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Rahul's roll number in lES Exam is a number consisting of three non-zero distinct digits, such that the sum of the digits at hundreds and unit’s place is equal to that half of the digit at ten’s place. Also the sum of all possible three digit numbers obtained using these three digits without repetition is 2664.
Q. The digits in the unit is
  • a)
    2
  • b)
    1
  • c)
    3
  • d)
    can't say
Correct answer is option 'D'. Can you explain this answer?
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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.
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Community Answer
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Let the digits be a. y. z such that the number is 106r + 10y + z
Thus, the omer rive 3 digit number which we may obtained using these 3 digits will be
100x + 10z + y
100y + 10x + z
100y + 10z + x
100z + 10x + y
100z + 10y + x
Now when we add ail the six three digit numbers possible to be formed by these three digits:
222 (x + y + z) = 2664 or x + y + z = 12
Also x + z = y/2 thus y = 8
Thus, x + z = 4
As the digits are non zero and distinct thus x and z have to be 1 and 3 but not necessarily in the same order. Thus we cannot say whether the number is 183 or 381.
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Direction : Read the following Information carefully and answer the question below it.Rahul's roll number in lES Exam is a number consisting of three non-zero distinct digits, such that the sum of the digits at hundreds and unit’s place is equal to that half of the digit at ten’s place. Also the sum of all possible three digit numbers obtained using these three digits without repetition is 2664.Q. The digits in the unit isa)2b)1c)3d)can't sayCorrect answer is option 'D'. Can you explain this answer?
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Direction : Read the following Information carefully and answer the question below it.Rahul's roll number in lES Exam is a number consisting of three non-zero distinct digits, such that the sum of the digits at hundreds and unit’s place is equal to that half of the digit at ten’s place. Also the sum of all possible three digit numbers obtained using these three digits without repetition is 2664.Q. The digits in the unit isa)2b)1c)3d)can't sayCorrect answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Direction : Read the following Information carefully and answer the question below it.Rahul's roll number in lES Exam is a number consisting of three non-zero distinct digits, such that the sum of the digits at hundreds and unit’s place is equal to that half of the digit at ten’s place. Also the sum of all possible three digit numbers obtained using these three digits without repetition is 2664.Q. The digits in the unit isa)2b)1c)3d)can't sayCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction : Read the following Information carefully and answer the question below it.Rahul's roll number in lES Exam is a number consisting of three non-zero distinct digits, such that the sum of the digits at hundreds and unit’s place is equal to that half of the digit at ten’s place. Also the sum of all possible three digit numbers obtained using these three digits without repetition is 2664.Q. The digits in the unit isa)2b)1c)3d)can't sayCorrect answer is option 'D'. Can you explain this answer?.
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