Hi,
Question:
What is the area of rectangle ABCD?
i.e., Area of rectangle = l * w
We need to find the values of l *w or any relation which gives l*w
Statement I is insufficient:l^2 + 2lw + w^2 = 16
Immediately we can think of (a+b)^2 = a^2 + b^2 + 2ab.
(l+w)^2 = 16.
Taking square root on both sides(side length and area can’t be negative).
l+w = 4
But “l” and “w” can take different values.
l = w = 2. Then the area would be 4.
Or
l = 1 and w = 3. Then the area would be 3.
So insufficient.
Statement II is insufficient:l^2 – 2lw + w^2 = 4
similar to statement I, it is (a-b)^2 = a^2 + b^2 - 2ab
(l-w)^2 = 4.
Taking square root on both sides(side length and area can’t be negative).
l-w = 2
But “l” and “w” can take different values.
l =4 and w = 2. Then the area would be 8.
Or
l = 3 and w = 1. Then the area would be 3.
We can come up with different values of l and w. So area keep changing.
So insufficient.
Together it is sufficient.
l – w = 2
and l + w = 4
Solving we get l = 3 and w = 1
So, the area of the rectangle has to be 3.
So the answer is C (together sufficient).
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GMAT Mentors