700+ Level: Practicing Geometry Word Problems

nbc jack chalkboard referenceAlgebraic translation (turning the description of relationships between x and y, apples and oranges, Todd’s income to Sarah’s income, perimeter to area, etc.) is a fundamental GMAT skill. Some students see this skill as a “trap” or some kind of nightmare. 😉

The truth is, you cannot avoid Problem Solving word problems on Test Day. BUT…you can conquer your fear of them by practicing specific types of Word Problems to hone particular skills. It’s always better to focus on one area at a time and build up your skill-set that way than do a million mixed Word Problems all at once.

Remember, word smarter, not harder!

Below are two GMAT questions that involve Geometry. Students get particularly frustrated with questions like these because Geometry is so inherently visual. When the GMAT doesn’t provide us with the diagram or image, we feel cheated. 😉

“What?! You mean I have to draw something AND come up with my own equations for it!”

These problems are especially good practice for anyone looking to break a Q40 or boost their Geometry abilities. Before you tackle these problems, you may want to read through my Reddit post of these types of questions.

Ready to go? Set a timer for 5 minutes, and see if you can get through both of them!

Question #1

A rectangular park has a perimeter of 340 feet and a diagonal measurement of 130 feet.What is its area, in square feet?

(A) 2500

(B) 1440

(C) 6000

(D) 7040

(E) 8080

Question #2

2017-11-07_0941

The above figure represents a square plot measuring x feet on a side. The plot consists of a rectangular garden, 48 square feet in area, surrounded by a walk that is 3 feet wide on two opposite sides and 2 feet wide on the other two sides. What is the value of x?

(A) 8
(B) 10
(C) 12
(D) 16
(E) 18

 

Scroll down for explanations!

 

 

 

 

 

EXPLANATIONS

Question #1

Let x and y equal the length and width of the rectangle. The perimeter is 340.

2x+2y=340

x+y=170

The diagnonal is 130.

x^2 + y^2 = 130^2

We want to find the value of xy, so let’s square both sides of the first equation to make it look like the second:

x^2 + 2xy + y^2 = 170^2

We can substitute 130^2 in for x^2 + y^2 in the second equation:

2xy + 130^2 = 170^2

2xy = 170^2 – 130^2

The right-hand side of our equation looks like our common Quadratic x^2 – y^2 = (x + y)(x – y).

2xy = (170 + 130)(170 – 130)

2xy = (300)(40)

xy = (300)(20)

xy = 6000

The correct answer is (C).

Question #2

We can say that the length of the rectangle is x – 4, and that the width is x – 6.

Area = (x-4)(x-6) = 48
x = 12

The correct answer is (C).

Here’s similar questions on GMATClub that you may want to practice:

Rectangular Yard + Hedge Question

Border and Photograph Question

Ratios with Brass Inlay Question