What is the qualifying mark?

A and B are shooters and having their exam. A and B fall short of 10 and 2 shots respectively to the qualifying mark. If each of them fired atleast one shot and even by adding their total score together, they fall short of the qualifying mark, what is the qualifying mark?
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Mark Haynes

  • Jan 17th, 2012
 

The Qualifying Mark is: 11

Given:
A = the shots by A
B = the shots by B
Q = the Qualifying Mark

We know that:

A + 10 = Q
B + 2 = Q
A + B < Q
A >= 1
B >= 1

If A + B < Q and B + 2 = Q Then A < 2

If A >= 1 and all shots are of course whole numbers Then A = 1

If A = 1 then Q = 11
If Q = 11 then B = 9

Thus:

(A + 10 = Q)
1 + 10 = 11

(B + 2 = Q)
9 + 2 = 11

(A + B < Q)
1 + 9 < 11

(A >= 1)
1 >= 1

(B >= 1)
9 >= 1

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