Apr 27 07:00 AM PDT  09:00 AM PDT Attend this webinar and master GMAT SC in 10 days by learning how meaning and logic can help you tackle 700+ level SC questions with ease. Apr 28 07:00 AM PDT  09:00 AM PDT Attend this webinar to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes. Apr 29 08:00 AM PDT  09:00 AM PDT Join a free live webinar and learn timemanagement tactics that will guarantee you answer all questions, in all sections, on time. Save your spot today! May 01 10:00 PM PDT  11:00 PM PDT Target Test Prep is kicking off spring with a fresh giveaway contest! For a limited time, you have a chance to win 4 months of full, FREE access to our 5star rated GMAT Quant course.
Author 
Message 
TAGS:

Hide Tags

CEO
Joined: 21 Jan 2007
Posts: 2545
Location: New York City

If points A, B, and C form a triangle, is angle ABC>90 degre
[#permalink]
Show Tags
16 Nov 2007, 08:59
Question Stats:
46% (01:46) correct 54% (01:47) wrong based on 334 sessions
HideShow timer Statistics
If points A, B, and C form a triangle, is angle ABC>90 degrees? (1) AC = AB + BC − 0.001 (2) AC = AB M1524
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 54543

PathFinder007 wrote: HI Bunnel,
Could you please provide your comments on statement defined in question.
Thanks. THEORY:Say the lengths of the sides of a triangle are a, b, and c, where the largest side is c. For a right triangle: \(a^2 +b^2= c^2\). For an acute (a triangle that has all angles less than 90°) triangle: \(a^2 +b^2>c^2\). For an obtuse (a triangle that has an angle greater than 90°) triangle: \(a^2 +b^2<c^2\). Points A, B and C form a triangle. Is ABC > 90 degrees?(1) AC = AB + BC  0.001. If AC=0.001, AB=0.001 and BC=0.001, then the triangle will be equilateral, thus each of its angles will be 60 degrees. If AC=10, AB=5 and BC=5.001, then AC^2>AB^2+BC^2, which means that angle ABC will be more than 90 degrees. Not sufficient. (2) AC = AB > triangle ABC is an isosceles triangle > angles B and C are equal, which means that angle B cannot be greater than 90 degrees. Sufficient. Answer: B. Similar questions to practice: areallanglesoftriangleabcsmallerthan90degrees129298.htmlif1012andxaresidesofanacuteangledtriangleho90462.htmlHope it's clear.
_________________




Senior Manager
Joined: 09 Aug 2006
Posts: 489

Re: C 15.24 degrees of a triangle
[#permalink]
Show Tags
16 Nov 2007, 21:04
bmwhype2 wrote: Points A, B and C form a triangle. Is ABC > 90 degrees?
1. AC = AB + BC  .001 2. AC = AB
Please explain your answer.
I think the answer is A.
S1 :
AC = AB + BC  .001
AC + .001 = AB + BC
Squaring B.S,
(AC + .001) ^ 2 = (AB + BC )^2
AC^2 + 2AC*.001 = AB^2 + 2AB.BC + BC^2
AC^2 = AB^2 + BC^2 + 2AB.BC + 2AC*.001
By Pythagoras Thm, Angle ABC is 90 if AC^2 = AB^2 + BC^2.
Here AC is bigger than that.. which implies that Angle ABC is > 90. Hence Suff.
PS : (I do not know of any formal rule/theorem that states that if Hypotenuse exceeds more than sum of the squares of the sides that the angle > 90. In fact that triangle is no more a right triangle but I just based this on my intuition. I just took an example of triangle with sides 3,4 and 5. )
St2 :
As AC is the Hypo which should be the longest side of a triangle. But here, the Hypotenuse is equal to a side hence this triangle is not a right triangle but we don't know if angle ABC > 90.. Hence Insuff.



