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# Are all the angles of triangle ABC less than 90 degrees? (1) AB^2 + B

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Retired Moderator
Joined: 22 Aug 2013
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Location: India
Are all the angles of triangle ABC less than 90 degrees? (1) AB^2 + B  [#permalink]

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21 Jul 2018, 21:44
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Difficulty:

65% (hard)

Question Stats:

40% (01:23) correct 60% (01:05) wrong based on 33 sessions

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

(1) AB^2 + BC^2 > AC^2

(2) BC^2 + AC^2 > AB^2
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Joined: 31 Jul 2017
Posts: 515
Location: Malaysia
GMAT 1: 700 Q50 V33
GPA: 3.95
WE: Consulting (Energy and Utilities)
Re: Are all the angles of triangle ABC less than 90 degrees? (1) AB^2 + B  [#permalink]

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21 Jul 2018, 22:46
amanvermagmat wrote:
Are all the angles of triangle ABC less than 90 degrees?

(1) AB^2 + BC^2 > AC^2

(2) BC^2 + AC^2 > AB^2

From Statement I: B < 90

From Statement II: C < 90

Combining I & II:

We cannot decide if Angle A < or > 90. Hence, E.
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Retired Moderator
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Re: Are all the angles of triangle ABC less than 90 degrees? (1) AB^2 + B  [#permalink]

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23 Jul 2018, 07:20
1

CONCEPT: How to find the nature of angles in a triangle.

If $$a^2+b^2 < c^2$$, it means the angle between side a & b is obtuse, the triangle is obtuse.
If $$a^2+b^2 > c^2$$, it means the angle between a & b is acute, but since other angle can be obtuse, the triangle cant be taken as acute.
If $$a^2+b^2 =c^2$$, it means the angle between a & b is 90 deg, hence the triangle is right.

Solution:
Statement 1) AB^2 + BC^2 > AC^2
it means angle B is acute, No other information.
INSUFFICIENT.

Statement 2) BC^2 + AC^2 > AB^2
it means angle C is acute, No other information.
INSUFFICIENT.

Even Combing Statement 1 & 2, we get angle B & C are acute, but angle A can be Acute, 90 deg or Obtuse.
Angles (A, B, C) can be (60,60,60) or (30,60, 90) or (30,50,100)
Hence INSUFFICIENT.

Attachment:

gmatbusters.jpg [ 120.91 KiB | Viewed 283 times ]

Must Do similar questions based on same logic:
1) https://gmatclub.com/forum/is-triangle-abc-with-sides-a-b-and-c-acute-angled-263435.html?hilit=acute
2) https://gmatclub.com/forum/is-triangle-abc-obtuse-angled-203020.html?hilit=acute
3) https://gmatclub.com/forum/are-all-angles-of-triangle-abc-smaller-than-90-degrees-129298.html?hilit=acute
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Re: Are all the angles of triangle ABC less than 90 degrees? (1) AB^2 + B   [#permalink] 23 Jul 2018, 07:20
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