Are all the Angles of Triangle ABC Smaller than 90 Degrees? GMAT Data Sufficiency

Question: Are all the angles of triangle ABC smaller than 90 degrees?

1. AB < BC < AC
2. Angle AB = 80 degrees

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer:
Solution with Explanation:
Approach Solution (1):

1. AB < BC < AC > : Angle ABC > Angle CAB > Angle BCA

But all of them might be less than 90 degrees also OR Angle ABC might be more than 9-
So it is insufficient

2. Angle AB = 80 degrees – Doesn’t give much option about other angle ‘so insufficient

From one and two angle ABC = 80 > angle CAB > angle BCA so all are led than 90 degrees
Hence both are required to answer

Correct Option: C

Approach Solution (2):

(1) This statement is insufficient

The longest side should be less than the sum of the 2 shortest sides: AC < AC + BC

8 < 6 + 3 --- We have one angle that is > 90
8 < 8 + 8 --- All angles = 60

(2) This statement is also insufficient

Angle ABC = 80 --- the sum of the other 2 angles = 100, so it can be 50 + 50 or 95 + 5
Together both the statements are sufficient

Correct Option: C

Approach Solution (3):

S1:
If AB = 3, BC = 4, AC = 5, then we have a right triangle
Hence insufficient

S2:
Angle ABC = 80
But the other angles can be 90 degrees and 10 degrees
Hence insufficient
(1) + (2) says that AC is the greatest sides
Angle ABC = 80 is the greatest angle
Every angle < 90
Hence sufficient

Correct Option: C

“Are all the angles of triangle ABC smaller than 90 degrees?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

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