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Math Expert V
Joined: 02 Sep 2009
Posts: 58318
In the figure above, point D is on AC. What is the degree measure of  [#permalink]

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Difficulty:   5% (low)

Question Stats: 88% (01:03) correct 12% (01:30) wrong based on 1383 sessions

HideShow timer Statistics In the figure above, point D is on AC. What is the degree measure of ∠BAC?

(1) The measure of ∠BDC is 60°
(2) The degree measure of BAC is less than the degree measure of BCD.

Attachment: 2016-06-17_1624.png [ 27.72 KiB | Viewed 17857 times ]

Attachment: DS17639_f001.jpg [ 8.93 KiB | Viewed 8896 times ]

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Re: In the figure above, point D is on AC. What is the degree measure of  [#permalink]

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The diagram is not clear is 20 the angle measure of ABD or length of BD?
Math Expert V
Joined: 02 Sep 2009
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Re: In the figure above, point D is on AC. What is the degree measure of  [#permalink]

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Senthil7 wrote:
The diagram is not clear is 20 the angle measure of ABD or length of BD?

___________
It's angle ABD.
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Re: In the figure above, point D is on AC. What is the degree measure of  [#permalink]

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Thanks. Answer is A
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Re: In the figure above, point D is on AC. What is the degree measure of  [#permalink]

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4
Case1 : angle BDC = 60 deg

Angle BDC + Angle BDA = 180 degree ( as points ADC form a straight line )

If angle BDC = 60.
Then angle BDA = 180 - 60 =120

The sum of the angles of triangle ABD = 180 degrees.

Angle BDA + Angle ABD + angle BAD = 180 degree

I.e. 120 + 20 + angle BAD = 180 degree.

Angle BAD = angle BAC = 40 degs

Case 2 : clearly insufficient

Therefore A is the correct answer.

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Re: In the figure above, point D is on AC. What is the degree measure of  [#permalink]

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2
IMO A
1).bdc is known
therefore bda=180-bdc
dba=20
so bda+dba+dab=180.
sufficient
2)BCA<BDC
this doesnit give us any information
Insufficient
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Re: In the figure above, point D is on AC. What is the degree measure of  [#permalink]

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Bunuel wrote: In the figure above, point D is on AC. What is the degree measure of ∠BAC?

(1) The measure of ∠BDC is 60°
(2) The degree measure of BAC is less than the degree measure of BCD.

Attachment:
2016-06-17_1624.png

Figure appears to be mirror-image. Could you please correct it
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Re: In the figure above, point D is on AC. What is the degree measure of  [#permalink]

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2
Bunuel wrote: In the figure above, point D is on AC. What is the degree measure of ∠BAC?

(1) The measure of ∠BDC is 60°
(2) The degree measure of BAC is less than the degree measure of BCD.

Attachment:
2016-06-17_1624.png

We are given the following diagram: We need to determine the degree measure of ∠BAC, which is also the degree measure of ∠BAD.

Statement One Alone:

The measure of ∠BDC is 60°.

We can fill the above information into our diagram. Since ∠ADB and ∠BDC are supplementary, their total degree measurement is equal to 180.

Thus, m∠ADB = 180 – 60 = 120 degrees.

Since we have 2 of the 3 angles in triangle ABD, we can determine the measure of ∠BAC:

m∠BAC = 180 – 120 – 20 = 40 degrees.

Statement one alone is sufficient to answer the question. We can eliminate answer choices B, C, and E.

Alternate solution:

We can see that ∠ADB is an exterior angle of triangle ABD, and it is equal to the sum of the measures of ∠BAD and ∠ABD (recall that the measure of an exterior angle of a triangle is the sum of the measures of the two remote interior angles).

Therefore, m∠BAD = m∠ADB - m∠ABD = 60 - 20 = 40 degrees.

Statement Two Alone:

The degree measure of ∠BAC is less than the degree measure of ∠BCD.

Knowing that the measure of ∠BAC is less than the measure of ∠BCD does not allow us to determine the measure of ∠BAC. Statement two is not sufficient.

