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# Is quadrilateral PQRS a parallelogram? (1) Adjacent sides PQ and QR

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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

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Bunuel wrote:

(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

Statement One Alone:

Adjacent sides PQ and QR have the same length.

Quadrilateral PQRS might or might not be a parallelogram. For example, if RS and SP also have the same length as PQ and QR (for example, PQ = QR = RS = SP = 4), then it’s a parallelogram (in fact, it’s a rhombus). On the other hand, if RS and SP don’t have the same length as PQ and QR (for example, PQ = QR = 4 and RS = SP = 5), then it’s not a parallelogram. Statement one alone is not sufficient.

Statement Two Alone:

Adjacent sides RS and SP have the same length.

Quadrilateral PQRS might or might not be a parallelogram. For example, if PQ and QR also have the same length as RS and SP (for example, RS = SP = PQ = QR = 4), then it’s a parallelogram (in fact, it’s a rhombus). On the other hand, if PQ and QR don’t have the same length as RS and SP (for example, RS = SP = 4 and PQ = QR = 5), then it’s not a parallelogram. Statement two alone is not sufficient.

Statements One and Two Together:

Even with two statements, quadrilateral PQRS might or might not be a parallelogram. If all 4 sides have the same length (for example, PQ = QR = RS = SP = 4), then it’s a parallelogram (in fact, it’s a rhombus). However, if PQ = QR = 4 and RS = SP = 5, then it’s not a parallelogram.

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Bunuel wrote:

(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

The Features of Parallelogram are;

Two pairs of opposite sides are parallel (by definition).
Two pairs of opposite sides are equal in length.
Two pairs of opposite angles are equal in measure.

Insufficient.

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Hey Bunuel , is there any article available on how to identify figures because I have seen that such questions are widely repeated in GMAT land?
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gagan0303 wrote:
Hey Bunuel , is there any article available on how to identify figures because I have seen that such questions are widely repeated in GMAT land?

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Bunuel wrote:

(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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