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Simple coordinate geometry Quant Review 2nd Ed #22

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by runningguy » Sat Sep 21, 2013 11:41 am
In the xy-plane, point (r,s) lies on a circle with center at the origin. What is the value of r^2 + s^2?

1) The circle has a radius 2.
2) The point (sqrt2, -sqrt2) lies on the circle.



Would someone mind drawing a picture for this. I'm not understanding how to set up this problem.
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Source: — Data Sufficiency |
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by theCodeToGMAT » Sat Sep 21, 2013 6:50 pm
Image

ANWER [spoiler]{D}[/spoiler]
R A H U L
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by mevicks » Sun Sep 22, 2013 8:09 am
runningguy wrote:In the xy-plane, point (r,s) lies on a circle with center at the origin. What is the value of r^2 + s^2?

1) The circle has a radius 2.
2) The point (sqrt2, -sqrt2) lies on the circle.



Would someone mind drawing a picture for this. I'm not understanding how to set up this problem.
Step 1: (Simplify):
Consider the following diagram, (r,s) is on the circle and can be any where (depends on the value of r and s). However the question just asks us to find Image so essentially it is asking us to find the radius of the circle. Restated question => What is the radius of the circle?
Image

Step 2: (Consider the statements 1 and 2)
St1: Gives the radius directly, SUFFICIENT
St2: Gives another point which is again on the circle, and thus by Pythagoras theorem Image
Thus, radius =Image= 2
SUFFICIENT.

ANSWER is D
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by lunarpower » Mon Sep 23, 2013 3:23 am
mevicks wrote:St2: Gives another point which is again on the circle, and thus by Pythagoras theorem Image
Thus, radius =Image= 2
SUFFICIENT.
Way too much work for statement 2.
* You have the center (= the origin).
* You're given a specific point.
* So, you have the radius.
Done. Sufficient.

If you calculate anything for this statement, you're wasting your time -- and, more importantly, you're forgetting the goal of the problem!
The goal of DS problems is not to find answers. If you know that the answer can be found, that's enough.
Ron has been teaching various standardized tests for 20 years.

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