BTGModeratorVI wrote: ↑

Mon Jul 13, 2020 7:41 am

The area of a rectangular garden would be increased by 150 square feet if either the length were increased by 7.5 feet or the width were increased by 5 feet. What is the area of the garden, in square feet?

A. 600
B. 525
C. 375
D. 300
E. 225

Answer: A
Source: GMAT Prep

Say the length is a feet and the width is b feet; thus, the area = ab sq feet

=> (a + 7.5)*b – ab = 150 => b = 20 feet; similarly,
=> a*(b + 5) – ab = 150 => a = 30 feet.

=> ab = 30*20 = 600 sq feet

Correct answer: A

Hope this helps!

-Jay
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BTGModeratorVI wrote: ↑

Mon Jul 13, 2020 7:41 am

The area of a rectangular garden would be increased by 150 square feet if either the length were increased by 7.5 feet or the width were increased by 5 feet. What is the area of the garden, in square feet?

A. 600
B. 525
C. 375
D. 300
E. 225

Answer: A
Source: GMAT Prep

Let L = the ORIGINAL length of the rectangle
Let W = the ORIGINAL width of the rectangle

So, LW = the ORIGINAL area of the rectangle

The area of a rectangular garden would be increased by 150 square feet if the length were increased by 7.5 feet
So we have the following "word equation": (area of NEW rectangle) - (area of ORIGINAL rectangle) = 150

NEW length = L + 7.5
In this case, the width remains at W
So, the NEW area = (L + 7.5)(W)

Plug values into the word equation to get: (L + 7.5)(W) - LW = 150
Expand: LW + 7.5W - LW = 150
Simplify: 7.5W = 150
Divide both sides by 7.5 to get: W = 20


The area of a rectangular garden would be increased by 150 square feet if the width were increased by 5 feet
Once again, we have the "word equation": (area of NEW rectangle) - (area of ORIGINAL rectangle) = 150

NEW with = W + 5
In this case, the length remains at L
So, the NEW area = (L)(W + 5)

Plug values into the word equation to get: (L)(W + 5) - LW = 150
Expand: LW + 5L - LW = 150
Simplify: 5L = 150
Divide both sides by 5 to get: L = 30

What is the area of the garden, in square feet?
ORIGINAL area of the rectangle = LW
= (30)(20)
= 600

Answer: A

Cheers,
Brent

BTGModeratorVI wrote: ↑

Mon Jul 13, 2020 7:41 am

The area of a rectangular garden would be increased by 150 square feet if either the length were increased by 7.5 feet or the width were increased by 5 feet. What is the area of the garden, in square feet?

A. 600
B. 525
C. 375
D. 300
E. 225

Answer: A

Solution:

Let L = the length of the garden and W = the width of the garden. We can create the equations:

(L + 7.5)W = LW + 150

and

L(W + 5) = LW + 150

Solving the first equation, we have:

LW + 7.5W = LW + 150

7.5W = 150

W = 20

Solving the second equation, we have:

LW + 5L = LW + 150

5L = 150

L = 30

Therefore, the area of the garden is 30 x 20 = 600 sq. ft.

Answer: A