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Sufficient condition to be a rectangle

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by suchoudh » Sun Jan 24, 2010 3:49 pm
Is quadrilateral ABCD a rectangle?
(1) The diagonal AC divides ABCD into two congruent triangles.
(2) ABCD has at least two right angles and at least two equal sides.


(1) statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;
(2) statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;
(3) BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked;
(4) EACH statement ALONE is sufficient to answer the question asked;
(5) statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

OA 3

BTW, what is right, "Sufficient condition to be a rectangle" or "Sufficient condition for a rectangle"
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Source: — Data Sufficiency |
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by Amiman » Mon Jan 25, 2010 1:40 pm
I think the answer is E

1. The Diagonal of a Parallelogram also makes 2 congruent triangles but Parallelogram is not a rectangle - Insufficient
2. With 2 or 3 right angles and 2 or 3 equal sides, you can have a trapezium. With 4 right angles and 2 equal sides you can have a rectangle. With 4 right angles and 4 equal sides you can have a square - Insufficent

Combining both 1 & 2,

you can have either a sqaure or a rectangle but not rectangle only - Insufficient
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by Brent@GMATPrepNow » Mon Jan 25, 2010 2:31 pm
Amiman wrote:I think the answer is E

1. The Diagonal of a Parallelogram also makes 2 congruent triangles but Parallelogram is not a rectangle - Insufficient
2. With 2 or 3 right angles and 2 or 3 equal sides, you can have a trapezium. With 4 right angles and 2 equal sides you can have a rectangle. With 4 right angles and 4 equal sides you can have a square - Insufficent

Combining both 1 & 2,

you can have either a sqaure or a rectangle but not rectangle only - Insufficient
We should be careful with the statement that the figure is "either a square or a rectangle," since a square is a type of rectangle. It's just a special rectangle. In other words, it meets all criteria for a rectangle AND it happens to have 4 equal sides.

The answer is E and you can see this from the two possible quadrilaterals (given statements 1 and 2)

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by suchoudh » Mon Jan 25, 2010 4:19 pm
Thanks for explaining Brent.
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