Question: Are all the angles of triangle ABC smaller than 90 degrees?
- AB < BC < AC
- Angle AB = 80 degrees
- Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
- Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
- BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- EACH statement ALONE is sufficient.
- Statements (1) and (2) TOGETHER are NOT sufficient.
Answer:
Solution with Explanation:
Approach Solution (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
- 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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