Are all the angles in triangle ABC less than 90 degrees?

Question

(1)  AB < BC < AC .
 
(2)  \angle ABC = 80  degrees.

M23-18

manpreetsingh86 · Answer

st.1 not sufficient as different orientations of triangles are possible. for example, if sides are 3,4,5 then possible value of angles is 30,60 and 90. we can also have a orientation in which all angles of the triangle will be less than 90. hence st.1 alone is not sufficient

st.2 clearly not sufficient as we need the information about the other angles as well.

st.1 and st.2 we know that angle opposite side AC=80. Also, since AC is the largest side of the triangle. thus angle opposite to AC will also be the largest. now since largest angle is less than 80. thus all angles of the triangle are less than 90.

hence answer is C

EMPOWERgmatRichC · Answer

Hi honchos,

manpreetsingh86's explanation is right on, but I do want to point out one error in it:

A 3/4/5 right triangle is NOT a 30/60/90 right triangle - those are 2 different triangles.

Here's another way to look at this question:

We're asked if all 3 angles in triangle ABC are less than 90 degrees. This is a YES/NO question.

Fact 1: AB < BC < AC

This tells us the relationship among the lengths of the 3 sides. We know that none of the sides are equal to one another, so none of the corresponding angles are equal to one another.

We could have....

...a 30/60/90 and the answer to the question would be NO.
...a 50/60/70 and the answer to the question would be YES.
Fact 1 is INSUFFICIENT

Fact 2: Angle ABC = 80

This tells us one of the angles, but we don't know if it's the biggest angle or not.

We could have...

a...10/80/90 and the answer to the question would be NO.
a...30/70/80 and the answer to the question would be YES.
Fact 2 is INSUFFICIENT

Combined, we know...
Angle ABC = 80
Angle ABC is across from AC
AB < BC < AC
The biggest angle is always across from the biggest side

Thus the biggest angle is 80, so the other 2 angles are BOTH less than 80.
The answer to the question is ALWAYS YES.
Combined, SUFFICIENT.

Final Answer:  C

GMAT assassins aren't born, they're made,
Rich

TheGraceful · Answer

Thank you Rich...

I struggled with question and your explnation made sense to me.

EMPOWERgmatRichC · Answer

Hi TheGraceful,

I'm glad that you found my explanation helpful. With DS questions, it's often a good idea to think in terms of what is possible (based on whatever information you're given). To that end, you should write down some examples that fit whatever 'restrictions' the prompt has given - and then see what happens when you vary the numbers involved. You'll find that the 'math' behind most DS questions isn't too difficult, but the GMAT writers sometimes find ways to ask you about concepts that you know - but in ways that you are not used to thinking about. Having "proof" on your notepad is one of the keys to earning that higher Score.
 
GMAT assassins aren't born, they're made,
Rich

Bunuel · Answer

Official Solution:

Are all the angles in triangle ABC less than 90 degrees? 
 
(1)  AB < BC < AC /
 
Knowing that the lengths of all three sides are different is not sufficient to answer the question. 
 
(2)  \angle ABC = 80  degrees.
 
This information alone is also insufficient. For example, consider the angles to be 80°, 80°, and 20°, in which case all the angles are less than 90 degrees. Alternatively, consider the angles to be 80°, 95°, and 5°, in which case not all the angles are less than 90 degrees.
 
(1)+(2) The first statement indicates that AC is the longest side of the triangle. Since the largest angle in a triangle is opposite the longest side,  \angle ABC  is the largest angle. From statement (2), we know that the largest angle is 80°, which means that all angles in the triangle are less than 90°. Sufficient.

Answer: C

Are all the angles in triangle ABC less than 90 degrees?

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GMAT Data Sufficiency (DS) Questions

Are all the angles in triangle ABC less than 90 degrees?

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