GMAT Exam > GMAT Questions > What is the area of the 144o sector of the ci...
Start Learning for Free
What is the area of the 144o sector of the circle?
(1) The square with one of the sides as the chord that subtends an angle of 90o on the circle measures 64 sq. cm. in area.
(2) When an isosceles triangle is constructed by taking the longest chord of the circle and the other vertex on the circumference of the circle, the length of each of the equal sides of the triangle is 4√2 cm.
(2) When an isosceles triangle is constructed by taking the longest chord of the circle and the other vertex on the circumference of the circle, the length of each of the equal sides of the triangle is 4√2 cm.
- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
- b)Statement (2) ALONE is sufficient, but statement (1) alone 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.
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
What is the area of the 144o sector of the circle?(1)The square with o...
Steps 1 & 2: Understand Question and Draw Inferences
We need to find the area of a sector subtending an angle of 144o at the center of the circle.
For this we need either the radius of the circle or the area of a known portion of the circle.
Step 3: Analyze Statement 1
The chord that subtends an angle of 90o on the circle is the diameter itself.
(Please note that the chord here subtends an angle of 90o on the circle, and not on the center of the circle)
Area of the square with the side as the diameter is 64 sq. cm.
Therefore the length of the diameter = √(64) = 8 cm.
- Radius of the circle = 4 cm.
We can find the area of the 144o sector by using the formula
Therefore statement 1 is sufficient to arrive at a unique answer.
Step 4: Analyze Statement 2
The longest chord of the circle is the diameter itself.
We know that the diameter subtends an angle of 90o on the circle.
Therefore the isosceles triangle constructed would be an isosceles right angled triangle with the diameter as the hypotenuse.
Given that the length of the equal sides is 4√2 cm.
Let the diameter = D
Therefore, D2 = (4√2)2 + (4√2)2 (Applying Pythagoras)
⇒ D2 = 64
⇒ D = 8 cm.
⇒ Radius = 4 cm.
We can find the area of the 144o sector by using the formula
Therefore statement 2 is sufficient to arrive at a unique answer.
Step 5: Analyze Both Statements Together (if needed)
We arrived at a unique answer in both Step 3 and Step 4 above. So this step is not required.
Correct Answer: D
Most Upvoted Answer
What is the area of the 144o sector of the circle?(1)The square with o...
Statement (1) gives us the area of a square that has one of its sides as the chord that subtends an angle of 90o on the circle. This means that the diagonal of the square is also the diameter of the circle. We can use the Pythagorean theorem to find the diameter of the circle, which is equal to the diagonal of the square:
Diagonal of square = √(2 x side²) = √(2 x 64) = 8√2
Diameter of circle = 8√2 cm
The area of the circle is given by the formula A = πr², where r is the radius of the circle. We know that the radius is half of the diameter, so:
Radius of circle = 4√2 cm
The area of the whole circle is therefore:
A = πr² = π(4√2)² = 32π
The area of the 144o sector is 144/360 times the area of the whole circle:
Area of sector = (144/360) x (32π) = 12π
Therefore, statement (1) alone is sufficient to answer the question.
Statement (2) gives us the length of the equal sides of an isosceles triangle that is constructed using the longest chord of the circle and the other vertex on the circumference of the circle. However, this information is not enough to determine the area of the 144o sector of the circle. Therefore, statement (2) alone is not sufficient to answer the question.
When we combine the information from both statements, we can find the area of the 144o sector of the circle using the method described above. Therefore, both statements together are sufficient to answer the question.
Hence, the correct answer is option (D).
Diagonal of square = √(2 x side²) = √(2 x 64) = 8√2
Diameter of circle = 8√2 cm
The area of the circle is given by the formula A = πr², where r is the radius of the circle. We know that the radius is half of the diameter, so:
Radius of circle = 4√2 cm
The area of the whole circle is therefore:
A = πr² = π(4√2)² = 32π
The area of the 144o sector is 144/360 times the area of the whole circle:
Area of sector = (144/360) x (32π) = 12π
Therefore, statement (1) alone is sufficient to answer the question.
Statement (2) gives us the length of the equal sides of an isosceles triangle that is constructed using the longest chord of the circle and the other vertex on the circumference of the circle. However, this information is not enough to determine the area of the 144o sector of the circle. Therefore, statement (2) alone is not sufficient to answer the question.
When we combine the information from both statements, we can find the area of the 144o sector of the circle using the method described above. Therefore, both statements together are sufficient to answer the question.
Hence, the correct answer is option (D).
|
Explore Courses for GMAT exam
|
|
Similar GMAT Doubts
Top Courses for GMATView all
What is the area of the 144o sector of the circle?(1)The square with one of the sides as the chord that subtends an angle of 90o on the circle measures 64 sq. cm. in area.(2) When an isosceles triangle is constructed by taking the longest chord of the circle and the other vertex on the circumference of the circle, the length of each of the equal sides of the triangle is 4√2 cm.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone 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.Correct answer is option 'D'. Can you explain this answer?
