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M03 02: Is quadrilateral J a square?

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M03 02: Is quadrilateral J a square? [#permalink] New post 26 Oct 2012, 23:46
Is quadrilateral J a square?

(1) All sides of J are equal.

(2) The area of J is a multiple of 10.

----- My ans : C (BOTH statements TOGETHER are sufficient)

based on above to statement: to find diagonal (as to prove it is square , we need to prove that all angels are 90)..
i thght : sqrt (10 ^2 + 10^2) = diagonal (i.e. \sqrt{2} (10^2)). therefore, 1:1:\sqrt{2} triangle that means angle between the sides of quadilateral is 90.

therefore , sufficient .
But is my fault that i am assuming two equal angles are 45. It can be 30 , right?
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Re: M03 02: Is quadrilateral J a square? [#permalink] New post 26 Oct 2012, 23:55
greatps24 wrote:
Is quadrilateral J a square?

(1) All sides of J are equal.

(2) The area of J is a multiple of 10.

----- My ans : C (BOTH statements TOGETHER are sufficient)

based on above to statement: to find diagonal (as to prove it is square , we need to prove that all angels are 90)..
i thght : sqrt (10 ^2 + 10^2) = diagonal (i.e. \sqrt{2} (10^2)). therefore, 1:1:\sqrt{2} triangle that means angle between the sides of quadilateral is 90.

therefore , sufficient .
But is my fault that i am assuming two equal angles are 45. It can be 30 , right?


Basically, for a square - all sides must be equal and all angles must be 90.

Statement 1 tells us that all sides are equal. But it could still be a rhombus. all angles may or may not be 90. So you cant say conclusively whether its a square or not. Not sufficient.
Statement 2 tells us that area is multiple of 10. This actually doesnt give us anything about sides or shape. Not sufficient.

Combining these two we know that all sides are equal and area is multiple of 10. But it still doesnt give you any clue about shape , it could still be a rhombus and square both.

Hence ans should be E.

Hope it helps.
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Re: M03 02: Is quadrilateral J a square?   [#permalink] 26 Oct 2012, 23:55
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M03 02: Is quadrilateral J a square?

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