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If the length of side AB is 17, is triangle ABC a right tria  [#permalink]

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Question Stats: 70% (01:15) correct 30% (01:36) wrong based on 298 sessions

### HideShow timer Statistics If the length of side AB is 17, is triangle ABC a right triangle?

(1) The length of side BC is 144.
(2) The length of side AC is 145.

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Re: Is ABC a right angle triangle?  [#permalink]

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enigma123 wrote:
If the length of side AB is 17, is triangle ABC a right triangle?
(1) The length of side BC is 144.
(2) The length of side AC is 145.

I have got the answer C and its the correct answer. But I arrived at answer by doing the actual calculation. Is there any shortcut?

If the length of side AB is 17, is triangle ABC a right triangle?

(1) The length of side BC is 144 --> there are infinitely many triangles possible with the sides of 17 and 144, two of them will be right triangles (17^2+144^2=x^2, where x is a hypotenuse and 17^2+y^2=144^2, where y is an another leg) and others will not. Not sufficient.

(2) The length of side AC is 145. Not sufficient for the same reason.

(1)+(2) We know all the sides hence, even without actual calculation, we can find out whether the triangle is right or not. Sufficient. (As a matter of fact it is a right triangle: 17^2+144^2=145^2)

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Re: If the length of side AB is 17, is triangle ABC a right tria  [#permalink]

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Bunuel or anyone else can I ask a question. So if a triangle fits into the Pa Theorem then it has to be a right angle or could it fit the theorem n not be a right angle. Thanks
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Re: If the length of side AB is 17, is triangle ABC a right tria  [#permalink]

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kys123 wrote:
Bunuel or anyone else can I ask a question. So if a triangle fits into the Pa Theorem then it has to be a right angle or could it fit the theorem n not be a right angle. Thanks

Yes, the reverse of Pythagorean theorem is also true: for any triangle with sides a, b, and c, if a^2+b^2=c^2, then the angle between the sides a and b is 90 degrees.
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(1) INSUFFICIENT: With only two sides of the triangle, it is impossible to determine whether a2 + b2 = c2.

(2) INSUFFICIENT: With only two sides of the triangle, it is impossible to determine whether a2 + b2 = c2.

(1) AND (2) SUFFICIENT: With all three side lengths, we can determine if a2 + b2 = c2. It turns out that 172 + 1442 = 1452, so this is a right triangle. However, even if it were not a right triangle, this formula would still be sufficient, so it is unnecessary to finish the calculation.
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Re: If the length of side AB is 17, is triangle ABC a right tria  [#permalink]

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Hi Experts,
Do we really see such calculation intensive Questions on GMAT? Regards,
Sachin
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Re: If the length of side AB is 17, is triangle ABC a right tria  [#permalink]

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sachindia wrote:
Hi Experts,
Do we really see such calculation intensive Questions on GMAT? Regards,
Sachin

Actually there is no intensive calculation involved. The only calculation required here is to check - when combining statement 1 and 2, a triangle can be formed or not, that is sum of 2 lengths is greater than third or not.
Once it is known that a triangle can be formed and you have lenght of each side, you have sufficient details to answer if it is a right angle or not. Data sufficiency question wants to know only that. you dont need to apply theorem to calculate it.
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Re: If the length of side AB is 17, is triangle ABC a right tria  [#permalink]

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I beg to differ..
Its already stated that it is a triangle, Our job is to check if its a right angled triangle..and to check that we need to apply the theorem of the great pythagorus and this application of theorem in my opinion is calculation intensive.

Regards,
Sachin
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Re: If the length of side AB is 17, is triangle ABC a right tria  [#permalink]

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sachindia wrote:
I beg to differ..
Its already stated that it is a triangle, Our job is to check if its a right angled triangle..and to check that we need to apply the theorem of the great pythagorus and this application of theorem in my opinion is calculation intensive.

Regards,
Sachin

Please check the following post to see that no calculations are needed to solve the question: if-the-length-of-side-ab-is-17-is-triangle-abc-a-right-tria-127069.html#p1039631
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Re: If the length of side AB is 17, is triangle ABC a right tria  [#permalink]

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Oh yeah.. Its only a DS Question not a PS. Thanks Bunuel..
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Re: If the length of side AB is 17, is triangle ABC a right tria  [#permalink]

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For such large calculations, how do you find out that it's a right triangle? Thanks.
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GMAT 1: 770 Q51 V42 Re: If the length of side AB is 17, is triangle ABC a right tria  [#permalink]

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chigiwigi wrote:
For such large calculations, how do you find out that it's a right triangle? Thanks.
Did you read the replies in this thread? The question is whether we have sufficient information to determine whether it is a right triangle. The question is NOT whether it is a right triangle.

We know all 3 sides of the triangle. Therefore, we have sufficient information to determine whether it is a right triangle. It is NOT necessary to actually calculate whether it indeed is one.
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Re: If the length of side AB is 17, is triangle ABC a right tria  [#permalink]

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Ya, makes sense, thanks again.
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Re: If the length of side AB is 17, is triangle ABC a right tria  [#permalink]

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For a triangle to be isosceles triangle sides of the triangle must follow a2 + b2 = c2 where ‘c’ is the largest side of the triangle.
Statement 1. Here, we know the length of 2 sides but we are still unaware of the third side. So, we can use the above given equation. Hence, Insufficient.
Statement 2. We know the length of 2 sides of the triangle but we are unaware of the third side of the triangle. So, we can’t use the above equation. Hence, Insufficient.
Statement 1 & 2 together. Using the data given in the question statement and statement 1 and 2 together, we know all three sides of triangle.
1442 + 172 = 20736 + 289 = 21025 = 1452.
So, the triangle is a right triangle. Hence, Sufficient. Re: If the length of side AB is 17, is triangle ABC a right tria   [#permalink] 21 Dec 2018, 22:37
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