2023 · Q93
Question: What is the 3-digit number which is divisible by 10?
Statement IIf the digits in hundred's place and ten's place of the number are interchanged, the resulting number is diminished by 180.
Statement IIIf the digit in hundred's place is halved and digit in ten's place and unit place of the number are interchanged, the resulting number is diminished by 336. Mark option (a) if the question can be answered by using one of the statements alone, but cannot be answered using the other statement alone. Mark option (b) if the question can be answered by using either statement alone. Mark option (c) if the question can be answered by using both the statements together, but cannot be answered using either statement alone. Mark option (d) if the question cannot be answered even by using both the statements together.
Elementary MathematicsNumber System
- AThe question can be answered by using one of the statements alone, but cannot be answered using the other statement alone
- BThe question can be answered by using either statement alone
- CThe question can be answered by using both the statements together, but cannot be answered using either statement alone
- DThe question cannot be answered even by using both the statements together
Explanation
N=100a+10b. St.I: 90(a-b)=180, a-b=2: 8 possibilities, insufficient. St.II: 50a+9b=336 uniquely (a,b)=(6,4), N=640: sufficient alone. One statement alone suffices. Option (a). Key disputed: verify against the official UPSC key.