = 2 by (1/3) L_b

A_small = 12. therefore L_b = 18.

so L = L_b + (1/3) L_b = (4/3) L_b = 24.

Werewolf · Answer

Don't you mean that since L/3 = 6, therefore total length, L = 18?

puneetpratik · Answer

good one, getting pass the awkward wording is the butt of the question. calc are very simple.

KarishmaB · Answer

Consider this:
The question says, "Length of shorter piece is 1/3rd the length of longer  of the two new pieces "
This means after I split it into two pieces, I have a shorter piece and a longer one. The length of shorter is 1/3rd the length of longer. The 6 I found out was length of shorter piece. Then length of longer should be 18 and total length should be 24.

Had it been the other way, the questions would have said "The length of shorter piece is 1/3rd the total length."

Werewolf · Answer

Thanks for the explanation Karishma. I misunderstood the language of the question. My apologies!!

rg1 · Answer

I agree with @ VeritasPrepKarishma.
I got 24 too. I've learnt one thing from NOVA GMAT Prep book. For any hard problems, always remove answer choices which are result of elementary operation( like +,-,/ and*) on numbers mentioned in the question. It won't be a hard problem if answer can be reached using simple elementary operations.

(L/3)*2=12
=> L=18
So we can remove B option.

VeritasPrepKarishma explained the solution correctly.

madn800 · Answer

Firstly, understand that length "shorter piece=1/3*longer piece". Therefore if shorter piece is say 'x' then longer piece is '3x'. Total length is x+3x=4x. Answer must be a multiple of 4. So, answer choices A and B are eliminated. Secondly he says that area of shorter piece is 12. Shorter piece represents 1/4 of total length. Now start with option C. Length of shorter piece=24/4=6. So, area of shorter piece is 2(given width)*6=12. This matches with the info given in the question and hence C. Is the answer.

ScottTargetTestPrep · Answer

Since the shorter piece has an area of 12 square feet and a width of 2 feet, its length is 12/2 = 6 feet. Furthermore, since this is 1/3 of the length of the longer piece, the longer piece has a length of 6 x 3 = 18 feet. Therefore, the original piece of cloth has a total length of 6 + 18 = 24 feet.

Answer: C

Eduardo86 · Answer

Let us consider the old segment C which was divided into two-pieces A and B. A=1/3B so 3A=B C=A+B or we can rewrite as C=4A.

The area of a rectangular is bxh. 
1/3lxl=12 
l^2=36 
l=6

where l=A so C is 4x6=24

Abhishek009 · Answer

\frac{L}{3} = 6

So,  L = 18

Thus, Total length is  18 + 6 = 24 , Answer must be (C)

A rectangular piece of cloth 2 feet wide was cut lengthwise

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A rectangular piece of cloth 2 feet wide was cut lengthwise

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