Preeti thought of a two-digit number and divided the number by the sum of the digits of the number. She found that the remainder is 3. Sarosh also thought of a two-digit number and divided the number by the sum of the digits of the number. He also found that the remainder is 3. Find the probability that the two digit number thought by Preeti and Sarosh is same?
Preeti thought of a two-digit number and divided the number by the sum of the digits of the number. She found that the remainder is 3. Sarosh also thought of a two-digit number and divided the number by the sum of the digits of the number. He also found that the remainder is 3. Find the probability that the two digit number thought by Preeti and Sarosh is same?
The correct option is A
Let the two digit number that Preeti thought be 'xy', where x and y are single digit numbers.
10x + y = p(x+y) + 3, where p is a natural number.
Thus, y+x > 3 (since remainder is equal to 3)
So, y+x will range from 4 to 18.
Possible numbers for which the condition holds true are:
31, 23, 33, 15, 51, 52, 35, 73, 47, 39, 75, 94, 59, 78.
There are 14 such two-digit numbers that give a remainder of 3 when divided by the sum of the digits.
The probability that Sarosh thought of the same number as Preeti = 114.
Let the two digit number that Preeti thought be 'xy', where x and y are single digit numbers.
10x + y = p(x+y) + 3, where p is a natural number.
Thus, y+x > 3 (since remainder is equal to 3)
So, y+x will range from 4 to 18.
Possible numbers for which the condition holds true are:
31, 23, 33, 15, 51, 52, 35, 73, 47, 39, 75, 94, 59, 78.
There are 14 such two-digit numbers that give a remainder of 3 when divided by the sum of the digits.
The probability that Sarosh thought of the same number as Preeti = 114.
