Let O be the intersection point of medians AP and CQ of triangle ABC. If OQ is 3 inches, then OP, in inches, is:

1968 AMC 12 Problem 7

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Let

O

be the intersection point of medians

AP

and

CQ

of triangle

ABC.

OQ

3

inches, then

OP,

in inches, is:

3

\dfrac92

6

9

undetermined

A centroid gives a ratio only along each individual median

Knowing part of

CQ

does not determine the length of

AP

The centroid divides each median in a

2:1

ratio, so

OQ=3

determines

CQ=9.

It gives no relation between the lengths of the two different medians

CQ

and

AP.

Triangles with

CQ=9

can have different

AP,

OP

is undetermined.

Therefore, the correct answer is E.