If J and K are points in a plane and J lies inside the circle C with c

Question

If J and K are points in a plane and J lies inside the circle C with center O and radius 4, does K lie inside circle C?

(1) The length of line segment JK is 1
(2) The length of line segment OJ is 2.5

Bunuel · Answer

0akshay0 · Answer

St I JK = 1, for this there are 2 possibilities, a. Both J and K are inside the circle b. Only J is inside the circle. (see image - part 1) St I is insufficient St II OJ = 2.5 - this gives no information about K St II is insufficient Combining both statements we can deduce that K lies inside the circle (see image - part 2) Since OJ = 2.5 and JK = 1, point K will always be inside the circle with Radius = 4 Hence Option C is correct. Hit Kudos If you liked it. 8-)

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ScottTargetTestPrep · Answer

Solution:
 
 Statement One Alone:
 
The length of line segment JK is 1.

We can’t determine whether K lies inside circle C or not based on the information given. For example, if J is very close to O, then K is inside the circle. However, if J is very close to the circumference of circle O, then K could be outside the circle. Statement one alone is not sufficient.

Statement Two Alone:
 
The length of line segment OJ is 2.5.

Since this doesn’t tell us anything about K, statement two alone is not sufficient.

Statements One and Two Together:
 
With the information from both statements, we see that line segment OK is no longer than JK + OJ = 1 + 2.5 = 3.5 (note: OK = 3.5 if points O, J and K are collinear; otherwise, OK < 3.5). Since the radius of circle C is 4, this means K must lie inside the circle. Both statements together are sufficient.

Answer: C

If J and K are points in a plane and J lies inside the circle C with c

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GMAT Data Sufficiency (DS) Questions

If J and K are points in a plane and J lies inside the circle C with c

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