Which of the numbers A, B, C, D is the largest number, if the following threeConditions are meet. A + B

Well, Given these
conditions:

A + B < C + D
B + D
< A + C 
A + D < B + C

By the
property of inequalities, same signed inqualities can add or subtract each
other

by adding the first
two

A+ 2B +D < A+ 2C +
D

subtract A+D from both sides, we
have

2B<2C

B<C

add
the last two equations together, we
have:

A+B+2D<A+B+2C

subtract
A+B from both sides, we
have:

2D<2C

D<C

ok,
without evaluating A and C's relationship, we know that B and D are out of the
game

add the first and last
together

2A+B+D<2C+B+D

Subtract
b+d from both
sides

2A<2C

A<C

the
winner is C

C is the biggest number among the
four given the conditions