On a perfectly square wall of her office, Christine mounts a whiteboar

Question

On a perfectly square wall of her office, Christine mounts a whiteboard that touches the floor and leaves a one-foot border of painted wall space on the other three sides. If that painted wall space around the whiteboard measures 46 square feet, what is the area of the whiteboard, in square feet?

A. 180
B. 210
C. 240
D. 270
E. 300

A. 180
B. 210
C. 240
D. 270
E. 300

Jayshoot · Accepted Answer

This question is practically begging you to backsolve!
Since the question tells you the wall is a perfect square, then you just need to find out which answer choice is a perfect square once you add 46.

16 x 16 = 256.
With (B), you get 210 + 46 = 256, which is 16*16.

ScottTargetTestPrep · Answer

We can let the length of a side of the wall be x. Thus, the area of the wall is x^2. The height of the whiteboard is (x - 1) because the whiteboard has 1 foot of wall above it. The width of the whiteboard is (x - 2) because there is 1 foot of wall to its left and 1 foot of wall to its right. Thus, the area of the whiteboard is (x - 1)(x - 2). Since the area of the painted wall space around the whiteboard is 46 square feet, we can say:

x^2 - (x - 1)(x - 2) = 46

x^2 - (x^2 - 3x + 2) = 46

3x - 2 = 46

3x = 48

x = 16

Thus, the area of the whiteboard is (16 - 1)(16 - 2) = (15)(14) = 210 square feet.

Answer: B

Sasindran · Answer

B

Let s be the side of the square wall. And s^2 is the area of the square.

Now the sides of the whiteboard are (s-1) and (s-2).

Also s^2-((s-1)(s-2))=46

Solving we get s=16

Hence the area of whiteboard = (16-1)(16-2)
=210

Sent from my iPhone using GMAT Club Forum

rahul16singh28 · Answer

Let l & b be the length & breadth of whiteboard. a - Side of the square.

a = l + 2 = b+ 1 
 (l+2)^2 -l(l+1) = 46 
 l = 14, b = 15 
 lb = 210.

sarvesh93sah · Answer

I approached the question in the following method.

Let the sides of the whiteboard be X.
Given the area of the wall=46.
(1*X)+(1*X)+(1*(X+2))=46
X+X+X+2=46.
3X=44
X= 14.66. (Side of the whiteboard)

So, 14.66*14.66= 214.91. (Area of the whiteboard)

ScottTargetTestPrep  Can you please point out the mistake I made? Why I didn't get the right answer?

ScottTargetTestPrep · Answer

I am guessing that you would like to solve the question by equating the area of the wall around the whiteboard to 46. The mistake in your calculations is that you are assuming that the whiteboard is a square, whereas the whiteboard is a rectangle. The wall (together with the whiteboard) is a square; so you should let x be the side of that square and find the sides of the whiteboard to be x - 1 and x - 2. Now, you can divide the area around the whiteboard into three regions: two regions of height x and width 1 and one region of height 1 and width x - 2. When we correct the equation this way, you'll get the correct answer:

x*1 + x*1 + 1*(x - 2) = 46

x + x + x - 2 = 46

3x = 48

x = 16

So, the sides of the whiteboard are x - 1 = 15 and x - 2 = 14 and the area is 15*14 = 210.

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On a perfectly square wall of her office, Christine mounts a whiteboar

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