In the figure shown below, the circle has center at the origin O, and

Question

https://gmatclub.com/forum/download/file.php?id=44965 In the figure shown below, the circle has center at the origin O, and point A has coordinates (13, 0). If point B is on the circle, what is the length of line segment AB? (1) The X-coordinate of point B is −5. (2) The Y-coordinate of point B is −12. 2018-11-07_1305.png

u1983 · Answer

OA = 13  & again  OA^2 =13^2 +0^2 (x^2 +y^2 = a^2 , as centre at origin) 
Also given B is on the circle  x^2 +y^2 = a^2

1) for point B :  x=-5 , thus we will get the value of  y  from  x^2 +y^2 = a^2  and also the value of  AB  from  AB^2 = (13-x)^2 + (0-y)^2  as we have both the value  x  &  y  -----  Sufficient .
2) for point B :  y=-12  , thus we will get the value of  x  from  x^2 +y^2 = a^2  and also the value of  AB  from  AB^2 = (13-x)^2 + (0-y)^2  as we have both the value  x  &  y  -----  Sufficient .
 Ans D .

EzequielLasVelez · Answer

From statemnt 1 there are two posible points for B: (-5,12) and (-5,-12). However both of them give the same line lenght. Hence sufficient.

From statemnt 2 there are two posible points for B: (-5,-12) and (5,-12). Each of them has different line lenghts. Hence insufficient.

Answer A

amanvermagmat · Answer

Hello

I dont understand how from (1), you concluded (-5, 12) and how from (2), you concluded (5, -12). 
The point B is very clearly in the III quadrant where both x and y coordinates are negative.

Can you please explain?

KrishnakumarKA1 · Answer

Hi,

Interesting question, one can fall for a trap answer as “D”, if they have assumed the “point B” to be in the third quadrant.

Given,

Circle centered at Origin(O) and point A has co-ordinates(13,0).

So, OA is the radius of the circle. Length of OA is 13.

Also given, point B is on the circle. Hence OB is also the radius of the circle.

So, OB is also the radius of the circle. Length of OB is 13.

Question: Length of line segment AB?

AB is the chord of the circle.

Statement I is sufficient:

The X-coordinate of point B is −5.

Since we know the radius of the circle, if x – coordinate is -5, then y-coordinate could be either +12 or -12(Refer to the below diagram).

If “point B” is either (-5,12) or (-5,-12) the length of the line segment would be AB is sqrt(468).

So sufficient.

Statement II is insufficient:

The Y-coordinate of point B is −12.

Again we know the radius of the circle already, if y – coordinate is -12, then x-coordinate could be either +5 or -5(Refer to the below diagram).

If “point B” is (-5,-12) the length of the line segment would be AB is sqrt(468).

If “point B” is (5,-12) the length of the line segment would be AB is sqrt(208).

So insufficient.

So the answer is A.

sanjayparihar16 · Answer

Are we also considering the fact that point B can be present in any of the four quadrant? I was thinking of it to be in third quadrant only and that’s why both statements were individually sufficient to me.

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Sent from my iPhone using GMAT Club Forum

KrishnakumarKA1 · Answer

Yes Sanjay. They have mentioned only that Point B is on the circle, so we cant assume that its on the third quadrant. Diagram are just a representation, we cant assume lengths, angles and directions from the pic given in the question(In specific - DS question).

nitesh50 · Answer

Hi

Can someone please explain to me how not to fall in the trap of this question.
When I did this question for the first time, I like most of those who have solved the question up till now went for option D.
I presume we did this, because we saw x2 +y2=169
and B was given in the 3rd quadrant, we assumed it to only be in the 3rd quadrant. and hence eliminated all other possibilities.
So what exactly can i infer or not infer from the question?

Looking forward to any valuable opinion I can get.
 VeritasKarishma   gmatbusters   Gladiator59   Bunuel

Regards

Gladiator59 · Answer

Hi  nitesh50 
The one thing to infer from the question is that not all figures are to be taken at face value. Even though figures used in the GMAT will always be accurate ( unless mentioned not drawn to scale) they need not show the full picture as was the case here... the figure just showed one possible point B ( based on statements B can be anywhere!)

Hope this helps.

Best,
Gladi

BjornMattsson · Answer

Could anyone tell me how is it obvious from statement 1, that point A is on the circle? :/ I mean I can't see any clear dot or similar.

In the figure shown below, the circle has center at the origin O, and

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