Direction : Read the following Information carefully and answer the q...
Information:
- Rahul's roll number in IES Exam is a number consisting of three non-zero distinct digits.
- The sum of the digits at hundreds and unit’s place is equal to half of the digit at ten’s place.
- The sum of all possible three-digit numbers obtained using these three digits without repetition is 2664.
Question: The digits in the unit is
Answer: Can't say
Explanation: To find out the digits in the unit place, we need to first find out the three-digit number that Rahul has.
Let's assume the digit at the ten’s place is x.
According to the given information, the sum of the digits at hundreds and unit’s place is equal to half of the digit at ten’s place.
So, the sum of digits at hundreds and unit’s place is x/2.
Let's list down all possible values of x, along with the possible values of hundreds and units place digits, and calculate the sum of all possible three-digit numbers.
- If x=2, then hundreds place digit and units place digit can be 1 and 3 or 3 and 1. The sum of all possible three-digit numbers is 123+132+213+231+312+321=1332.
- If x=4, then hundreds place digit and units place digit can be 1 and 3 or 3 and 1. The sum of all possible three-digit numbers is 143+134+214+241+314+341=1387.
- If x=6, then hundreds place digit and units place digit can be 1 and 3 or 3 and 1. The sum of all possible three-digit numbers is 163+136+316+361+613+631=2110.
- If x=8, then hundreds place digit and units place digit can be 1 and 3 or 3 and 1. The sum of all possible three-digit numbers is 183+138+318+381+813+831=2464.
- If x=9, then hundreds place digit and units place digit can be 1 and 2 or 2 and 1. The sum of all possible three-digit numbers is 192+129+219+291+921+912=2764.
As per the given information, the sum of all possible three-digit numbers is 2664, which is not matching with any of the calculated values. Hence, we can't say what digit is in the unit place.
Therefore, the correct answer is option D, i.e. can't say.