Bunuel wrote:

If the width of the rectangle above is increased by 50 percent and the length remains the same, by what percent will the area of the rectangle be increased?

(A) 50%

(B) 100%

(C) 150°

(D) 200°

(E) cannot be determined from the information given

Attachment:

2017-10-04_1124.png

Assume x = 10 and y = 4. (Choose easily multiplied numbers. For y, choose a number that, when multiplied by 1.5 or \(\frac{3}{2}\), yields an integer.)

Original area = (L * W) = 40

Width increases by 50 percent. New width is \((4)*\frac{3}{2} = 6\)

New area = (L * W) = 10 * 6 = 60

Percent increase in area =

\(\frac{New - Old}{Old} * 100\)

\(\frac{60 - 40}{40} =(\frac{20}{40}) * 100\) = 50 percent

ANSWER A

Algebra might be faster (not by much). Typically, both lengths increase. There are more multipliers, often squared. Here, just one length increases:

Original area = (y)(x)

New area = (1.5y)(x)

Percent increase:

\(\frac{1.5yx - 1yx}{yx} =

\frac{.5}{1} * 100\) = 50 percent

_________________

In the depths of winter, I finally learned

that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"