Students AB and C compete in a series of tests For coming in

Students A,B and C compete in a series of tests. For coming in first on any given test, one is awarded x points; for placing second, y points; and for third place, z points. Let x, y, and z be natural numbers with x > y > z. Assume no ties on any of the tests. Student A accumulated 20 points; student B got 10 points, and student C got 9 points. Student A came in second on the Algebra test. Who finished second on the Geometry test?

Solution

Student A came 2nd in Algebra. But he has the highest point. So, in gometry test he must be 1st.

Student B if 1st in Algebra he must be 3rd in geometry and C being 3rd in Algebra came 2nd in geometry to get the lowest point.

So, C came 2nd in Geometry.