Problem: In triangle ABC the medians AM and CN to sides BC and AB, respectively intersect in point O. P is the midpoint of side AC and MP intersects CN in Q. If the area of triangle OMQ is n, then the area of triangle ABC is:
Answer Choices:
A. 16 n
B. 18 n
C. 21 n
D. 24 n
E. 27 n
Solution:
In area △COM=21​△COB=21​⋅31​△ABC=61​△ABC=△CQM+n=81​△ABC+n
∴61​△ABC=81​△ABC+n
∴n=241​△ABC∴△ABC=24n