Manager
Joined: 25 Jul 2007
Posts: 105

Re: C 15.24 degrees of a triangle
[#permalink]
Show Tags
16 Nov 2007, 21:47
Amit05 wrote: bmwhype2 wrote: Points A, B and C form a triangle. Is ABC > 90 degrees?
1. AC = AB + BC  .001 2. AC = AB
Please explain your answer. I think the answer is A. S1 : AC = AB + BC  .001 AC + .001 = AB + BC Squaring B.S, (AC + .001) ^ 2 = (AB + BC )^2 AC^2 + 2AC*.001 = AB^2 + 2AB.BC + BC^2 AC^2 = AB^2 + BC^2 + 2AB.BC + 2AC*.001 By Pythagoras Thm, Angle ABC is 90 if AC^2 = AB^2 + BC^2. Here AC is bigger than that.. which implies that Angle ABC is > 90. Hence Suff. PS : (I do not know of any formal rule/theorem that states that if Hypotenuse exceeds more than sum of the squares of the sides that the angle > 90. In fact that triangle is no more a right triangle but I just based this on my intuition. I just took an example of triangle with sides 3,4 and 5. ) St2 : As AC is the Hypo which should be the longest side of a triangle. But here, the Hypotenuse is equal to a side hence this triangle is not a right triangle but we don't know if angle ABC > 90.. Hence Insuff.
I find myself inclined to agree with your logic about statement 1.
However, I find statement 2 to be sufficient by itself as well.
If ac=ab, then angle ABC = angle ACB.
Therefore angle ABC cannot be greater than 90.



Senior Manager
Joined: 09 Aug 2006
Posts: 489

Re: C 15.24 degrees of a triangle
[#permalink]
Show Tags
16 Nov 2007, 22:18
jbs wrote: Amit05 wrote: bmwhype2 wrote: Points A, B and C form a triangle. Is ABC > 90 degrees?
1. AC = AB + BC  .001 2. AC = AB
Please explain your answer. I think the answer is A. S1 : AC = AB + BC  .001 AC + .001 = AB + BC Squaring B.S, (AC + .001) ^ 2 = (AB + BC )^2 AC^2 + 2AC*.001 = AB^2 + 2AB.BC + BC^2 AC^2 = AB^2 + BC^2 + 2AB.BC + 2AC*.001 By Pythagoras Thm, Angle ABC is 90 if AC^2 = AB^2 + BC^2. Here AC is bigger than that.. which implies that Angle ABC is > 90. Hence Suff. PS : (I do not know of any formal rule/theorem that states that if Hypotenuse exceeds more than sum of the squares of the sides that the angle > 90. In fact that triangle is no more a right triangle but I just based this on my intuition. I just took an example of triangle with sides 3,4 and 5. ) St2 : As AC is the Hypo which should be the longest side of a triangle. But here, the Hypotenuse is equal to a side hence this triangle is not a right triangle but we don't know if angle ABC > 90.. Hence Insuff. I find myself inclined to agree with your logic about statement 1. However, I find statement 2 to be sufficient by itself as well. If ac=ab, then angle ABC = angle ACB. Therefore angle ABC cannot be greater than 90.
Ooops .. I missed that .. I think these are the traps that are set by GMAC to fool us around..
yes, D it is ..
Good question !!



Director
Joined: 09 Aug 2006
Posts: 717

Re: C 15.24 degrees of a triangle
[#permalink]
Show Tags
16 Nov 2007, 23:20
Amit05 wrote: bmwhype2 wrote: Points A, B and C form a triangle. Is ABC > 90 degrees?
1. AC = AB + BC  .001 2. AC = AB
Please explain your answer. I think the answer is A. S1 : AC = AB + BC  .001 AC + .001 = AB + BC Squaring B.S, (AC + .001) ^ 2 = (AB + BC )^2 AC^2 + 2AC*.001 = AB^2 + 2AB.BC + BC^2 AC^2 = AB^2 + BC^2 + 2AB.BC + 2AC*.001 > AC^2 = AB^2 + BC^2 + 2AB.BC  (2AC*.001 + .001^2)
By Pythagoras Thm, Angle ABC is 90 if AC^2 = AB^2 + BC^2. Here AC is bigger than that.. which implies that Angle ABC is > 90. Hence Suff. PS : (I do not know of any formal rule/theorem that states that if Hypotenuse exceeds more than sum of the squares of the sides that the angle > 90. In fact that triangle is no more a right triangle but I just based this on my intuition. I just took an example of triangle with sides 3,4 and 5. ) St2 : As AC is the Hypo which should be the longest side of a triangle. But here, the Hypotenuse is equal to a side hence this triangle is not a right triangle but we don't know if angle ABC > 90.. Hence Insuff.
Please see the correction in blue above.
I pick B.