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Intern  Joined: 19 Jun 2018
Posts: 2
Re: In the figure above, point D is on AC. What is the degree measure of  [#permalink]

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Hi, I have been practicing for the gmat for a while now and never struggled much with a question, but I've spend hours reading the explanation of this question and still don't get it. Maybe there is something wrong in my basic triangle knowledge.

Things that confuse me:
- Is there a difference between ''measure of'' and ''degree measure of'' and what is this difference?
- Is there a difference between m∠ADB and m∠ABD and what is this difference?
- What does the 20 mean? I assumed this was the angle degree of ∠BAD but this does not seem to be the case
-The first option gives ∠BDC is 60 degrees, why is this in the answers placed next to the letter D, and not near B, since it gives the angle of BDC?

I probably make one or more basic trangle calculating mistakes but it would be really nice if someone could explain this to me!
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Joined: 22 Aug 2013
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Location: India
Re: In the figure above, point D is on AC. What is the degree measure of  [#permalink]

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1
KoenvZandvoort wrote:
Hi, I have been practicing for the gmat for a while now and never struggled much with a question, but I've spend hours reading the explanation of this question and still don't get it. Maybe there is something wrong in my basic triangle knowledge.

Things that confuse me:
- Is there a difference between ''measure of'' and ''degree measure of'' and what is this difference?
- Is there a difference between m∠ADB and m∠ABD and what is this difference?
- What does the 20 mean? I assumed this was the angle degree of ∠BAD but this does not seem to be the case
-The first option gives ∠BDC is 60 degrees, why is this in the answers placed next to the letter D, and not near B, since it gives the angle of BDC?

I probably make one or more basic trangle calculating mistakes but it would be really nice if someone could explain this to me!

Hello
I will try to answer as per my knowledge

- 'measure of' and 'degree measure of' mean almost same. Although we can measure an angle in 'radians' also than degrees (180 degrees means 'pi' radians), but for GMAT purpose, measure of an angle can be taken to mean 'degree measure of' an angle

- measure of ADB is indeed DIFFERENT from measure of ABD. Its always the alphabet in the middle of which the measure is being spoken about. Eg, in our given figure, '20 degrees' is the measure of angle ABD, and its NOT the measure of angle ADB or angle BAD

- what does 20 mean? I think I have answered this question above

- as I said, angle BDC is the measure of angle D (the alphabet in the middle), its NOT the measure of angle DBC or angle BCD
Intern  Joined: 19 Jun 2018
Posts: 2
Re: In the figure above, point D is on AC. What is the degree measure of  [#permalink]

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Yes, thanks a lot! i always learned to look at the first letter, by looking at the middle its all clear and easy to me. Weird how that differs per country/region. Thanks a lot for the explanation!
Intern  S
Joined: 11 Sep 2017
Posts: 36
Re: In the figure above, point D is on AC. What is the degree measure of  [#permalink]

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2
Can I say for statement 2, as any other angle is not given hence not sufficient.

Ie to determine a angle we need two angles ..
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Intern  Joined: 13 Jun 2018
Posts: 1
Re: In the figure above, point D is on AC. What is the degree measure of  [#permalink]

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Where are the answer options?
Math Expert V
Joined: 02 Sep 2009
Posts: 58318
Re: In the figure above, point D is on AC. What is the degree measure of  [#permalink]

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luckyleo wrote:
Where are the answer options?

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.
D. EACH 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 posts:
ALL YOU NEED FOR QUANT.
Ultimate GMAT Quantitative Megathread

Hope this helps.
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Re: In the figure above, point D is on AC. What is the degree measure of  [#permalink]

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Hello.

Has anyone noticed that the answer to this question in the Answer Key of the OFFICIAL GUIDE is C !? I'm shocked that the OFFICIAL guide could make such an error. Can anyone explain? This is question number 237 in the official GMAT guide.

Thanks. Re: In the figure above, point D is on AC. What is the degree measure of   [#permalink] 06 May 2019, 06:33
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