Finding the unit digit of a large power sum
Question
A Question is given followed by two Statements I and II. Consider the Question 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.
Options
The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
The Question can be answered by using either Statement alone
The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
The Question cannot be answered even by using both the Statements together
Explanation
Let the total sum distributed be T = X + Y + Z. To rank the individual amounts, translate the statements into fractional shares of T:
Statement I: X = 4/5(Y + Z). Add X to both sides or use ratio components: X/Y+Z = 4/5. This implies X gets 4 parts out of a total 4+5=9 parts. Hence, X = 4/9T = 0.444T. This leaves Y+Z = 5/9T, but doesn't isolate the individual sizes of Y or Z. Insufficient.
Statement II: Y = 2/7(X + Z). This implies Y/X+Z = 2/7, meaning Y receives 2 parts out of 2+7=9 total parts. Hence, Y = 2/9T = 0.222T. This leaves X+Z = 7/9T, but doesn't isolate X or Z individually. Insufficient.
Combine both statements: From Statement I, X = 4/9T. From Statement II, Y = 2/9T. Calculate Z's share: Z = T - X - Y = T - 4/9T - 2/9T = 3/9T = 0.333T.
Comparing the final shares: Y (0.222T) < Z (0.333T) < X (0.444T). This definitively proves Y received the least amount, satisfying sufficiency when combined.
Answer: (c).
Question details
Year
2024
Paper
CSAT
Question
Q65
Section
Numerical Ability
Sub-topic
Unit Digits
Type
Factual single
Difficulty
Medium
Source hint
Number theory cyclicity
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