Bunuel wrote:

In the diagram above, O is the center of the circle and angle AOB = 144º. What is the area of the circle?

(1) The area of sector AOB is 40% of the area of the circle

(2) Arc ACB has a length of \(14\pi\).

MAGOOSH OFFICIAL SOLUTION:First of all, we should think about the prompt a bit. This angle, 144º, is what fraction of a full circle? Well, both 144 and 360 are divisible by 4: 144 ÷ 4 = 36 and 360 ÷ 4 = 90, so 144/360 = 2/5.

This angle is 2/5 of the whole circle, so the arc is 2/5 of the whole circumference. Also, remember that if we can find anything about the whole circle, for example, the circumference, then we can find the radius, which would allow us to find the area.

Statement #1: This is a tautological statement. A tautological statement is a statement that, by definition, has to be true, and because of this, it contains no information. Statements such as “My car is a car” and “My employer employs me” are verbal tautologies: they contain no useful information. Much in the same way, we already know from the prompt that the angle takes up 2/5 of the circle, so of course the sector would take up 2/5, or 40%, of the area. This statement repeats information in the prompt, and contains no new information, so it doesn’t help us at all to figure out anything else. This statement, alone and by itself, is not sufficient.

Statement #2: We already know this arc is 2/5 of the whole circumference, so we could set up a proportion to find the circumference. From that, we could find the radius, and that would allow us to find the area. This statement, alone and by itself, is sufficient.

Answer = (B)

_________________

New to the Math Forum?

Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:

GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:

PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.

What are GMAT Club Tests?

Extra-hard Quant Tests with Brilliant Analytics