Question Description
What is the area of the 144o sector of the circle?(1)The square with one of the sides as the chord that subtends an angle of 90o on the circle measures 64 sq. cm. in area.(2) When an isosceles triangle is constructed by taking the longest chord of the circle and the other vertex on the circumference of the circle, the length of each of the equal sides of the triangle is 4√2 cm.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone 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.Correct answer is option 'D'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about What is the area of the 144o sector of the circle?(1)The square with one of the sides as the chord that subtends an angle of 90o on the circle measures 64 sq. cm. in area.(2) When an isosceles triangle is constructed by taking the longest chord of the circle and the other vertex on the circumference of the circle, the length of each of the equal sides of the triangle is 4√2 cm.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone 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.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the area of the 144o sector of the circle?(1)The square with one of the sides as the chord that subtends an angle of 90o on the circle measures 64 sq. cm. in area.(2) When an isosceles triangle is constructed by taking the longest chord of the circle and the other vertex on the circumference of the circle, the length of each of the equal sides of the triangle is 4√2 cm.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone 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.Correct answer is option 'D'. Can you explain this answer?.
What is the area of the 144o sector of the circle?(1)The square with one of the sides as the chord that subtends an angle of 90o on the circle measures 64 sq. cm. in area.(2) When an isosceles triangle is constructed by taking the longest chord of the circle and the other vertex on the circumference of the circle, the length of each of the equal sides of the triangle is 4√2 cm.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone 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.Correct answer is option 'D'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about What is the area of the 144o sector of the circle?(1)The square with one of the sides as the chord that subtends an angle of 90o on the circle measures 64 sq. cm. in area.(2) When an isosceles triangle is constructed by taking the longest chord of the circle and the other vertex on the circumference of the circle, the length of each of the equal sides of the triangle is 4√2 cm.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone 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.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the area of the 144o sector of the circle?(1)The square with one of the sides as the chord that subtends an angle of 90o on the circle measures 64 sq. cm. in area.(2) When an isosceles triangle is constructed by taking the longest chord of the circle and the other vertex on the circumference of the circle, the length of each of the equal sides of the triangle is 4√2 cm.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone 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.Correct answer is option 'D'. Can you explain this answer?.
Solutions for What is the area of the 144o sector of the circle?(1)The square with one of the sides as the chord that subtends an angle of 90o on the circle measures 64 sq. cm. in area.(2) When an isosceles triangle is constructed by taking the longest chord of the circle and the other vertex on the circumference of the circle, the length of each of the equal sides of the triangle is 4√2 cm.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone 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.Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT.
Download more important topics, notes, lectures and mock test series for GMAT Exam by signing up for free.
Here you can find the meaning of What is the area of the 144o sector of the circle?(1)The square with one of the sides as the chord that subtends an angle of 90o on the circle measures 64 sq. cm. in area.(2) When an isosceles triangle is constructed by taking the longest chord of the circle and the other vertex on the circumference of the circle, the length of each of the equal sides of the triangle is 4√2 cm.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone 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.Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
What is the area of the 144o sector of the circle?(1)The square with one of the sides as the chord that subtends an angle of 90o on the circle measures 64 sq. cm. in area.(2) When an isosceles triangle is constructed by taking the longest chord of the circle and the other vertex on the circumference of the circle, the length of each of the equal sides of the triangle is 4√2 cm.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone 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.Correct answer is option 'D'. Can you explain this answer?, a detailed solution for What is the area of the 144o sector of the circle?(1)The square with one of the sides as the chord that subtends an angle of 90o on the circle measures 64 sq. cm. in area.(2) When an isosceles triangle is constructed by taking the longest chord of the circle and the other vertex on the circumference of the circle, the length of each of the equal sides of the triangle is 4√2 cm.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone 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.Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of What is the area of the 144o sector of the circle?(1)The square with one of the sides as the chord that subtends an angle of 90o on the circle measures 64 sq. cm. in area.(2) When an isosceles triangle is constructed by taking the longest chord of the circle and the other vertex on the circumference of the circle, the length of each of the equal sides of the triangle is 4√2 cm.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone 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.Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice What is the area of the 144o sector of the circle?(1)The square with one of the sides as the chord that subtends an angle of 90o on the circle measures 64 sq. cm. in area.(2) When an isosceles triangle is constructed by taking the longest chord of the circle and the other vertex on the circumference of the circle, the length of each of the equal sides of the triangle is 4√2 cm.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone 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.Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice GMAT tests.
|
|
Explore Courses for GMAT exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup