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what should be the answer?

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what should be the answer?

by sana.noor » Fri Jul 05, 2013 7:04 am
Is the quadilateral a rectangle ?

1) Two of the sides measure 6 long and 2 of them measure 8 long.

2) the diagonals are perpendicular to each other.

the answer is C but i guess it should be B because we know that in rectangle the diagonals arnt perpendicular to each other.
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by faraz_jeddah » Sat Jul 06, 2013 8:26 am
sana.noor wrote:Is the quadilateral a rectangle ?

1) Two of the sides measure 6 long and 2 of them measure 8 long.

2) the diagonals are perpendicular to each other.

the answer is C but i guess it should be B because we know that in rectangle the diagonals arnt perpendicular to each other.
Good Question. Whats the explanation?
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by sana.noor » Sat Jul 06, 2013 8:34 am
to be a rectangle following are the conditions
1) a parallelogram with at least one right angle
2) a quadrilateral with four right angles
3) equrangle
4) a parallelogram with diagnoals of equal lenght
However, the only thing that is confusing is "to consider square in this case as square is a special type of rectangle". if we are considering square in this case then the answer will be C but if not then it will be B
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by Brent@GMATPrepNow » Sun Jul 07, 2013 5:45 am
sana.noor wrote: the answer is C but i guess it should be B because we know that in rectangle the diagonals arnt perpendicular to each other.
A rectangle is a quadrilateral (4-sided figure) with 4 right angles.
Given this definition, a square is a type of rectangle. In a square, the diagonals are perpendicular to each other. So, statement 2 does not rule out the possibility that the quadrilateral is a rectangle.

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by Brent@GMATPrepNow » Sun Jul 07, 2013 5:58 am
sana.noor wrote:Is the quadrilateral a rectangle ?

1) Two of the sides measure 6 long and 2 of them measure 8 long.

2) The diagonals are perpendicular to each other.
Target question: Is the quadrilateral a rectangle?

Statement 1: Two of the sides measure 6 long and 2 of them measure 8 long.
The two quadrilaterals below both satisfy the condition in statement 1.
Image
So, the quadrilateral could be a rectangle, or the quadrilateral might not be a rectangle
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The diagonals are perpendicular to each other.
The two quadrilaterals below both satisfy the condition in statement 2.
Image
IMPORTANT: As I mentioned in my earlier post, a square is a type of rectangle.
So, the quadrilateral could be a rectangle, or the quadrilateral might not be a rectangle
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined:
Consider statement 2 first. If the diagonals are perpendicular to each other, then the quadrilateral could be a rectangle AS LONG AS THAT RECTANGLE IS A SQUARE.
Then, when we consider statement 1 (two sides of length 6 and two sides of length 8), we see that we cannot have a square.
So, from this, we can be certain that the quadrilateral is not be a rectangle
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

By the way, the shape looks something like this:
Image

Answer = C

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