SVP
Joined: 29 Aug 2007
Posts: 2326

Re: C 15.24 degrees of a triangle
[#permalink]
Show Tags
17 Nov 2007, 01:28
jbs wrote: Amit05 wrote: bmwhype2 wrote: Points A, B and C form a triangle. Is ABC > 90 degrees?
1. AC = AB + BC  .001 2. AC = AB
Please explain your answer. I think the answer is A. S1 : AC = AB + BC  .001 AC + .001 = AB + BC Squaring B.S, (AC + .001) ^ 2 = (AB + BC )^2 AC^2 + 2AC*.001 = AB^2 + 2AB.BC + BC^2 AC^2 = AB^2 + BC^2 + 2AB.BC + 2AC*.001 By Pythagoras Thm, Angle ABC is 90 if AC^2 = AB^2 + BC^2. Here AC is bigger than that.. which implies that Angle ABC is > 90. Hence Suff. PS : (I do not know of any formal rule/theorem that states that if Hypotenuse exceeds more than sum of the squares of the sides that the angle > 90. In fact that triangle is no more a right triangle but I just based this on my intuition. I just took an example of triangle with sides 3,4 and 5. ) St2 : As AC is the Hypo which should be the longest side of a triangle. But here, the Hypotenuse is equal to a side hence this triangle is not a right triangle but we don't know if angle ABC > 90.. Hence Insuff. I find myself inclined to agree with your logic about statement 1. However, I find statement 2 to be sufficient by itself as well. If ac=ab, then angle ABC = angle ACB. Therefore angle ABC cannot be greater than 90.
Since AC = AB + BC  .001, what if BC = 0.001? then AC = AB again as in statement 2.



CEO
Joined: 21 Jan 2007
Posts: 2545
Location: New York City

Re: C 15.24 degrees of a triangle
[#permalink]
Show Tags
17 Nov 2007, 23:39
GMAT TIGER wrote: jbs wrote: Amit05 wrote: bmwhype2 wrote: Points A, B and C form a triangle. Is ABC > 90 degrees?
1. AC = AB + BC  .001 2. AC = AB
Please explain your answer. I think the answer is A. S1 : AC = AB + BC  .001 AC + .001 = AB + BC Squaring B.S, (AC + .001) ^ 2 = (AB + BC )^2 AC^2 + 2AC*.001 = AB^2 + 2AB.BC + BC^2 AC^2 = AB^2 + BC^2 + 2AB.BC + 2AC*.001 By Pythagoras Thm, Angle ABC is 90 if AC^2 = AB^2 + BC^2. Here AC is bigger than that.. which implies that Angle ABC is > 90. Hence Suff. PS : (I do not know of any formal rule/theorem that states that if Hypotenuse exceeds more than sum of the squares of the sides that the angle > 90. In fact that triangle is no more a right triangle but I just based this on my intuition. I just took an example of triangle with sides 3,4 and 5. ) St2 : As AC is the Hypo which should be the longest side of a triangle. But here, the Hypotenuse is equal to a side hence this triangle is not a right triangle but we don't know if angle ABC > 90.. Hence Insuff. I find myself inclined to agree with your logic about statement 1. However, I find statement 2 to be sufficient by itself as well. If ac=ab, then angle ABC = angle ACB. Therefore angle ABC cannot be greater than 90. Since AC = AB + BC  .001, what if BC = 0.001? then AC = AB again as in statement 2.
when dealing with triangles, i usually look for defined size and shape.
.001 is a concrete size. however, we dont know whether that is a material size that can change the size of the sides of a triangle. From 1, we cannot infer anything.



