GMAT Math : DSQ: Calculating the length of the diagonal of a square

Study concepts, example questions & explanations for GMAT Math

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Example Questions

Example Question #1 : Dsq: Calculating The Length Of The Diagonal Of A Square

Find the length of the diagonal of square G.

I) The area of G is  fathoms squared.

II) The side length of G is  fathoms.

Possible Answers:

Each statement alone is enough to solve the question.

Both statements taken together are sufficient to solve the problem.

Statement 2 is sufficient to solve the question, but statement 1 is not sufficient to solve the question.

Neither statement is sufficient to solve the question. More information is needed.

Statement 1 is sufficient to solve the question, but statement 2 is not sufficient to solve the question.

Correct answer:

Each statement alone is enough to solve the question.

Explanation:

We can use the side length and the Pythagorean Theorem to find the diagonal of a square.

We can find side length from area, so we could solve this with either I or II.

Example Question #2 : Dsq: Calculating The Length Of The Diagonal Of A Square

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The circle with center  is inscribed in square . What is the length of diagonal ?

(1) The area of the circle is .

(2) The side of the square is .

Possible Answers:

Statement 1 alone is sufficient.

Both statements together are sufficient.

Each statement alone is sufficient.

Statements 1 and 2 together are not sufficient.

Statement 2 alone is sufficient.

Correct answer:

Each statement alone is sufficient.

Explanation:

The diagonal of the square can be calculated as long as we have any information about the lengths or area of the circle or of the square.

Statement 1, by giving us the area of the circle, allows us to find the radius of the circle, which is half the length of the side. Therefore statement 1 alone is sufficient.

Statement 2, by telling us the length of a side of the square is also sufficient, and would allow us to calculate the length of the diagonal.

Therefore, each statement alone is sufficient.

Example Question #3 : Quadrilaterals

On your college campus there is a square grassy area where people like to hangout and enjoy the sun. While walking with some friends, you decide to take the shortest distance to the corner of the square opposite from where you are. Find the distance you traveled.

I) The perimeter of the square is  meters.

II) The square covers an area of  square meters.

Possible Answers:

Neither statement is sufficient to answer the question. More information is needed.  

Either statement is sufficient to answer the question.

Statement I is sufficient to answer the question, but statement II is not sufficient to answer the question. 

Statement II is sufficient to answer the question, but statement I is not sufficient to answer the question.

Both statements are needed to answer the question.

Correct answer:

Either statement is sufficient to answer the question.

Explanation:

We are asked to find the length of a diagonal of a square.

We can do this if we have the side length. We can find side length from either perimeter or area.

 

From Statement I)

In this case, our side length is 15 meters.

We can use this and Pythagorean Theorem or 45/45/90 triangles to find our diagonal.

From Statement II)

From here, we can plug the side length into the Pythagorean Theorem like before and solve for the diagonal.

Therefore, either statement alone is sufficient to answer the question.

 

Example Question #4 : Quadrilaterals

Find the length of the diagonal of square A if the diagonal of square B is .

  1. The perimeter of square B is 
  2. The area of square A is 
Possible Answers:

Each statement alone is sufficient to answer the question.

Statements 1 and 2 are not sufficient, and additional data is needed to answer the question.

Statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question.

Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient.

Statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question.

Correct answer:

Statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question.

Explanation:

Statement 1: The information provided would only be useful if the ratio of square A to square B was known. 

Statement 2: We need the length of the square's side to find the length of the diagonal and we can use the area to solve for the length of the side. 

Now we can find the diagonal: 

Example Question #5 : Quadrilaterals

What is the length of the diagonal of the square?

  1. The area of the square is .
  2. The perimeter is .
Possible Answers:

Statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question.

Statements 1 and 2 are not sufficient, and additional data is needed to answer the question.

Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient.

Statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question.

Each statement alone is sufficient to answer the question.

Correct answer:

Each statement alone is sufficient to answer the question.

Explanation:

The length of the diagonal of a square is given by , where  represents the square's side. As such, we need the length of the square's side.

Statement 1: 

Statement 2: 

Both statements provide us with the length of the square's side. 

Example Question #6 : Quadrilaterals

The diagonal bracing of a square pallet measures . What is the area of the pallet?

Possible Answers:

Correct answer:

Explanation:

Squarecut To solve this problem, we must recognize that the diagonal bisector creates identical 45˚ - 45˚ - 90˚ right triangles. This means that, if the sides of the square are  then the diagonal must be . We can then set up the following equation:

If  then the area must be:

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