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# In triangle ABC, if AB = a, BC = b + 1/2, and AC = b, which of the

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In triangle ABC, if AB = a, BC = b + 1/2, and AC = b, which of the [#permalink]

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16 Sep 2017, 05:49
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In triangle ABC, if AB = a, BC = b + 1/2, and AC = b, which of the three angles has the greatest degree measure?

(1) b = a + 3/2
(2) a = 1/2

[Reveal] Spoiler:
Question from GMATFree dot com - Data Sufficiency, Module 37 #7. Their explanation is also on Youtube at watch?v=h_owg_Q_25Y
This question is similar to the greatest degree measure question from the Official Guide (Question 19 page 276, that question is discussed on the forum here. I can't post URLs yet, but if you search "Greatest Degree Measure" it comes up.) but it uses different numbers, & statements (1) and (2) are slightly different.

The answer from GMATFree is A. (1) alone is sufficient but (2) alone is not sufficient.

However, I think (2) alone would also be sufficient & therefore the answer would be D.
If a=1/2, then no matter what value b is, side BC will always be longest & therefore angleBAC will always be the greatest.
- Example 1: With a=1/2, if we say that b=5, then side AB is the smallest at 1/2 & side BC is the biggest at b+1/2 or 5+1/2=5.5.
- Example 2: If we say that b=0.001, then side AC is the smallest at 0.001 & side BC is still the biggest at b+1/2 or 0.001+1/2=0.501.
With the information a=1/2, we don't always know for sure which side is smallest, but we always know which side is biggest (side BC), which tells us which angle is always biggest (angleBAC), which is what the question is asking.

My guess is that the GMATFree website used the explanation of the Official Question from the Official Guide (that I noted above) as their answer for this question, but it is incorrect because the numbers used and the statements are different. Can anyone confirm this, or am I missing something? Thanks!
[Reveal] Spoiler: OA

Last edited by Bunuel on 16 Sep 2017, 06:04, edited 1 time in total.
Renamed the topic and edited the question.

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Concentration: Social Entrepreneurship, Nonprofit
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Re: In triangle ABC, if AB = a, BC = b + 1/2, and AC = b, which of the [#permalink]

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16 Sep 2017, 06:01
apblanker wrote:
In triangle ABC, if AB=a, BC=b+1/2, and AC=b, which of the three angles has the greatest degree measure?
(1) b=a+3/2
(2) a=1/2

Question from GMATFree dot com - Data Sufficiency, Module 37 #7. Their explanation is also on Youtube at watch?v=h_owg_Q_25Y
This question is similar to the greatest degree measure question from the Official Guide (Question 19 page 276, that question is discussed on the forum here. I can't post URLs yet, but if you search "Greatest Degree Measure" it comes up.) but it uses different numbers, & statements (1) and (2) are slightly different.

The answer from GMATFree is A. (1) alone is sufficient but (2) alone is not sufficient.

However, I think (2) alone would also be sufficient & therefore the answer would be D.
If a=1/2, then no matter what value b is, side BC will always be longest & therefore angleBAC will always be the greatest.
- Example 1: With a=1/2, if we say that b=5, then side AB is the smallest at 1/2 & side BC is the biggest at b+1/2 or 5+1/2=5.5.
- Example 2: If we say that b=0.001, then side AC is the smallest at 0.001 & side BC is still the biggest at b+1/2 or 0.001+1/2=0.501.
With the information a=1/2, we don't always know for sure which side is smallest, but we always know which side is biggest (side BC), which tells us which angle is always biggest (angleBAC), which is what the question is asking.

My guess is that the GMATFree website used the explanation of the Official Question from the Official Guide (that I noted above) as their answer for this question, but it is incorrect because the numbers used and the statements are different. Can anyone confirm this, or am I missing something? Thanks!

From the question, we already know that angle A is greater than angle B, because $$b+\frac{1}{2} > b$$.

So our question simply ask the relationship between angle A and angle C, or the relationship between $$b+\frac{1}{2}$$ and $$a$$.

--> $$b+\frac{1}{2} ... a$$

Statement 1
- $$b = a+\frac{3}{2}$$
- We subsitute b in our question, become ; $$(a+\frac{3}{2})+\frac{1}{2} ... a$$ --> $$a+2 ... a$$, clearly $$a+2>2$$, so the biggest angle is angle A.
SUFFICIENT

Statement 2
- $$a = \frac{1}{2}$$
- Substitute again --> $$b+\frac{1}{2} ... \frac{1}{2}$$ --> $$b+\frac{1}{2}>\frac{1}{2}$$
- Again, we know that angle A is the biggest.
SUFFICIENT
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Re: In triangle ABC, if AB = a, BC = b + 1/2, and AC = b, which of the [#permalink]

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20 Sep 2017, 11:46
In triangle ABC
AB = a
BC = b + 1/2
AC = b
which of the three angles has the greatest degree measure?

Theory : Angle opposite to longest side is largest angle in triangle
and Angle opposite to smallest side is smallest angle in triangle

(1) b = a + 3/2
=> b=a+1.5 => b+1/2 > b> a => Angle opposite to BC is greatest degree angle.
Sufficient

(2) a = 1/2
We don't have details of b.
Insufficient

Kudos [?]: 59 [0], given: 59

Re: In triangle ABC, if AB = a, BC = b + 1/2, and AC = b, which of the   [#permalink] 20 Sep 2017, 11:46
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