CEO
Joined: 17 Nov 2007
Posts: 3412
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth)  Class of 2011

1. AC=AB+BC0.001
this is the same as AC>AB+BC (common for triangles)
for example,
AC=1000.001, AB=500, BC=500 => ABC~180
AC=0.001, AB=500, BC=500.001 =>ABC~0
insuf.
2. AB=AC
ABC=ACB => 2ABC<180> ABC<90
suf.
B is correct
P.S if one can draw it solution will come easy.



CEO
Joined: 17 Nov 2007
Posts: 3412
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth)  Class of 2011

walker wrote: AC=0.001, AB=500, BC=500.001 =>ABC~0
BC=500.002 instead of 500.001



Manager
Joined: 09 Apr 2013
Posts: 192
Location: United States
Concentration: Finance, Economics
GMAT 1: 710 Q44 V44 GMAT 2: 740 Q48 V44
GPA: 3.1
WE: Sales (Mutual Funds and Brokerage)

If Angle ABC is > 90, then AC has to be the hypotenuse.
With Point 1:
If AB is 1, and BC is 1, then AC would be 1.999, making it the hypotenuse
But if AB is .0006, and BC is .0007, then AC would be .0003, making it not the hypotenuse.
Because the .001 gives us no reference, we cannot conclude anything from Point 1 alone.
If AB = AC, then that means that there is no possible way that AC could be the hypotenuse since there is another side of equal length right next to it. Even if BC is infinitely small, it is still >0 and therefore ABC cannot be >90. Therefore, Point 2 is enough for us to disqualify it alone.



Manager
Joined: 10 Mar 2014
Posts: 186

HI Bunnel,
Could you please provide your comments on statement defined in question.
Thanks.



Intern
Joined: 13 Dec 2013
Posts: 8

Re: If points A, B, and C form a triangle...
[#permalink]
Show Tags
24 May 2014, 20:41
bekerman wrote: If points A, B, and C form a triangle, is angle ABC>90 degrees? (1) AC=AB+BC−0.001 (2) AC=AB M1524 in GMATClub tests  I am wondering whether the OA is incorrect? IMO Answer is "B"Statement1: AC = AB+ BC  .001, If AB, BC are quite big numbers (greater than .01), then angle ABC would be greater than 90 degrees. But if length of AB, BC are in the same range of .001, then angle ABC could be acute angle also. So statement 1 is not sufficient.Statement 2: AC= AB, it means angle ABC = angle ACB, now in any triangle sum all the angles is 180 degree, thus ABC +ACB+BAC = 180 degree. Now as ABC = ACB > 2ABC + BAC = 180 > ABC = 90  BAC/2. Hence angle ABC is always less than 90 degree. Statement 2 is sufficient



Director
Joined: 19 Apr 2013
Posts: 567
Concentration: Strategy, Healthcare
GPA: 4

Re: If points A, B, and C form a triangle, is angle ABC>90 degre
[#permalink]
Show Tags
05 Mar 2015, 10:53
Bunuel, can we also claim that when the angle us obtuse c will be greater than a and b?
_________________
If my post was helpful, press Kudos. If not, then just press Kudos !!!



Math Expert
Joined: 02 Sep 2009
Posts: 54543

Re: If points A, B, and C form a triangle, is angle ABC>90 degre
[#permalink]
Show Tags
05 Mar 2015, 11:28
Ergenekon wrote: Bunuel, can we also claim that when the angle us obtuse c will be greater than a and b? Yes, the greatest side is opposite the greatest angle.
_________________



Manager
Joined: 13 Dec 2013
Posts: 151
Location: United States (NY)
Concentration: General Management, International Business
GMAT 1: 710 Q46 V41 GMAT 2: 720 Q48 V40
GPA: 4
WE: Consulting (Consulting)

