How many positive three-digit integers have the hundreds digit equal to multiple of 3 and the units digit is an even digit?

Hint: This question is totally logical to answer. We know there are many three-digit numbers starting from 100 to 999. But we have some conditions to solve. such that hundreds digit is multiple of 3 and units digit is an even number. So we get the hint as a single digit multiple of 3 are 3,6 and 9 only. Also there are only 5 even numbers that can be placed on the units place those are 0,2,4,6,8. This is the hint to lead.

Complete step by step solution:
There are three- digit numbers starting from 100 to 999.
Now from 100 to 299 all numbers are to be discarded because they do not have multiple of 3 in hundreds places.
Now from 300 to 310 we have all numbers a multiple of 3 on hundreds but not all are even numbers. There are only 5 even numbers.
Like this from 300 to 399 we have 50 numbers that satisfy the condition above.
From 600 to 799 we have 50 numbers that satisfy the condition above.
From 900 to 999 we have 50 numbers that satisfy the condition above.
So in total we have 150 numbers that are three digit and satisfy the condition above.
So, the correct answer is “150 ”.

Note: We can note that if the three- digit number is like abc.
a is multiple of 3 and that can be 3,6,9 that are three possibilities.
b can be any one digit from 0 to 9 that is 10 digits.
c can be the even number that is 0,2,4,6,8 that is there are five such numbers.
So in total there should be \[3 \times 10 \times 5 = 150\] numbers.