If a triangle inscribed in a circle has area 40, what is the area of the circle?
(1) One side of the triangle is equal to the diameter of the circle.
(2) The measure of one of the angles in the triangle is 30.
A)Statement (1) ALONE is sufficient, but statement (2) is not sufficient.
B)Statement (2) ALONE is sufficient, but statement (1) is not sufficient.
C)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D)EACH statement ALONE is sufficient.
E)Statements (1) and (2) TOGETHER are NOT sufficient.
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
DS Geometry
This topic has expert replies
-
prachi18oct
- Master | Next Rank: 500 Posts
- Posts: 269
- Joined: Sun Apr 27, 2014 10:33 pm
- Thanked: 8 times
- Followed by:5 members
GMAT/MBA Expert
-
[email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
Hi prachi18oct,
This DS question is more of a 'concept' question - you don't need to do any math to answer it, but you DO need to know the rules involved.
We're told that a triangle is INSCRIBED in a circle and the triangle has an area of 40. We're asked for the AREA of the circle (which means we need to know the radius). This question is going to 'hinge' on the type of triangle and how it is 'positioned' inside the circle.
Fact 1: One side of the triangle is equal to the diameter of the circle.
Since the triangle is inscribed in the circle, the 3 vertices are on the circumference of the circle. When one side of an inscribed triangle is equal to the diameter of the circle it's inscribed in, the triangle is a RIGHT TRIANGLE. Unfortunately, we don't have enough information to figure out the exact length of any of the 3 sides, so we can't figure out the radius of the circle.
Fact 1 is INSUFFICIENT
Fact 2: The measure of one of the angles in the triangle is 30.
Unfortunately, this doesn't tell us much about the triangle at all (the other 2 angles could vary and the placement of the triangle could vary).
Fact 2 is INSUFFICIENT
Combined, we know....
The triangle is a 30/60/90 right triangle
The hypotenuse = the diameter of the circle
The area of the triangle is 40
Area = 40 = (X)(Xroot3)
We now have 1 variable and 1 equation, so we CAN solve for X. Since it's a 30/60/90 right triangle, the hypotenuse = 2X = diameter. The radius = X.
Combined, SUFFICIENT
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
This DS question is more of a 'concept' question - you don't need to do any math to answer it, but you DO need to know the rules involved.
We're told that a triangle is INSCRIBED in a circle and the triangle has an area of 40. We're asked for the AREA of the circle (which means we need to know the radius). This question is going to 'hinge' on the type of triangle and how it is 'positioned' inside the circle.
Fact 1: One side of the triangle is equal to the diameter of the circle.
Since the triangle is inscribed in the circle, the 3 vertices are on the circumference of the circle. When one side of an inscribed triangle is equal to the diameter of the circle it's inscribed in, the triangle is a RIGHT TRIANGLE. Unfortunately, we don't have enough information to figure out the exact length of any of the 3 sides, so we can't figure out the radius of the circle.
Fact 1 is INSUFFICIENT
Fact 2: The measure of one of the angles in the triangle is 30.
Unfortunately, this doesn't tell us much about the triangle at all (the other 2 angles could vary and the placement of the triangle could vary).
Fact 2 is INSUFFICIENT
Combined, we know....
The triangle is a 30/60/90 right triangle
The hypotenuse = the diameter of the circle
The area of the triangle is 40
Area = 40 = (X)(Xroot3)
We now have 1 variable and 1 equation, so we CAN solve for X. Since it's a 30/60/90 right triangle, the hypotenuse = 2X = diameter. The radius = X.
Combined, SUFFICIENT
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
-
prachi18oct
- Master | Next Rank: 500 Posts
- Posts: 269
- Joined: Sun Apr 27, 2014 10:33 pm
- Thanked: 8 times
- Followed by:5 members
Yes thats what I did. It seems the OA is wrong.[email protected] wrote:Hi prachi18oct,
This DS question is more of a 'concept' question - you don't need to do any math to answer it, but you DO need to know the rules involved.
We're told that a triangle is INSCRIBED in a circle and the triangle has an area of 40. We're asked for the AREA of the circle (which means we need to know the radius). This question is going to 'hinge' on the type of triangle and how it is 'positioned' inside the circle.
Fact 1: One side of the triangle is equal to the diameter of the circle.
Since the triangle is inscribed in the circle, the 3 vertices are on the circumference of the circle. When one side of an inscribed triangle is equal to the diameter of the circle it's inscribed in, the triangle is a RIGHT TRIANGLE. Unfortunately, we don't have enough information to figure out the exact length of any of the 3 sides, so we can't figure out the radius of the circle.
Fact 1 is INSUFFICIENT
Fact 2: The measure of one of the angles in the triangle is 30.
Unfortunately, this doesn't tell us much about the triangle at all (the other 2 angles could vary and the placement of the triangle could vary).
Fact 2 is INSUFFICIENT
Combined, we know....
The triangle is a 30/60/90 right triangle
The hypotenuse = the diameter of the circle
The area of the triangle is 40
Area = 40 = (X)(Xroot3)
We now have 1 variable and 1 equation, so we CAN solve for X. Since it's a 30/60/90 right triangle, the hypotenuse = 2X = diameter. The radius = X.
Combined, SUFFICIENT
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
Here is the explanation given :-
Information given
Triangle inscribed in a circle has an area of 40. We know that a triangle inscribed in a semicirlce must be a right triangle.
Rephrase of the question:
What are the radius, circumference, and diameter of the circle?
Go to the statements
(1) This gives us the diameter relative to the base, but we don't know what the base of the triangle is.
Insufficient.
Eliminate A and D.
(2) This statement lets us know we are dealing with a 30-60-90 triangle. The area of a right triangle is half of the product of the legs, which will be across from the the 30 degree and 60 degree angles here. Therefore x(x3√)2=40
From that, we can determine a value for x, and, using the properties of a 30-60-90 triangle, 2x, which is the diameter of the circle.
Sufficient.
Choose B.
I couldnt understand how statement 2 tells that it is a 30-60-90 triangle. It could well be 100-50-30 or any other combination. SO I guess there is no such math rule that proves this. the OA must be C
GMAT/MBA Expert
-
Ian Stewart
- GMAT Instructor
- Posts: 2621
- Joined: Mon Jun 02, 2008 3:17 am
- Location: Montreal
- Thanked: 1090 times
- Followed by:355 members
- GMAT Score:780
I can count at least three mistakes in that official explanation. Where is it from?prachi18oct wrote:
Here is the explanation given :-
Information given
Triangle inscribed in a circle has an area of 40.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com
ianstewartgmat.com
ianstewartgmat.com
-
prachi18oct
- Master | Next Rank: 500 Posts
- Posts: 269
- Joined: Sun Apr 27, 2014 10:33 pm
- Thanked: 8 times
- Followed by:5 members
-
nikhilgmat31
- Legendary Member
- Posts: 518
- Joined: Tue May 12, 2015 8:25 pm
- Thanked: 10 times