Re: If points A, B, and C form a triangle, is angle ABC>90 degre
[#permalink]
Show Tags
10 May 2017, 12:28
Bunuel wrote: PathFinder007 wrote: HI Bunnel,
Could you please provide your comments on statement defined in question.
Thanks. THEORY:Say the lengths of the sides of a triangle are a, b, and c, where the largest side is c. For a right triangle: \(a^2 +b^2= c^2\). For an acute (a triangle that has all angles less than 90°) triangle: \(a^2 +b^2>c^2\). For an obtuse (a triangle that has an angle greater than 90°) triangle: \(a^2 +b^2<c^2\). Points A, B and C form a triangle. Is ABC > 90 degrees?(1) AC = AB + BC  0.001. If AC=0.001, AB=0.001 and BC=0.001, then the triangle will be equilateral, thus each of its angles will be 60 degrees. If AC=10, AB=5 and BC=5.001, then AC^2>AB^2+BC^2, which means that angle ABC will be more than 90 degrees. Not sufficient. (2) AC = AB > triangle ABC is an isosceles triangle > angles B and C are equal, which means that angle B cannot be greater than 90 degrees. Sufficient. Answer: B. Similar questions to practice: http://gmatclub.com/forum/areallangle ... 29298.htmlhttp://gmatclub.com/forum/if1012and ... 90462.htmlHope it's clear. Hi Bunuel, to find an obtuse angle within the constraints set by 1) I did the following (in bold). Is this approach okay? 1) If AB + BC = 100, then angle ABC will be close to 180. This triangle is allowed because AC<AB+AC. I felt that this triangle allowed easier visualization of the obtuse angle. And, as you stated if all sides = 0.001, then angle ABC will be 60. 2) Means that the triangle is isosceles and therefore has 2 equal angles. 2x+y=180 2x=180y Because y cannot be 0, x must be less than 90. Suff.



Senior Manager
Status: love the club...
Joined: 24 Mar 2015
Posts: 276

Re: If points A, B, and C form a triangle, is angle ABC>90 degre
[#permalink]
Show Tags
07 Feb 2018, 01:38
bmwhype2 wrote: If points A, B, and C form a triangle, is angle ABC>90 degrees?
(1) AC = AB + BC − 0.001
(2) AC = AB
M1524 hi I don't know whether this is okay, but I tried this problem this way statement 1 actually says that AC < AB + BC now, if we suppose that AC is the largest side, then it is true for any triangle, regardless of whether the triangle is acute or obtuse so clearly insufficient statement 2 says that the triangle is an isosceles triangle with its 2 angels equal now, since the sum of all the angles of a triangle adds up to 180 degrees, angle B cannot even equal to 90 degrees let alone be more than 90 degrees hence the statement 2 is clearly sufficient So the answer is B thanks



Manager
Joined: 23 Nov 2016
Posts: 113

Re: If points A, B, and C form a triangle, is angle ABC>90 degre
[#permalink]
Show Tags
27 Mar 2019, 19:10
Experts can someone please explain, Seems like S1 is sufficient. His explanation seems logical . Amit05 wrote: bmwhype2 wrote: Points A, B and C form a triangle. Is ABC > 90 degrees?
1. AC = AB + BC  .001 2. AC = AB
Please explain your answer. I think the answer is A. S1 : AC = AB + BC  .001 AC + .001 = AB + BC Squaring B.S, (AC + .001) ^ 2 = (AB + BC )^2 AC^2 + 2AC*.001 = AB^2 + 2AB.BC + BC^2 AC^2 = AB^2 + BC^2 + 2AB.BC + 2AC*.001 By Pythagoras Thm, Angle ABC is 90 if AC^2 = AB^2 + BC^2. Here AC is bigger than that.. which implies that Angle ABC is > 90. Hence Suff. PS : (I do not know of any formal rule/theorem that states that if Hypotenuse exceeds more than sum of the squares of the sides that the angle > 90. In fact that triangle is no more a right triangle but I just based this on my intuition. I just took an example of triangle with sides 3,4 and 5. ) St2 : As AC is the Hypo which should be the longest side of a triangle. But here, the Hypotenuse is equal to a side hence this triangle is not a right triangle but we don't know if angle ABC > 90.. Hence Insuff.
_________________
If my post anyway helped you,please spare Kudos !




Re: If points A, B, and C form a triangle, is angle ABC>90 degre
[#permalink]
27 Mar 2019, 19:10






