To determine who receives the smallest amount, we establish the relationships between the amounts received by A, B, C, and D based on the given statements.
Correct Option (A)
Let the amounts received by A, B, C, and D be represented by the variables A, B, C, and D, respectively.
- From the statement "A gets one less than B": A = B - 1. This implies that B receives more than A.
- From the statement "D gets 3 more than B": D = B + 3. This implies that D receives more than B.
- From the statement "C gets 5 more than D": C = D + 5. This implies that C receives more than D.
Now, we can express all amounts in terms of B:
- A = B - 1
- B = B
- D = B + 3
- Substitute D = B + 3 into the equation for C: C = (B + 3) + 5 = B + 8.
Comparing these expressions, we can establish the following order of amounts received:
- A = B - 1
- B = B
- D = B + 3
- C = B + 8
Arranging these in ascending order based on their values relative to B:
A < B < D < C
Therefore, A receives the smallest amount.
Incorrect Options:
Based on the derived order A < B < D < C:
- Option B (B): B receives more than A (B = A + 1), making B not the smallest amount.
- Option C (C): C receives the largest amount (C = B + 8), making C not the smallest amount.
- Option D (D): D receives more than B (D = B + 3), making D not the smallest amount.