Welcome! Check out our free B-School Guides to learn how you compare with other applicants.

intersect the y-axis

This topic has 1 expert reply and 14 member replies
Goto page
• 1,
• 2
abhi332 Really wants to Beat The GMAT!
Joined
30 Dec 2009
Posted:
117 messages
Thanked:
3 times
Target GMAT Score:
700+
intersect the y-axis Wed Feb 24, 2010 6:01 am
Elapsed Time: 00:00
• Lap #[LAPCOUNT] ([LAPTIME])
Does the curve (x-a)^2 + (y-b)^2=16 intersect the y-axis ?

(1) a^2+b^2>16
(2) a=|b|+5

_________________
What you think, you become.

Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
ldoolitt Really wants to Beat The GMAT!
Joined
14 Apr 2007
Posted:
184 messages
Thanked:
17 times
Test Date:
None
Target GMAT Score:
780
Wed Feb 24, 2010 9:07 am
abhi332 wrote:
Does the curve (x-a)^2 + (y-b)^2=16 intersect the y-axis ?

(1) a^2+b^2>16
(2) a=|b|+5
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.

ajith GMAT Titan
Joined
22 Sep 2006
Posted:
1274 messages
Followed by:
1 members
Thanked:
119 times
Test Date:
April 2010
Target GMAT Score:
740
Wed Feb 24, 2010 10:29 am
abhi332 wrote:
Does the curve (x-a)^2 + (y-b)^2=16 intersect the y-axis ?

(1) a^2+b^2>16
(2) a=|b|+5
(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.

ldoolitt Really wants to Beat The GMAT!
Joined
14 Apr 2007
Posted:
184 messages
Thanked:
17 times
Test Date:
None
Target GMAT Score:
780
Wed Feb 24, 2010 1:46 pm
ajith wrote:
abhi332 wrote:
Does the curve (x-a)^2 + (y-b)^2=16 intersect the y-axis ?

(1) a^2+b^2>16
(2) a=|b|+5
(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
That's a great way of looking at it. I didn't really see it that way.

vineetbatra GMAT Destroyer!
Joined
19 Feb 2009
Posted:
355 messages
Followed by:
1 members
Thanked:
2 times
Wed Feb 24, 2010 5:29 pm
ajith wrote:
abhi332 wrote:
Does the curve (x-a)^2 + (y-b)^2=16 intersect the y-axis ?

(1) a^2+b^2>16
(2) a=|b|+5
(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
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

sivareddy Just gettin' started!
Joined
21 Feb 2010
Posted:
4 messages
Test Date:
June
Target GMAT Score:
750+
Wed Feb 24, 2010 9:25 pm
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 ...

sivareddy Just gettin' started!
Joined
21 Feb 2010
Posted:
4 messages
Test Date:
June
Target GMAT Score:
750+
Wed Feb 24, 2010 9:26 pm
and (x-a)*2 + (y-a)*2 = a*2 is a circle with centre at (a,b)

_________________
I have a dream ...

kstv GMAT Destroyer!
Joined
15 Jan 2010
Posted:
610 messages
Followed by:
1 members
Thanked:
43 times
Thu Feb 25, 2010 1:58 am
In this qs within the scope of GMAT ?

ajith GMAT Titan
Joined
22 Sep 2006
Posted:
1274 messages
Followed by:
1 members
Thanked:
119 times
Test Date:
April 2010
Target GMAT Score:
740
Thu Feb 25, 2010 2:18 am
kstv wrote:
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.

ldoolitt Really wants to Beat The GMAT!
Joined
14 Apr 2007
Posted:
184 messages
Thanked:
17 times
Test Date:
None
Target GMAT Score:
780
Thu Feb 25, 2010 2:39 am
ajith wrote:
kstv wrote:
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.
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.

girish3131 Really wants to Beat The GMAT!
Joined
14 Jan 2010
Posted:
194 messages
Thanked:
2 times
Thu Feb 25, 2010 6:45 am
@ 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

abhi332 Really wants to Beat The GMAT!
Joined
30 Dec 2009
Posted:
117 messages
Thanked:
3 times
Target GMAT Score:
700+
Thu Feb 25, 2010 6:48 am
OA:B

_________________
What you think, you become.

ajith GMAT Titan
Joined
22 Sep 2006
Posted:
1274 messages
Followed by:
1 members
Thanked:
119 times
Test Date:
April 2010
Target GMAT Score:
740
Thu Feb 25, 2010 6:53 am
girish3131 wrote:
@ 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.

plz put OA
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.

abhi332 Really wants to Beat The GMAT!
Joined
30 Dec 2009
Posted:
117 messages
Thanked:
3 times
Target GMAT Score:
700+
Thu Feb 25, 2010 6:58 am
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.

amit.trivedi@ymail.com GMAT Destroyer!
Joined
09 Nov 2010
Posted:
934 messages
Followed by:
14 members
Thanked:
59 times
Test Date:
N.A
Target GMAT Score:
750
Wed Mar 14, 2012 12:38 am
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.

Best Conversation Starters

1 varun289 43 topics
2 greenwich 30 topics
3 sana.noor 21 topics
4 guerrero 20 topics
5 killerdrummer 19 topics
See More Top Beat The GMAT Members...

Most Active Experts

1 Brent@GMATPrepNow

GMAT Prep Now Teacher

202 posts
2 GMATGuruNY

The Princeton Review Teacher

143 posts
3 Anju@Gurome

Gurome

134 posts
4 Jim@StratusPrep

Stratus Prep

86 posts
5 David@VeritasPrep

Veritas Prep

41 posts
See More Top Beat The GMAT Experts