2004 · Q113
113. There are four persons A, B, C and D. The total amount of money with A and B together is equal to the total amount of money with C and D together. But the total amount of money with B and D together is more than the amount of money with A and C together. The amount of money with A is more than that with B. Who has the least amount of money?
MathematicsLogical Reasoning
- AB
- BC
- CD
- DCannot be determined
Explanation
Let the amounts be a, b, c, d. From a+b = c+d and b+d > a+c we get (b−a)+(d−c) > 0; since a > b, b−a is negative, so d−c must exceed a−b, giving d > c. Also b+d > a+c with c = a+b−d gives 2d > 2a, i.e. d > a. And c = a+b−d < b (since d > a). Thus c < b < a < d, so C has the least money.