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A three digit number is formed from the following digits - {1,2,4,6,7} without repetition. x+1 is added to the digit at hundreds place, x is added to the digit at tens place and x+1 is added to the digit at ones place of all the numbers formed. What is the probability that the new number is divisible by 3?
  • a)
    13/58
  • b)
    17/25
  • c)
    3/10
  • d)
    11/28
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A three digit number is formed from the following digits - {1,2,4,6,7...
For a number to be divisible by 3, the sum of its digits has to be a multiple of 3. Let the number be abc. It is given that, x+1 is added to a, x is added to b and x+1 is added to c.
Sum of digits of new number - a + b + c + 3x + 2
Total Numbers that can be formed = 5 × 4 × 3 = 60
We can see that there are 10 possible combinations of this, Hence we form the table as below -
There are 10 combinations and 6 numbers can be formed in each combination. 3 combinations are divisible by 3. Hence 18 out of 60 numbers are divisible by 3.
Hence, the correct option is (c).
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A three digit number is formed from the following digits - {1,2,4,6,7} without repetition. x+1 is added to the digit at hundreds place, x is added to the digit at tens place and x+1 is added to the digit at ones place of all the numbers formed. What is the probability that the new number is divisible by 3?a)13/58b)17/25c)3/10d)11/28Correct answer is option 'C'. Can you explain this answer?
Question Description
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