GMAT Math : Problem-Solving Questions

Study concepts, example questions & explanations for GMAT Math

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Example Questions

Example Question #3 : Calculating The Area Of A Square

A square, a regular pentagon, and a regular hexagon have the same sidelength. The sum of their perimeters is one mile. What is the area of the square?

Possible Answers:

Correct answer:

Explanation:

The square, the pentagon, and the hexagon have a total of 15 sides, all of which are of equal length; the sum of the lengths is one mile, or 5,280 feet, so the length of one side of any of these polygons is 

 feet.

The square has area equal to the square of this sidelength:

Example Question #4 : Calculating The Area Of A Square

A square and a regular pentagon have the same perimeter. The length of one side of the pentagon is 60 centimeters. What is the area of the square?

Possible Answers:

Correct answer:

Explanation:

The regular perimeter has sidelength 60 centimeters and therefore perimeter  centimeters. The square has as its sidelength  centimeters and area  square centimeters.

Example Question #2 : Calculating The Area Of A Square

Six squares have sidelengths 8 inches, 1 foot, 15 inches, 20 inches, 2 feet, and 25 inches. What is the sum of their areas?

Possible Answers:

Correct answer:

Explanation:

The areas of the squares are the squares of the sidelengths, so add the squares of the sidelengths. Since 1 foot is equal to 12 inches and 2 feet are equal to 24 inches, the sum of the areas is:

 square inches

Example Question #1 : Calculating The Area Of A Square

What polynomial represents the area of Square  if  ?

Possible Answers:

Correct answer:

Explanation:

As a square,  is also a rhombus. The area of a rhombus is half the product of the lengths of its diagonals, one of which is . Since the diagonals are congruent, this is equal to half the square of  :

Example Question #401 : Gmat Quantitative Reasoning

Given square FGHI, answer the following

Square1

If square  represents the surface of an ancient arena discovered by archaeologists, what is the area of the arena?

Possible Answers:

Correct answer:

Explanation:

This problem requires us to find the area of a square. Don't let the story behind it distract you, it is simply an area problem. Use the following equation to find our answer:

 is the length of one side of the square; in this case we are told that it is , so we can solve accordingly!

Example Question #2 : Calculating The Area Of A Square

Squares

Note: Figure NOT drawn to scale

Refer to the above figure, which shows Square  and Square  and Square  has area 49. Give the area of Square .

Possible Answers:

Correct answer:

Explanation:

Square  has area 49, so each of its sides has as its length the square root of 49, or 7. Each side of Square  is therefore a hypotenuse of a right triangle with legs 1 and , so each sidelength, including , can be found using the Pythagorean Theorem:

The square of this, which is 37, is the area of Square .

Example Question #401 : Gmat Quantitative Reasoning

Squares

Note: Figure NOT drawn to scale

Refer to the above figure, which shows Square  and Square  and Square  has area 25. Give the area of Square .

Possible Answers:

Correct answer:

Explanation:

Square  has area 25, so each side has length the square root of 25, or 5. 

Specifically, , and, as given, .

Since  is a right triangle with hypotenuse  and legs  and  can be found using the Pythagorean Theorem:

 

The area of  is 

 

Since all four triangles, by symmetry, are congruent, all have this area. the area of Square  is the area of Square  plus the areas of the four triangles, or .

Example Question #11 : Calculating The Area Of A Square

Squares

Note: Figure NOT drawn to scale

Refer to the above figure, which shows Square  and Square . The ratio of  to  is 13 to 2. What is the ratio of the area of Square  to that of Square ?

Possible Answers:

Correct answer:

Explanation:

To make this easier, assume that  and  - the reasoning generalizes. Then Square  has sidelength 15 and area . The sidelength of Square , each side being a hypotenuse of a right triangle with legs 2 and 13, is 

.

The square of this, 173, is the area of Square .

The ratio is .

Example Question #171 : Geometry

Squares

Note: Figure NOT drawn to scale

Refer to the above figure, which shows Square  and Square .  The ratio of  to  is 7 to 1.

Which of these responses comes closest to what percent the area of Square  is of that of Square ?

 

Possible Answers:

Correct answer:

Explanation:

To make this easier, assume that  and ; the results generalize. 

Each side of Square  has length 8, so the area of Square  is 64. 

Each of the four right triangles has legs 7 and 1, so each has area ; Square  has area four times this subtracted from the area of Square , or

.

The area of Square  is

of that of Square .

Of the five choices, 80% comes closest.

Example Question #61 : Quadrilaterals

The perimeter of a square is the same as the circumference of a circle with area 100. What is the area of the square?

Possible Answers:

Correct answer:

Explanation:

The formula for the area of a circle is

.

If the area is 100, the radius is as follows:

The circle has circumference  times its radius, or

This is also the perimeter of the square, so the sidelength of the square is one-fourth this, or

The area of the square is the square of this, or 

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