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555-605 Level|   Geometry|            
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С. only both can let us a square.
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yogachgolf
why 'a' is insuff?


you can imagine four sticks with same length that are pinned by hinges. you can easily transform the square to a different rhombuses and even to a line.
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Is quadrilateral Q a square?
(1) The sides of Q have the same length.
(2) The diagonals of Q have the same length


C

Here il post u a drawing.
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Statement 1 is not sufficient since a rhombus has 4 equal sides as well.

Statement 2 is not sufficient since a rectangle has equal diagonals.

Statements 1 and 2 are sufficient.
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walker
С. only both can let us a square.

why 'a' is insuff?

Because it can be a parellogram or rhombus..

In a parallelogram, not all the sides have the same length from what I understand.
Or am I missing something?
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HI Bunnel,

As you have mentioned that Parallelogram can have four sides equal then definitely its diagonals are also equal and it will become square. why A is not right?
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A is insufficient cause rhombus is a quadrilateral with four sides & diagonals of dfferent lengths
B is insufficient cause a uniform Trapezoid has both the diagonals equal..

C is sufficient as trapezoid and rhombus are both eliminated.Hence a square
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yogachgolf
Is quadrilateral Q a square?
(1) The sides of Q have the same length.
(2) The diagonals of Q have the same length

C

Here il post u a drawing.

This is an incorrect explanation cause a hexagon is not a quadrilateral and instead a uniform trapezium or a rectangle is a better alternative
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yogachgolf
Is quadrilateral Q a square?

(1) The sides of Q have the same length.
(2) The diagonals of Q have the same length


Statement I is insufficient:

Rhombus have same lengths and so does a square.

Statement II is insufficient:

Sides may or may not be same.

Combining is sufficient:

If sides are same and diagonals are same which means all the sides must intersect at ninety degrees hence answer is c.
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C is the answer as it can be solved by using both the statements.
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Just to be a bit more clearer to learners like myself - Rhombuses DONT have diagonals of equal length.

If the diagonals of a parallelogram are of equal length then the shape is a rectangle or square.

So if the diagonals of a rhombus are equal then the shape is a square.
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Parallelogram is a "parent" of some other quadrilaterals

Similar Questions:
https://gmatclub.com/forum/is-quadrilat ... 27888.html
https://gmatclub.com/forum/is-quadrilat ... 94321.html
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