1 How many threedigit numbers are there that have the proper

1. How many three-digit numbers are there that have the property that the product of two of the digits is equal to the third digit? (A) 52 (B) 126 (C) 252 (D) 1024 2. How many three-digit numbers are there that have the property that one digit is the sum of the other two digits? (A) 52 (B) 126 (C) 252 (D) 1024 3. How many three-digit numbers are there that have the property that one digit is repeated? (A) 52 (B) 126 (C) 252 (D) 1024

Solution

note we are suppose to answer one question at a time so i will give u answer for 3rd

for rest u have to repost the question again.

3) total 3 digit number which can be formed with repeatition are 9*10*10 = 900 as at 1st place we can only have 9 digits as 0 cant come at 1st place

so total 3 digit numbers are 900

we have to find the the 3 digit number such that one digit is repeating

now case 1 if the gigit at 1st and 2nd place are repeating

then at 1st place we have 9 options

then at second options we have only 1 option as the number which will come at 1st place will come at 2nd place

3rd place we will heve again 9 options

so total numbers in this case will be 81(9*9*1)

in case 2

we will have the same number 2nd and 3rd number

again total number will be 81

similarly in case 3rd the number 1st and 3rd will repeat

now total number are again 81

so total number will be 81+81+81 = 243

now if we consider the case when if the digit at 1st is repeating with digit at 2nd and 3rd place then total number will be 9

hence 243+9 = 252