ABC triangle

Expert replies

Previous Topic Next Topic

neoreaves: Master | Next Rank: 500 Posts; Posts: 208; Joined: Sun Sep 28, 2008 12:30 pm; Thanked: 22 times

by neoreaves » Thu Mar 11, 2010 4:53 am

Are all angles of triangle ABC smaller than 90 degrees?

1) 2AB=3BC=4AC

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

OA : Later

Like this post

Source: Beat The GMAT — Data Sufficiency | Thu Mar 11, 2010 4:53 am

kstv: Legendary Member; Posts: 610; Joined: Fri Jan 15, 2010 12:33 amFollowed by: 2 members; Thanked: 47 times

by kstv » Thu Mar 11, 2010 5:38 am

I) AC =3x, BC = 4x, AB = 6x. 3xÂ²+4xÂ²=5xÂ²
ACÂ² + BCÂ² < ABÂ² if it was = ABÂ² then angle C =90Â°
As the ratio are given it is possible to say angle C is > 90Â°
Sufficient.

II) ACÂ²+ABÂ²> BCÂ²
not sufficient as the ratio are not given. Insufficient

IMO A

Last edited by kstv on Thu Mar 11, 2010 7:18 am, edited 1 time in total.

Like this post

bpgen: Master | Next Rank: 500 Posts; Posts: 142; Joined: Sat Feb 20, 2010 7:23 pmFollowed by: 1 member; Thanked: 8 times

by bpgen » Thu Mar 11, 2010 7:02 am

Thanks all! Answer would be A alone sufficient. Here is bit detail explanation:

As we know cosine formulas, and cosX always >0 if it's angle <90 degree.
cosA=(-a^2+b^2+c^2)/(2bc)
cosB=(a^2-b^2+c^2)/(2ac)
cosC=(a^2+b^2-c^2)/(2ab)

i.e for acute angled triangle, (-a^2+b^2+c^2) ,(a^2-b^2+c^2) and (a^2+b^2-c^2) should be >0

Therefore, if you take ratio of sides: AC =3x, BC = 4x, AB = 6x
we have:
9+16>36
9+36>16
36+16>9

Hence triangle is acute angled triangle(all angles of triangle ABC smaller than 90 degrees).

"Ambition is the path to success. Persistence is the vehicle you arrive in."

Like this post

kstv: Legendary Member; Posts: 610; Joined: Fri Jan 15, 2010 12:33 amFollowed by: 2 members; Thanked: 47 times

by kstv » Thu Mar 11, 2010 7:32 am

In GMAT we try to reason just with the basics.
If one knows the cosines formula very good for him/her as it will help them to solve itquickly .
But I was just thinkin of it is this fashion so as not to feel discouraged if I am unable to recall the formula
I) AC =3x, BC = 4x, AB = 6x.
3xÂ²+4xÂ²=5xÂ²
when AC and BC are 3 and 4 respectively and AB = 5 angle ACB = 90Â°
the slightest enlongation of AC will make AC and BC diverge or angle ACB will be little > 90Â°
conversely contraction of AC will make AC and BC converge or angle ACB will be little < 90Â°
Even at this stage Option A is fine but

angle ACB will be the largest angle as it is opposite the longest side.
It value of ACB whether it is = < or > 90Â° will surely help decide the other.

Still for more clarity since AB = 6 angle ACB > 90Â°
angle CAB + ABC < 90Â°. Individually they have to less than 90Â°.

Like this post

yeahdisk: Senior | Next Rank: 100 Posts; Posts: 45; Joined: Tue Mar 02, 2010 4:27 am; Thanked: 2 times

by yeahdisk » Thu Mar 11, 2010 7:48 am

I think both are sufficient

the first one is obvious

the second one:

If angle BAC = 90 then AC^2 + AB^2 = BC^2

The only way to change the ratio, without changing the lengths, is to modify the angle BAC...

If you increase the angle above 90, then AC^2 + AB^2 < BC^2
If you decrease the angle below 90, then AC^2 + AB^2 > BC^2

Hence the info is sufficient (all angles are <90)

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review