GMAT Math : Problem-Solving Questions

Study concepts, example questions & explanations for GMAT Math

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Example Questions

Example Question #11 : Calculating The Area Of A Square

The perimeter of a square is the same as the circumference of a circle with radius 8. What is the area of the square?

Possible Answers:

The correct answer is not among the other choices.

Correct answer:

Explanation:

A circle with radius 8 has as its circumference  times this, or 

.

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

.

The area is the square of this, or

.

Example Question #15 : Calculating The Area Of A Square

The perimeter of a square is the same as the length of the hypotenuse of a right triangle with legs 8 and 12. What is the area of the square?

Possible Answers:

The correct answer is not among the other responses.

Correct answer:

Explanation:

The length of the hypotenuse of a right triangle with legs 8 and 12 can be determined using the Pythagorean Theorem:

Since this is also the perimeter of the square, its sidelength is one fourth of this, or

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

Example Question #11 : Calculating The Area Of A Square

If the perimeter of a square is , what is its area?

Possible Answers:

Correct answer:

Explanation:

The perimeter of a square, and any shape for that matter, is found by adding up all the exterior sides. Since all sides are equal in a square, we can say: 

where  represents the length of a side

We can solve for the side length using the information provided:

The area of a square is found by squaring the side length: 

Example Question #411 : Problem Solving Questions

The perimeter of a square is . Give its area.

Possible Answers:

Correct answer:

Explanation:

The length of one side of a square is the perimeter divided by 4:

Square this to get the area:

Example Question #1 : Calculating The Perimeter Of A Square

A square plot of land has area 256 square yards. Give its perimeter in inches.

Possible Answers:

Correct answer:

Explanation:

The sidelength of a square is the square root of its area - in this case,  yards. Its perimeter is therefore four times that, or   yards. Multiply by 36 to convert to inches:

 inches.

Example Question #412 : Problem Solving Questions

Five squares have sidelengths 3, 4, 5, 6, and 7 meters. What is the mean of their perimeters?

Possible Answers:

Correct answer:

Explanation:

Multiply each sidelength by four to get the perimeters - they will be 12, 16, 20, 24, and 28 meters, respectively. The mean will be

 meters

Example Question #2 : Calculating The Perimeter Of A Square

Given Square , answer the following questions.

Square1

Square  represents a small field for a farmer's sheep. How many meters of fence will the farmer require to completely enclose the field?

Possible Answers:

Correct answer:

Explanation:

This question is a thinly veiled perimeter of a square question. To find the total amount of fencing needed, use the following formula:

Where  is the perimeter of a square, and  is the length of one side.

Example Question #3 : Calculating The Perimeter Of A Square

A given square has a side length of . What is its perimeter?

Possible Answers:

Not enough information provided

Correct answer:

Explanation:

In order to find the perimeter  of a given square with side length , we use the equation . Given , we can therefore conclude that 

Example Question #2 : Calculating The Perimeter Of A Square

A given square has an area of . What is its perimeter?

Possible Answers:

Not enough information provided

Correct answer:

Explanation:

We are told that the area  of the square is . We know the area of a square is defined as , where  is the length of the side of the square. We can therefore deduce that  and that 

In order to find the perimeter  of a given square with side length , we use the equation . Given , we can therefore conclude that .

Example Question #4 : Calculating The Perimeter Of A Square

A given square has a side of length . What is the perimeter of the square?

Possible Answers:

Not enough information provided

Correct answer:

Explanation:

In order to find the perimeter  of a given square with side length , we use the equation . Given , we can therefore conclude that 

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