Is quadrilateral PQRS a parallelogram?

(1) Adjacent sides PQ and QR have the same length.
(2) Adjacent sides RS and SP have the same length.


DS51602.01
OG2020 NEW QUESTION
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The Logical approach to this question starts with the notion that the GMAC uses 5 different ways to tell us that a certain quadrilateral is a parallelogram:
1. We're given two pairs of equal opposite sides.
2. We're given two pairs of parallel sides.
3. We're given one pair of sides that are equal and parallel.
4. We're given two pairs of equal opposite angles.
5. The question states 'In the figure above, ABCD is a parallelogram...".
In this particular question it is the ADJACENT SIDES that are equal, which means that even if both statements are taken into account, all we know is that it is a deltoid. Can it be a parallelogram? Sure, if all 4 sides are equal (i.e. a rhombus), but it doesn't have to be.
The correct answer is (E).

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Hi All,

We're asked if quadrilateral PQRS is a parallelogram? This is a YES/NO question can be answered with a bit of logic (and a couple of drawings). By definition, a parallelogram must have 4 sides and each pair of 'opposite' sides must be parallel.

1) Adjacent sides PQ and QR have the same length.

'Adjacent' sides refer to two sides that are next to one another (and meet at a point):
-A Square fits this description - and is a parallelogram, so the answer to the question is YES.
-Any other 4-sided shape with 2 equal sides that touch and 2 others sides that are NOT the same length as the first 2 - that's NOT a parallelogram, so the answer to the question is NO.
Brent's explanation provides a nice example of the second shape.
Fact 1 is INSUFFICIENT

2) Adjacent sides RS and SP have the same length.

Fact 2 essentially provides the same information that Fact 1 provides (but about the other 2 sides). The examples that fit Fact 1 also fit Fact 2 - and lead us to two different answers (one "YES" and one "NO").
Fact 2 is INSUFFICIENT

Combined, we know...
1) Adjacent sides PQ and QR have the same length.
2) Adjacent sides RS and SP have the same length.

Even with both Facts, we can end up with shapes that are parallelograms or not, so the answer to the question is inconsistent.
Combined, INSUFFICIENT

Final Answer:

GMAT assassins aren't born, they're made,
Rich
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