GreenlightTestPrep wrote:

A project requires a rectangular sheet of cardboard satisfying the following requirement: When the sheet is cut into identical rectangular halves, each of the resulting rectangles has the same ratio of length to width as the original sheet. Which of the following sheets comes closest to satisfying the requirement?

(A) A sheet measuring 7 inches by 10 inches

(B) A sheet measuring 8 inches by 14 inches

(C) A sheet measuring 10 inches by 13 inches

(D) A sheet measuring 3 feet by 5 feet

(E) A sheet measuring 5 feet by 8 feet

Here's an algebraic solution:

Let x be length of the LONG side of the

original rectangle

Let y be length of the SHORT side of the

original rectangle

Then cut the rectangle into two pieces

We want the

resulting rectangles to have the same ratio of length to width as the original sheet.

In other words, we want x/y =

y/(x/2)Cross multiply to get: x²/2 = y²

Multiply both sides by 2 to get: x² = 2y²

Divide both sides by y² to get: x²/y² = 2

Take square root of both sides to get: x/y = √2

IMPORTANT: For the GRE, it's often useful to know the following APPROXIMATIONS: √2 ≈ 1.4, √3 ≈ 1.7, √5 ≈ 2.2 So, we know that

x/y ≈ 1.4In other words, the ratio (LONG side)/(SHORT side) ≈

1.4 Now check the answer choices:

(A) 10/7 = 1 3/7 ≈

1.4 LOOKS GOOD!

(B) 14/8 = 1 6/8 =

1.75 ELIMINATE

(C) 13/10 =

1.3 ELIMINATE

(D) 5/3 = 1 2/3 ≈

1.66 ELIMINATE

(E) 8/5 =

1.6 ELIMINATE

Answer: A

Cheers,

Brent

_________________

Brent Hanneson – Creator of greenlighttestprep.com

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