x is a positive integer of Z less than 500.
x is a positive integer of Z less than 500. When x is divided by 7, the remainder is 1; when x is divided by 3, the remainder is 2. How many x are there?
Answer/Solution
24
Steps/Work
Took me more than 2 mins to solve.
That's how I did it.
x is between 1-499 included.
Smallest number that can be written as 7n+1 (7*0+1) is 1
Largest number that can be written as 7n+1 is (7*71 +1) is 498
So there are total 72 numbers that can be written as 7n+1
Because x can also be written as 3m+2, we have to see how many numbers that can be written as 7n+1 also can be written as 3m+2
7*0+1 can not be written in the form 3m+2
7*1+1 can be written in the form 3m+2
7*2+1 can not be written in the form 3m+2
7*3+1 can not be written in the form 3m+2
7*4+1 can be written in the form 3m+2
Here we see a sequence that one out of every 4 numbers can be written as 3m+1
72/4= 24 numbers can be written as 3m+1
D is the answer
That's how I did it.
x is between 1-499 included.
Smallest number that can be written as 7n+1 (7*0+1) is 1
Largest number that can be written as 7n+1 is (7*71 +1) is 498
So there are total 72 numbers that can be written as 7n+1
Because x can also be written as 3m+2, we have to see how many numbers that can be written as 7n+1 also can be written as 3m+2
7*0+1 can not be written in the form 3m+2
7*1+1 can be written in the form 3m+2
7*2+1 can not be written in the form 3m+2
7*3+1 can not be written in the form 3m+2
7*4+1 can be written in the form 3m+2
Here we see a sequence that one out of every 4 numbers can be written as 3m+1
72/4= 24 numbers can be written as 3m+1
D is the answer