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50% (01:27) wrong based on 1 sessions
If curves x^2 + y^2 = 4 and y = |x| enclose a sector on the top part of XY-plane, what is the area of this sector? (A) \frac{\pi}{4}(B) \frac{\pi}{2}(C) \pi(D) 2\pi(E) 3\pi Source: GMAT Club Tests - hardest GMAT questions The area of the circle is \pi 2^2 = 4\pi . The area of the sector = \text{(the area of the circle)}*\frac{90}{360} = \pi . The correct answer is C. Shouldn't the answer be B, since the top part of the sector is only 45degrees. The whole thing is 90 degrees, but half of it is at the bottom of the xy plane.
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11MBA wrote: If curves x^2 + y^2 = 4 and y = |x| enclose a sector on the top part of XY-plane, what is the area of this sector?
(C) 2008 GMAT Club - m14#28
* \frac{\pi}{4}
* \frac{\pi}{2}
* \pi
* 2\pi
* 3\pi
The area of the circle is \pi 2^2 = 4\pi . The area of the sector = \text{(the area of the circle)}*\frac{90}{360} = \pi .
The correct answer is C.
Shouldn't the answer be B, since the top part of the sector is only 45degrees. The whole thing is 90 degrees, but half of it is at the bottom of the xy plane. x^2 + y^2 = 4 is an equation of a circle centered at the origin and the radius \sqrt{4}=2. Graph of the function y = |x| is given below: Attachment: 
graph_modulus.png [ 7.61 KiB | Viewed 4161 times ]
Top part of the sector would be a sector with 90 degrees angle, and its area would be 1/4 of that of the circle (circle 360 degrees). Area of the circle = {\pi}{r^2}=4\pi, 1/4 of this value = \pi.
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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory
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. NEW!!!
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. NEW!!!
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Manager
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My bad. I graphed abso(y)=x, and that's why i only had half of the graph be above the xy plane. Sorry.
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Intern
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I know these are supposed to be the toughest challenges, but is this something which is included in the scope of the GMAT? I thought coordinate plane on GMAT was restricted to straight line equations only.... Posted from my mobile device 
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From x^2 + y^2 = r^2 => radius = 2 Area of the circle = [img]\pi[/img]r^2 The line |x| has a reflection about the origin at [img]90^{\circ}[/img] Area of sector is 1/4 x area of circle = [img]\pi[/img]4/4 = [img]\pi[/img] Therefore ans is C
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The top most sector makes an angle of 90 degrees. But, here we are to find the enclosed angle as shown in the figure. How can that be 90 degree? Am i missing something here???
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Oh!!!! i got it....hehehe
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Its C.
The sector makes an angle of 90 degrees at the center of the circle. So area of the sector = area of the circle/4 = pi
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I did not know the equation for a circle, so had to spend extra seconds figuring out that x^2 + Y^2 = 4 was indeed the equation of a circle with radius 2. I ended up with C, but probably took 30-60s more than I should have.
Question - do these type of problems represent the problems at the 700-800 level on the GMAT? I thought the equation for a circle was pretty much out of scope for the GMAT. I hear that the GMAT quant section is getting tougher but is this (problems like this) the level where its headed?
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I saw a lot of questions with circle formulas (both in paper and digital tests) and suppose it's 650 question maximum.
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ulm wrote: I saw a lot of questions with circle formulas (both in paper and digital tests) and suppose it's 650 question maximum. Well, then I'm glad I came across this problem  Could you tell me in which paper and digital tests you saw questions with circle formulas? I've pretty much based my Math theory on the Manhattan guides and don't remember seeing the circle formula there (or for that matter OG11).
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Area of sector = Θ/360°*πr² Now we know that r= 2 and Θ= 90° So, area comes to be π. Answer is C
Attachments
Blank.png [ 196.1 KiB | Viewed 2776 times ]
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AriBenCanaan wrote: ulm wrote: I saw a lot of questions with circle formulas (both in paper and digital tests) and suppose it's 650 question maximum. Well, then I'm glad I came across this problem Could you tell me in which paper and digital tests you saw questions with circle formulas? I've pretty much based my Math theory on the Manhattan guides and don't remember seeing the circle formula there (or for that matter OG11). If we're talking about must-have tests, it definitely was in GMAT Prep.
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y = |x| ---- the slope of this line is (+1) if X is positive and (-1) if X is negative...which means the lines make a 45 degree angle with the x axis...and both the lines sweep a total of 90 degrees...
The circle is 360 degrees -- so the area swept is 1/4 of the total area.
(x^2) + (y^2) = (2)^2
radius = (+/-) 2
Area of the circle = pi*(2^2)
Area of the sector = (1/4)*Area of the circle
Ans: pi (C)
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C the sector has a 90 degree angle.. area of a sector theta(90 degree)/360 x (pi x sq. radius)
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Straight C. As seen in Microstrip's diagram, the area is a quarter of the total area of the circle.
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Why don't we extend both the lines and account for the 45 degree angle formed in the quadrants III & IV ? I am sorry if its a silly question.
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Bunuel wrote: 11MBA wrote: If curves x^2 + y^2 = 4 and y = |x| enclose a sector on the top part of XY-plane, what is the area of this sector?
(C) 2008 GMAT Club - m14#28
* \frac{\pi}{4}
* \frac{\pi}{2}
* \pi
* 2\pi
* 3\pi
The area of the circle is \pi 2^2 = 4\pi . The area of the sector = \text{(the area of the circle)}*\frac{90}{360} = \pi .
The correct answer is C.
Shouldn't the answer be B, since the top part of the sector is only 45degrees. The whole thing is 90 degrees, but half of it is at the bottom of the xy plane. x^2 + y^2 = 4 is an equation of a circle centered at the origin and the radius \sqrt{4}=2. Graph of the function y = |x| is given below: Attachment: graph_modulus.png Top part of the sector would be a sector with 90 degrees angle, and its area would be 1/4 of that of the circle (circle 360 degrees). Area of the circle = {\pi}{r^2}=4\pi, 1/4 of this value = \pi. How did you find the radius " x^2 + y^2 = 4 is an equation of a circle centered at the origin and the radius \sqrt{4}=2." can you please explain?
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kuttingchai wrote: Bunuel wrote: 11MBA wrote: If curves x^2 + y^2 = 4 and y = |x| enclose a sector on the top part of XY-plane, what is the area of this sector?
(C) 2008 GMAT Club - m14#28
* \frac{\pi}{4}
* \frac{\pi}{2}
* \pi
* 2\pi
* 3\pi
The area of the circle is \pi 2^2 = 4\pi . The area of the sector = \text{(the area of the circle)}*\frac{90}{360} = \pi .
The correct answer is C.
Shouldn't the answer be B, since the top part of the sector is only 45degrees. The whole thing is 90 degrees, but half of it is at the bottom of the xy plane. x^2 + y^2 = 4 is an equation of a circle centered at the origin and the radius \sqrt{4}=2. Graph of the function y = |x| is given below: Attachment: graph_modulus.png Top part of the sector would be a sector with 90 degrees angle, and its area would be 1/4 of that of the circle (circle 360 degrees). Area of the circle = {\pi}{r^2}=4\pi, 1/4 of this value = \pi. How did you find the radius " x^2 + y^2 = 4 is an equation of a circle centered at the origin and the radius \sqrt{4}=2." can you please explain? Check here: math-coordinate-geometry-87652.html (Circle on a plane chapter). Hope it helps.
_________________
PLEASE READ AND FOLLOW: 11 Rules for Posting!!!
RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory
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. NEW!!!
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. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
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