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Does x = y? (1) z = u (2) ABCD is a parallelogram

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Does x = y? (1) z = u (2) ABCD is a parallelogram  [#permalink]

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New post 17 Oct 2017, 23:42
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

56% (00:36) correct 44% (00:38) wrong based on 45 sessions

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Re: Does x = y? (1) z = u (2) ABCD is a parallelogram  [#permalink]

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New post 18 Oct 2017, 06:52
Question: x = y?

St1: z = u
y + z + B = 180 --> y + z = 180 - B
x + u + D = 180 --> x + u = 180 - D
We do not know whether B = D. Hence we cannot prove that x = y.
Not Sufficient.

St2: ABCD is a parallelogram --> B = D and x + y = u + z
Not sufficient.

Combining St1 and St2, we have
y + u = 180 - B
x + u = 180 - B (since B = D)
So, x = 180 - B - u = y
Sufficient.

Answer: C
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Re: Does x = y? (1) z = u (2) ABCD is a parallelogram  [#permalink]

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New post 18 Oct 2017, 07:08
Bunuel wrote:
Image
Does x = y?

(1) z = u
(2) ABCD is a parallelogram


Attachment:
2017-10-18_1040.png


S1 - z=u
But we don't know anything else, x and y could be or could not be equal.
Insufficient.
S2 - ABCD is a parallelogram and AC is the diagonal.
Therefore, y=u and x=z (Alternate angles of a line intersecting two parallel lines are equal)
But we don't know if x=y
Insufficient.

Combining S1 & S2, x=z=u=y
Sufficient
Answer C.
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Re: Does x = y? (1) z = u (2) ABCD is a parallelogram  [#permalink]

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New post 23 Oct 2017, 18:11
B, I got this wrong and I see what I did here, assuming I am wrong. I assumed that the diagonal bisected the angles in a parallelogram, but that's only the case if it's a rhombus.
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Re: Does x = y? (1) z = u (2) ABCD is a parallelogram &nbs [#permalink] 23 Oct 2017, 18:11
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