Does the rectangle have an area less than 30?
(1) Perimeter = 20.
(2) Diagonal < 10.
The OA is A.
(1) 2L + 2W = 20 --> L + W = 10, max 5, 5; max area 25; 25 < 30. Sufficient.
(2) 1/2 rectangle = right triangle; a^2 + b^2 = c^2, c < 10 (6 - 8 - 10 right triangle); sides less than 6 & 8
given that, does the possibility of the L & W being any combo of #'s < 6&8 make it INS?
Hence, A is the correct answer.
Has anyone another strategic approach to solve this DS question? Regards!
Does the rectangle have an area less than 30?
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We have to find out whether the rectangle has an area of less than 30.BTGmoderatorLU wrote:Does the rectangle have an area less than 30?
(1) Perimeter = 20.
(2) Diagonal < 10.
The OA is A.
(1) 2L + 2W = 20 --> L + W = 10, max 5, 5; max area 25; 25 < 30. Sufficient.
(2) 1/2 rectangle = right triangle; a^2 + b^2 = c^2, c < 10 (6 - 8 - 10 right triangle); sides less than 6 & 8
given that, does the possibility of the L & W being any combo of #'s < 6&8 make it INS?
Hence, A is the correct answer.
Has anyone another strategic approach to solve this DS question? Regards!
Say the length and the breadth of the rectangle are a and b, respectively,
Thus we have to determine whether ab < 30.
Let's take each statement one by one.
(1) Perimeter = 20.
=> 2(a + b) = 20
=> a + b = 10
Note that for two numbers (here a and b), whose sum is constant (here 10), their product would be maximum if the numbers are equal.
Thus, the maximum value of a*b is when a = b = 10/2 = 5.
=> the maximum value of the area of the rectangle = a*b = 5*5 = 25 < 30. The answer is yes, the rectangle has an area of less than 30. Sufficient.
(2) Diagonal < 10.
=> a^2 + b^2 < 10^2
=> a^2 + b^2 < 100
Again, the maximum value of (a^2)*(b^2) would be attained when a^2 = b^2.
=> 2a^2 < 100 => a^2 < 50 => Maximum possible value of a = ~7.
Thus, the maximum value of (a^2)*(b^2) = (7^2)*(7^2) = 7^4
=> the maximum value of the area of the rectangle = a*b = sqrt[(a^2)*(b^2)] = sqrt[7^4] = 7^2 = 49 > 30. The answer is no, the rectangle does not have an area of less than 30.
Given a^2 + b^2 < 100, the minimum value of a*b can be too less than 30. Say a = b = 1, then 1^1 + 1^2 < 100. The area of the rectangle = a*b = 1*1 = 1 < 30. The answer is yes, the rectangle has an area of less than 30. Sufficient.
No unique answer. Insufficient.
The correct answer: A
Hope this helps!
-Jay
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