GMAT Prep Test Math doubts

[gulshank1]

Hi,
I am unable to arrive at the correct answers for the 2 questions attached. The correct answers are highlighted.

[macattack]

For the DS question:
Each statement alone is clearly insufficient.
Taking the combined statement:
Case 1: p=10 and n= 6--->(10+6)(10-6) 16:5 R=1 and 4:3 R=1 and (16*4):15 R=4
Case 2: p=5 and n=1--->(5+1)(5-1) 6:5 R=1 and 4:3 R=1 and (6*4):15 R=9

Since we can get different answers we should choose E.

[macattack]

Now for the geometry problem here is how it goes:
Step 1: calculate the radius of the circle--->R=sqrt((sqrt(3)^2)+1^2)=2
Step 2: Calculate the legth of the hypotenuse of the isosceles right triangle= R*sqrt(2)=2sqrt(2)

Now set up the equations:
Equation 1: s^2+t^2=4 (pythagorean theorem)
Equation 2: sqrt((s+sqrt(3))^2+(t-1)^2)=2sqrt(2) (distance between P and Q = legth of hypotenuse)

Step 3: square Equation 2:
(s+sqrt(3))^2+(t-1)^2=8
s^2+t^2+3+1+2sqrt(3)s-2t=8

Step 4: substitute equation one into equation 2 (s^2+t^2=4)
--->2sqrt(3)s-2t=0

Step 5: Rearrange the terms: t=sqrt(3)*s

Step 6: Plug the possible answer choice and check which one verifies s^2+t^2=4
The only possible answer is 1!
Hope that helped

[Brent@GMATPrepNow]

Note: When posting questions, please use the spoiler function to hide the correct answer. This will allow others to attempt the question without seeing the final answer.


Here's my solution to the geometry question.

So, as you can see s = 1, so the answer is B

Cheers,
Brent

[gulshank1]

Thanks!!

I will make sure the answers are hidden next time.

[macattack]

Hi Brent would like to know if my method is correct? THanks