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23 Dec 2020, 19:00
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D
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Difficulty:
65%
(hard)
Question Stats:
56% (02:15) correct
44%
(02:06)
wrong
based on 208
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12 Days of Christmas GMAT Competition with Lots of Fun
Is the perimeter of a rectangle more than 60 cm ?
(1) The area of the rectangle is 226 cm^2.
(2) The length of a diagonal of the rectangle is 30 cm.
M36-92
Is the perimeter of a rectangle more than 60 cm ?
(1) The area of the rectangle is 226 cm^2.
(2) The length of a diagonal of the rectangle is 30 cm.
M36-92
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Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
statement 1:
Area is 226 cm^2
assume Square, l=b
then l^2 = 226
l=15.xx (approx)
so perimeter 4l is more than 60. For rectangle then l is greater than breadth. so obviously perimeter is greater than 60
Hence Statement 1 is sufficient
Statement 2:
hypotenuse is 30. That means sum of two sides should be greater than 30. Hence perimeter will be greater than 60.
So Statement 2 is also sufficient.
Hence option D
Area is 226 cm^2
assume Square, l=b
then l^2 = 226
l=15.xx (approx)
so perimeter 4l is more than 60. For rectangle then l is greater than breadth. so obviously perimeter is greater than 60
Hence Statement 1 is sufficient
Statement 2:
hypotenuse is 30. That means sum of two sides should be greater than 30. Hence perimeter will be greater than 60.
So Statement 2 is also sufficient.
Hence option D
23 Dec 2020, 19:40
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My answer is (D): Either (1）or (2) is SUFFICIENT.
(1) The area of the rectangle is 226 cm^2.
Consider a square with 60 cm perimeter. Its area is 15 * 15 = 225, which is smaller than 226.
And we know that for a given rectangle of 60 cm, square yields the largest area.
So, if the area of the rectangle is 226 cm^2, its rectangle must be more than 60cm. (Otherwise, the maximum area is 225 cm^2)
SUFFICIENT
(2) The length of a diagonal of the rectangle is 30 cm.
That means the sum of the length and height of the rectangle is > 30cm.
So the perimeter of a rectangle is > 60cm.
SUFFICIENT.
(1) The area of the rectangle is 226 cm^2.
Consider a square with 60 cm perimeter. Its area is 15 * 15 = 225, which is smaller than 226.
And we know that for a given rectangle of 60 cm, square yields the largest area.
So, if the area of the rectangle is 226 cm^2, its rectangle must be more than 60cm. (Otherwise, the maximum area is 225 cm^2)
SUFFICIENT
(2) The length of a diagonal of the rectangle is 30 cm.
That means the sum of the length and height of the rectangle is > 30cm.
So the perimeter of a rectangle is > 60cm.
SUFFICIENT.
