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06 Nov 2019, 02:29
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
47% (02:26) correct
53%
(02:21)
wrong
based on 153
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The sides of a triangle are a, b, and c. Are the three angles all less than 90 measure degrees?
(1) The areas of the semi-circles with the radius a, b, c are 4, 5, 6, respectively.
(2) \(c < a + b < c + 2\)
Are You Up For the Challenge: 700 Level Questions
(1) The areas of the semi-circles with the radius a, b, c are 4, 5, 6, respectively.
(2) \(c < a + b < c + 2\)
Are You Up For the Challenge: 700 Level Questions
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
06 Nov 2019, 05:46
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Statement 1
We know the areas of triangle; hence, we can find the radius of the circles.
We know all the sides of the triangle; we can calculate all the angles using cosine formula or we can check whether all the angles are acute or not using pythagorean inequality.
Sufficient
Statement 2-
a+b<c+2
1. if a=1.4; b=1.4; and c=1.4 (it's an equilateral triangle)
2. if a=0.6; b=0.6; and c=0.9 (it's an obtuse angle triangle)
(0.6)^2+(0.6)^2<(0.9)^2
0.72<0.81
Insufficient
We know the areas of triangle; hence, we can find the radius of the circles.
We know all the sides of the triangle; we can calculate all the angles using cosine formula or we can check whether all the angles are acute or not using pythagorean inequality.
Sufficient
Statement 2-
a+b<c+2
1. if a=1.4; b=1.4; and c=1.4 (it's an equilateral triangle)
2. if a=0.6; b=0.6; and c=0.9 (it's an obtuse angle triangle)
(0.6)^2+(0.6)^2<(0.9)^2
0.72<0.81
Insufficient
Bunuel
20 Nov 2019, 04:34
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Statement 1 : From the area of the semi circles we can find the sides.The triangle will have a unique set of sides and hence a unique set of angles .From the angles we will be able to tell if the triangle is acute or isn't.
OR
Once we have the sides, we will perform the acute angle test: that is for all the angles of the triangle to be acute(<90) , the sum of the squares of any two sides MUST be greater than the square of the last side. That is, a^2 +b^2>c^2 and c^2 +b^2>b^2 and a^2 +c^2>b^2 .However, since c is the largest side, we only to need to do it for a^2 +b^2>c^2 .After all, the largest side is opposite the largest angle and if it happens to be acute,the other angles must also be acute
SUFFICIENT
Statement 2 :
If the sides are either 1/1/1( equilateral triangle)or if the sides are 1/1/1.414 (right angled isosceles) the statement holds true.
INSUFFICIENT
answer is A
OR
Once we have the sides, we will perform the acute angle test: that is for all the angles of the triangle to be acute(<90) , the sum of the squares of any two sides MUST be greater than the square of the last side. That is, a^2 +b^2>c^2 and c^2 +b^2>b^2 and a^2 +c^2>b^2 .However, since c is the largest side, we only to need to do it for a^2 +b^2>c^2 .After all, the largest side is opposite the largest angle and if it happens to be acute,the other angles must also be acute
SUFFICIENT
Statement 2 :
If the sides are either 1/1/1( equilateral triangle)or if the sides are 1/1/1.414 (right angled isosceles) the statement holds true.
INSUFFICIENT
answer is A
