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# What does q equal in the figure shown above where ABCD is a rectangle?

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Math Expert
Joined: 02 Sep 2009
Posts: 60555
What does q equal in the figure shown above where ABCD is a rectangle?  [#permalink]

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13 Nov 2019, 02:21
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Difficulty:

55% (hard)

Question Stats:

60% (02:13) correct 40% (02:55) wrong based on 25 sessions

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What does q equal in the figure shown above where ABCD is a rectangle?

(1) The length of line segment AM is the same as the length of line segment LM.

(2) The length of line segment LN is the same as the length of line segment DN.

Are You Up For the Challenge: 700 Level Questions

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Untitled.png [ 19.19 KiB | Viewed 324 times ]

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Re: What does q equal in the figure shown above where ABCD is a rectangle?  [#permalink]

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13 Nov 2019, 02:44
It will be 80 degree. But where are the options???

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Joined: 02 Sep 2009
Posts: 60555
Re: What does q equal in the figure shown above where ABCD is a rectangle?  [#permalink]

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13 Nov 2019, 02:46
chowdhurysakib71 wrote:
It will be 80 degree. But where are the options???

Posted from my mobile device

This is a data sufficiency question. Options for DS questions are always the same.

The data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), you must indicate whether—

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

I suggest you to go through the following post ALL YOU NEED FOR QUANT.

Hope this helps.
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What does q equal in the figure shown above where ABCD is a rectangle?  [#permalink]

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13 Nov 2019, 09:14
2
Bunuel wrote:

What does q equal in the figure shown above where ABCD is a rectangle?

(1) The length of line segment AM is the same as the length of line segment LM.

(2) The length of line segment LN is the same as the length of line segment DN.

Are You Up For the Challenge: 700 Level Questions

Statement 1:
If we fix the rectangle, AK, and LM, we can tweak point N and LN's position so angle q can vary, insufficient.

Statement 2:
If we fix the rectangle, DK, and LN, we can tweak point M and LM's position so angle q can vary, insufficient.

Combined:
Let angle KAD = a and angle KDA = b. We know a + b = 100 from triangle KDA. From statement 1, angle MLA = LAM = a. From statement 2, angle DLN = LDN = b. Then observe the 180 degree angle q lies on, we have q + a + b = 180, which is q + 100 = 180.

Ans: C

Attachment:

labelled angles.png [ 35.95 KiB | Viewed 215 times ]

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What does q equal in the figure shown above where ABCD is a rectangle?   [#permalink] 13 Nov 2019, 09:14
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