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# Is the triangle ABC with sides a,b,c a right-angled triangle?

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Retired Moderator
Joined: 27 Oct 2017
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Is the triangle ABC with sides a,b,c a right-angled triangle?  [#permalink]

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31 Mar 2020, 20:49
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65% (hard)

Question Stats:

24% (00:59) correct 76% (01:03) wrong based on 21 sessions

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Is the triangle ABC with sides a,b,c a right-angled triangle?
1) $$a^2+b^2>c^2$$
2) $$a^2+c^2<b^2$$

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Is the triangle ABC with sides a,b,c a right-angled triangle?  [#permalink]

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Updated on: 01 Apr 2020, 11:20
ST (1) : a2+b2>c2
if, a=3,b=3,c=3 ; the triangle is not right angled triangle .
if, a=3, b=5, c=4 : the triangle is not right angled triangle . INSUFFICIENT

ST (1) : a2+b2<c2
angle C is >90
so, the triangle is an obtuse triangle, NOT right angled triangle. SUFFICIENT

Originally posted by preetamsaha on 31 Mar 2020, 21:08.
Last edited by preetamsaha on 01 Apr 2020, 11:20, edited 1 time in total.
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Re: Is the triangle ABC with sides a,b,c a right-angled triangle?  [#permalink]

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31 Mar 2020, 21:59
1
Statement 1 -

Case 1- a=5; b=3; c=4 (right angled triangle)
a^2+b^2>c^2

Case 2 - a=3; b=3; c=3 (acute angled triangle)

a^2+b^2>c^2

Insufficient

Statement 2- a^2+b^2 < c^2
Angle C > 90 degrees

Hence it can't be right angle triangle

Sufficient

B

Tho it's a faulty question, as both statements are contradicting each other.

GMATBusters wrote:
Is the triangle ABC with sides a,b,c a right-angled triangle?
1) $$a^2+b^2>c^2$$
2) $$a^2+b^2<c^2$$

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Retired Moderator
Joined: 27 Oct 2017
Posts: 1782
WE: General Management (Education)
Re: Is the triangle ABC with sides a,b,c a right-angled triangle?  [#permalink]

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31 Mar 2020, 22:23
Nice observation

nick1816 wrote:
Statement 1 -

Case 1- a=5; b=3; c=4 (right angled triangle)
a^2+b^2>c^2

Case 2 - a=3; b=3; c=3 (acute angled triangle)

a^2+b^2>c^2

Insufficient

Statement 2- a^2+b^2 < c^2
Angle C > 90 degrees

Hence it can't be right angle triangle

Sufficient

B

Tho it's a faulty question, as both statements are contradicting each other.

GMATBusters wrote:
Is the triangle ABC with sides a,b,c a right-angled triangle?
1) $$a^2+b^2>c^2$$
2) $$a^2+b^2<c^2$$

GMATBuster's Collection

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Re: Is the triangle ABC with sides a,b,c a right-angled triangle?  [#permalink]

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01 Apr 2020, 09:21
GMATBusters wrote:
Is the triangle ABC with sides a,b,c a right-angled triangle?
1) $$a^2+b^2>c^2$$
2) $$a^2+c^2<b^2$$

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Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.

$$a^2 + c^2 < b^2$$ from condition 2) means the angle B is greater than 180° and the triangle ABC is obtuse.
No obtuse triangle has a right interior angle and we have an answer 'no'

Since 'no' is also a unique answer by CMT (Common Mistake Type) 1, condition 2) is sufficient.

Condition 1)

IF $$a = 3, b = 5, c = 4$$, then the triangle is a right triangle and the answer is 'yes'.
If $$a = b = c = 1$$, the triangle is not a right triangle and the answer is 'no'

Since condition 1) does not yield a unique solution, it is not sufficient.

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Re: Is the triangle ABC with sides a,b,c a right-angled triangle?   [#permalink] 01 Apr 2020, 09:21