A Question is given followed by two Statements I and II. Consider the Questions and the Statements. A certain amount was distributed among X, Y and Z. Question : Who received the least amount? Statement-I : X received 4/5 of what Y and Z together received. Statement-II: Y received 2/7 of what X and Z together received. Which one of the following is correct in respect of the above Question and the Statements?

1. A. The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
2. B. The Question can be answered by using either Statement alone
3. C. The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
4. D. The Question cannot be answered even by using both the Statements together

Answer: C

Explanation

Let the total amount distributed be T = X + Y + Z.

**Statement I: X received 4/5 of what Y and Z together received.**
X = (4/5)(Y + Z)
Since Y + Z = T – X, we have X = (4/5)(T – X)
5X = 4T – 4X => 9X = 4T => X = 4T/9.
This statement tells us X’s share relative to the total, but we cannot compare X, Y, and Z individually. So, Statement I alone is insufficient.

**Statement II: Y received 2/7 of what X and Z together received.**
Y = (2/7)(X + Z)
Since X + Z = T – Y, we have Y = (2/7)(T – Y)
7Y = 2T – 2Y => 9Y = 2T => Y = 2T/9.
This statement tells us Y’s share relative to the total, but we cannot compare X, Y, and Z individually. So, Statement II alone is insufficient.

**Combining Statement I and Statement II:**
From Statement I, X = 4T/9.
From Statement II, Y = 2T/9.
Since X + Y + Z = T, we can find Z:
(4T/9) + (2T/9) + Z = T
6T/9 + Z = T
2T/3 + Z = T
Z = T – 2T/3 = T/3 = 3T/9.

Now we have the shares:
X = 4T/9
Y = 2T/9
Z = 3T/9
Comparing these values, Y (2T/9) received the least amount. Thus, both statements together are sufficient to answer the question. This question tests data sufficiency and algebraic reasoning with ratios.