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# If x inches are cut from the length, l, of a rectangle and y inches ar

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Manager
Joined: 02 Jun 2015
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Location: Ghana
If x inches are cut from the length, l, of a rectangle and y inches ar  [#permalink]

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21 Oct 2016, 01:08
00:00

Difficulty:

55% (hard)

Question Stats:

66% (02:08) correct 34% (02:10) wrong based on 100 sessions

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If x inches are cut from the length, l, of a rectangle and y inches are cut from the width, w, of the same rectangle, then which of the following correctly expresses the amount of the area of the original rectangle that was removed in terms of l, w, x, and y?

A) xy
B) lw – yx
C) ly + wx – xy
D) lx + wy – xy
E) xy – lw – wy

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Re: If x inches are cut from the length, l, of a rectangle and y inches ar  [#permalink]

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21 Oct 2016, 04:57
duahsolo wrote:
If x inches are cut from the length, l, of a rectangle and y inches are cut from the width, w, of the same rectangle, then which of the following correctly expresses the amount of the area of the original rectangle that was removed in terms of l, w, x, and y?

A) xy
B) lw – yx
C) ly + wx – xy
D) lx + wy – xy
E) xy – lw – wy

Initial Area = l*w

Area after cutting rectangle = (l-x)*(w-y)

Area removed = Initial Area - Final Area = l*w - (l-x)*(w-y) = l*w - [l*w-x*w-l*y+x*y) = x*w+l*y-x*y

Alternatively You may assume values of l, w, x and y and check options
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Re: If x inches are cut from the length, l, of a rectangle and y inches ar  [#permalink]

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22 Oct 2016, 04:42
Removed area = l*w - (l-x)*(w-y) = l*w - [l*w-x*w-l*y+x*y) = x*w+l*y-x*y

C
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Re: If x inches are cut from the length, l, of a rectangle and y inches ar  [#permalink]

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22 Oct 2016, 05:13
Original Area of Rectangle = l*w

New length = l - x

New Width = w - y

New area = (l - x)*(w - y)

Area removed = Original area - New Area

= l*w - (l - x)*(w - y)

= ly + wx – xy

Option C
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Re: If x inches are cut from the length, l, of a rectangle and y inches ar  [#permalink]

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20 Feb 2017, 06:32
duahsolo wrote:
If x inches are cut from the length, l, of a rectangle and y inches are cut from the width, w, of the same rectangle, then which of the following correctly expresses the amount of the area of the original rectangle that was removed in terms of l, w, x, and y?

A) xy
B) lw – yx
C) ly + wx – xy
D) lx + wy – xy
E) xy – lw – wy

$$Initial area=l*w$$
$$New area=(l-x)*(w-x)=-(-lw+ly+wx-xy)$$
$$Difference=lw-[-(-lw+ly+wx-xy)]=lw-lw+ly+wx-xy=ly+wx-xy$$

C.
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Re: If x inches are cut from the length, l, of a rectangle and y inches ar  [#permalink]

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06 Jul 2017, 14:08
Very silly question-- why xy is an incorrect answer?

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Joined: 16 Feb 2017
Posts: 20
Re: If x inches are cut from the length, l, of a rectangle and y inches ar  [#permalink]

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06 Jul 2017, 16:39
AR15J wrote:
Very silly question-- why xy is an incorrect answer?

This question can be best solved by using values for all variables - l,w,x,y in the question.
Let l =15, w = 10, x = 5, y = 2.

This means Orig. Area = 15X10 = 150
New Area = (15-5) X (10-2) = 10X8 = 80

Reduction in area = 150-80=70

AR15J To answer your question - xy will be incorrect coz reduction in area is not 10 here.

Back to main question:
putting these values in all answer choices that we have, only C comes out with valid answer = 70
ly+wx-xy = 15X2+10X5-10X2 = 30+50-10 = 80-10 = 70.

Hope this helps!
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Re: If x inches are cut from the length, l, of a rectangle and y inches ar  [#permalink]

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09 Feb 2019, 09:10
duahsolo wrote:
If x inches are cut from the length, l, of a rectangle and y inches are cut from the width, w, of the same rectangle, then which of the following correctly expresses the amount of the area of the original rectangle that was removed in terms of l, w, x, and y?

A) xy
B) lw – yx
C) ly + wx – xy
D) lx + wy – xy
E) xy – lw – wy

So lets see, plug in some values

l = 10 , w = 5
Initial area = 50

x = 2 , y =3
New area = 10 -2 * 5-3
= 8 * 2
= 16

Area difference = 50 - 16 = 34

C) ly + wx – xy
30 + 10 - 6
40 - 6
34
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If x inches are cut from the length, l, of a rectangle and y inches ar  [#permalink]

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09 Feb 2019, 10:07
duahsolo wrote:
If x inches are cut from the length, l, of a rectangle and y inches are cut from the width, w, of the same rectangle, then which of the following correctly expresses the amount of the area of the original rectangle that was removed in terms of l, w, x, and y?

A) xy
B) lw – yx
C) ly + wx – xy
D) lx + wy – xy
E) xy – lw – wy

If x inches are cut from the length, then wx square inches are cut from one end of the rectangle.

If y inches are cut from the width, then ly square inches are cut from one long side of the rectangle.

There is an overlap of the two cut pieces in one corner. The area of the overlap is xy. By adding the lx and wy areas, we include this overlap twice. So, to account for the overlap, we have to subtract xy one time from the total.

The total removed is thus:

wx + ly - xy

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If x inches are cut from the length, l, of a rectangle and y inches ar   [#permalink] 09 Feb 2019, 10:07
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