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

Question

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

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

GMATinsight · Answer

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

Answer: Option C

Alternatively You may assume values of l, w, x and y and check options

Manonamission · Answer

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

gauravk · Answer

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

Sirakri · Answer

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

C.

AR15J · Answer

Very silly question-- why xy is an incorrect answer?

Please help !

GMATAspirer09 · 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!

KanishkM · Answer

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

MartyTargetTestPrep · Answer

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

The correct answer is (C).

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

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

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