DSQ: Calculating the perimeter of a rectangle - GMAT Quantitative

Let be the sidelength of the square. Then its perimeter is .

From Statement 1 alone, the length of the rectangle is , and, if is the width, the perimeter of the rectangle is . Therefore, we can prove that the rectangle has the greater perimeter.

From Statement 2 alone, the width of the rectangle is , and its perimeter is at least - but unless we know the length, we do not know whether the total perimeter is greater than, equal to, or less than .

To find perimeter we need length and width. We are given the length.

I) Is irrelevant.

II) We are given a way of relating area and width. Since we know that area is length times width, we can use II to set up an equation where we substitute in the known length along with the given statement to solve for our width

Solve the second one for w and you're good to go!

.

Therefore the perimeter would be:

To find perimeter, we need the lengths of both sides.

I) Gives us the area, which gives us one equation and two unknowns. Alone this statement is not sufficient.

II) Gives us one side length of the field.

We can use this with I) to find the other side length.

Once we have both sides, we can find perimeter easily.

Thus the perimeter is,

.

Statement 1: Although the area is given, we need more information in order to answer the question.

but this can means our dimenions are or

Statement 2: We're told the width measures which means our dimensions are .

Using BOTH statements, we can find the perimeter:

Statement 1 alone provides insufficient information. For example:

Case 1:

The area of a rectangle with these dimensions is their product, which is 120; this exceeds 100.

Case 2:

The area of a rectangle with these dimensions is their product, which is 480; this exceeds 100.

Assume Statement 2 alone. The perimeter of a rectangle is twice the sum of their dimensions, so

, answering the question in the affirmative.

To know the perimeter of a rectangle, we need to know length and width.

Statement (1) provides Area, which does not provide the necessary information. NOT SUFFICIENT

Statement(2) provides one side, but we still need the other to determine perimeter. NOT SUFFICIENT.

Both together are sufficent however since if we know one side and the area, we can find the remaining side using division, and then use the two side lengths to find the perimeter.

Let be the sidelength of the square. Then its perimeter is .

From Statement 1 alone, the length of the rectangle is , and, if is the width, the perimeter of the rectangle is . Therefore, we can prove that the rectangle has the greater perimeter.

From Statement 2 alone, the width of the rectangle is , and its perimeter is at least - but unless we know the length, we do not know whether the total perimeter is greater than, equal to, or less than .

To find perimeter we need length and width. We are given the length.

I) Is irrelevant.

II) We are given a way of relating area and width. Since we know that area is length times width, we can use II to set up an equation where we substitute in the known length along with the given statement to solve for our width

Solve the second one for w and you're good to go!

.

Therefore the perimeter would be:

To find perimeter, we need the lengths of both sides.

I) Gives us the area, which gives us one equation and two unknowns. Alone this statement is not sufficient.

II) Gives us one side length of the field.

We can use this with I) to find the other side length.

Once we have both sides, we can find perimeter easily.

Thus the perimeter is,

.

Statement 1: Although the area is given, we need more information in order to answer the question.

but this can means our dimenions are or

Statement 2: We're told the width measures which means our dimensions are .

Using BOTH statements, we can find the perimeter:

Statement 1 alone provides insufficient information. For example:

Case 1:

The area of a rectangle with these dimensions is their product, which is 120; this exceeds 100.

Case 2:

The area of a rectangle with these dimensions is their product, which is 480; this exceeds 100.

Assume Statement 2 alone. The perimeter of a rectangle is twice the sum of their dimensions, so

, answering the question in the affirmative.

To know the perimeter of a rectangle, we need to know length and width.

Statement (1) provides Area, which does not provide the necessary information. NOT SUFFICIENT

Statement(2) provides one side, but we still need the other to determine perimeter. NOT SUFFICIENT.

Both together are sufficent however since if we know one side and the area, we can find the remaining side using division, and then use the two side lengths to find the perimeter.

Let be the sidelength of the square. Then its perimeter is .

From Statement 1 alone, the length of the rectangle is , and, if is the width, the perimeter of the rectangle is . Therefore, we can prove that the rectangle has the greater perimeter.

From Statement 2 alone, the width of the rectangle is , and its perimeter is at least - but unless we know the length, we do not know whether the total perimeter is greater than, equal to, or less than .

To find perimeter we need length and width. We are given the length.

I) Is irrelevant.

II) We are given a way of relating area and width. Since we know that area is length times width, we can use II to set up an equation where we substitute in the known length along with the given statement to solve for our width

Solve the second one for w and you're good to go!

.

Therefore the perimeter would be:

To find perimeter, we need the lengths of both sides.

I) Gives us the area, which gives us one equation and two unknowns. Alone this statement is not sufficient.

II) Gives us one side length of the field.

We can use this with I) to find the other side length.

Once we have both sides, we can find perimeter easily.

Thus the perimeter is,

.

Statement 1: Although the area is given, we need more information in order to answer the question.

but this can means our dimenions are or

Statement 2: We're told the width measures which means our dimensions are .

Using BOTH statements, we can find the perimeter:

Statement 1 alone provides insufficient information. For example:

Case 1:

The area of a rectangle with these dimensions is their product, which is 120; this exceeds 100.

Case 2:

The area of a rectangle with these dimensions is their product, which is 480; this exceeds 100.

Assume Statement 2 alone. The perimeter of a rectangle is twice the sum of their dimensions, so

, answering the question in the affirmative.

To know the perimeter of a rectangle, we need to know length and width.

Statement (1) provides Area, which does not provide the necessary information. NOT SUFFICIENT

Statement(2) provides one side, but we still need the other to determine perimeter. NOT SUFFICIENT.

Both together are sufficent however since if we know one side and the area, we can find the remaining side using division, and then use the two side lengths to find the perimeter.

Let be the sidelength of the square. Then its perimeter is .

From Statement 1 alone, the length of the rectangle is , and, if is the width, the perimeter of the rectangle is . Therefore, we can prove that the rectangle has the greater perimeter.

From Statement 2 alone, the width of the rectangle is , and its perimeter is at least - but unless we know the length, we do not know whether the total perimeter is greater than, equal to, or less than .