Beat The GMAT a GMAT & MBA community

I believe the answer is (a) but I am not totally sure.

What you really want to know is, given (1) or (2), does the above equation definitely have a solution at x=0 (the y intercept)

For (1), let x=0. You have

x^2 + y^2 - 2yb + b^2 = 16
y^2 - 2yb = 16 - (a^2 + b^2)

since a^2 + b^2 = 16 from (1), we know that the right hand side of that equation has to be negative. In other words

y^2 - 2yb = some number less than zero
y^2 - 2yb < 0

y^2 < 2yb

either

y < 2b if y is positive
y > 2b if y is negative

There is a definite solution for these two possibilities.

To check for (2), observe the 2 situations

a = b+5 if b is positive
a = 5-b if b is negative

(b+5)^2 + (y-b)^2 = 16
(y-b)^2 = 16 - (b+5)^2

This obviously has a solution when b=-1 because that reduces to

(y+1)^2 = 0, which y =-1

But note that this has no solution when 16-(b+5)^2 < 0 because (y-b)^2 will always be a positive number. So this does NOT always yield the same answer. Thus (2) does not provide enough information.

(x-a)^2 + (y-b)^2=16

the curve is a a circle with a radius of 4 having center at (a,b)

now for this to cut the y axis |a| <4

1) Doesn't help - Insufficient

2) a >5; sufficient the curve doesnt cut the y axis

B

_________________
Always borrow money from a pessimist, he doesn't expect to be paid back.

That's a great way of looking at it. I didn't really see it that way.

Ajith, I am not sure if it is a stupid question, but how did you find that the curve is a circle. Also, after identifying its a circle how did you solve the rest of the problem.

I will really appreciate if you can explain this in more detail. I am not very good in XY plane Q's.

Vineet

x*2 + y*2 = a*2 is the standard form of a circle.. (Read * as power of)


Cheers,
Siva
GMAT Aspirant

_________________
I have a dream ...

and (x-a)*2 + (y-a)*2 = a*2 is a circle with centre at (a,b)

_________________
I have a dream ...

In this qs within the scope of GMAT ?

I do not think so

I can see 2 ways to solve it
1. Using geometry (involves equation of a circle etc etc)
2. Using Quadratic Equations (Involves finding out whether quadratic equation has real roots etc..)

Both of which are beyond the scope of GMAT.

_________________
Always borrow money from a pessimist, he doesn't expect to be paid back.

While I agree this isn't a "standard" GMAT problem, solving quadratics is certainly within the scope of the GMAT. I don't think its easy but it certainly COULD be asked.

@ Ajith

acc to yr equations , u can assume that point a and point b will be less than 4 always. N this may be or may not is not the case here.


they can be any point. Let say a , b are 8, 10 then even radius is 4 then ofcourse do not cut Y axis but let say

point is 1 and 2 then circle will cut Y axis.



plz put OA

_________________
What you think, you become.

When did I make that assumption?

I only said radius is 4 and the circle will cut y axis if the absolute value of a is less than 4. These are not assumptions, these are facts [There is a slight difference]

a,b can be anything

and 2) proves that a is greater than 5 - again no assumptions -

I am not getting the "assumption" you talk about here

_________________
Always borrow money from a pessimist, he doesn't expect to be paid back.

Ajit have solved this question beautifully

another way is

curve will touch the y axis when x =0

therefore, a^2 + (y-b)^2 = 16

y^2 - 2yb + a^2 + b^2 -16 = 0

b^2 - 4ac >= 0, checking the roots

4b^2 - 4(1)(a^2 + b^2 -16) >=0
a^2 <=16

a^2-16<=0
(a+4)(a-4)<=0

a<= -4 or a<= 4

|a| <= 4


which is same what Ajit has found quickly

_________________
What you think, you become.

What I understand from this question is that we need to know the distance between the center point of the circle and the y - axis i.e the y - intercept of the point.

(2) a=|b|+5

from this we do not care about the value for 'a' which is the x-intercept.

So could any of the experts please guide whether i m correct or wrong.

I am getting the value b as + or - 5. Hence the correct answer is B.

Could any of you help...

_________________
IT IS TIME TO BEAT THE GMAT

LEARNING, APPLICATION AND TIMING IS THE FACT OF GMAT AND LIFE AS WELL... KEEP PLAYING!!!

Whenever you feel that my post really helped you to learn something new, please press on the 'THANK' button.