A circle with center (1, 0) and radius 2 lies in the

Question

A circle with center (1, 0) and radius 2 lies in the coordinate plane . If point (x, y) lies on the circle is (x, y) in quadrant 2?

(1) | y | > 1
(2) | x | > 1

KarishmaB · Accepted Answer

As fluke pointed out, it is a good idea to draw a diagram here. In fact, in most co-ordinate geometry questions, a diagram is almost a must. Ques: Is (x, y) in quadrant II? Ques2.jpg Stmnt 1: | y | > 1 Look at the red lines above. Here | y | > 1 on the y axis. So (x,y) can be any point on the green region. It may or may not lie in the second quadrant. Not sufficient. Stmnt 2: | x | > 1 Look at the blue line above. Here | x | > 1 on the x axis. So (x,y) can be any point on the orange line. None of these points lie in the second quadrant. Sufficient. Answer (B).

ozwizard · Answer

the answer is B.
let us consider the 1st statement. y could be y>1 or y<-1. Since we do not know anything about x, the point (x,y) may lie in any of the quadrants. Not suff.
St. 2. If |x|>1, then x>1 or x<-1. But x<-1 is impossible since it lies outside the circle. So we are left with x>1. Is a point (x,y) has x>1, it definitely cannot lie on the second quadrant, but only in the first or fourth. Suff.

fluke · Answer

If you draw a circle, you can solve it quickly. We can see that for the 2nd quadrant, the (x,y) coordinate must be between (0,\sqrt{3}) and (-1,0) . As we can clearly see that, if the radius is 2 and center is at (1,0); the extreme value of x for 2nd quadrant will be 1-2=-1, where y will be 0. We know the extreme value for x; i.e. -1 Let's find out the extreme value for y; y will be maximum when x=0; We can find y where x=0 by Pythagoras theorem; Distance between origin and the center is 1. Distance between center and the intersection of circle and y-axis is 2(radius). Thus, distance between origin and extreme value of y in 2nd quadrant = \sqrt{2^2-1^2}=\sqrt{3}\approx 1.73 Thus we know the extreme(maximum) value for both x and y in the 2nd quadrant. x<=-1 & y<=1.73 1. |y| > 1 Thus y can be 1.2 or 1.8. 1.2<1.73 1.8>1.73 (x,y) may or may not be in the 2nd quadrant Not Sufficient. 2. |x| > 1 As we know that the maximum value of x in 2nd quadrant is 1. (x,y) can't be in the 2nd quadrant because |x|>1. Sufficient. Ans: "B" ***************** Please take a look at the image to get a visual clarification as well.

brandy96 · Answer

Thanks Fluke. Great explanation.

gmat1220 · Answer

Interesting! Consider this we move the center to origin then both statements are insufficient. But not now.

Posted from my mobile device

jlgdr · Answer

Statement 1 Could be any quadrant actually Statement 2 | x | > 1 means either x>1 or x<-1 Since circle has radius 2 and centered at (1,0) then x cannot be less than -1. Therefore, x>1 So it CANNOT be on the second quadrant Hence, answer is B only Hope it helps! Cheers! J

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

A circle with center (1, 0) and radius 2 lies in the

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

A circle with center (1, 0) and radius 2 lies in the

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards