SOLUTION: How many 3 digit positive integers exist that when divided by 3 leave a reminder of 2? 9 8 27 40

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Question 1132599: How many 3 digit positive integers exist that when divided by 3 leave a reminder of 2?
9
8
27
40

Found 3 solutions by ikleyn, MathTherapy, MathLover1:
Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.

The  ANSWER  is  300,  which is not in the list.


Solution

In all, there are 900 three-digit positive integer numbers from 100 to 999.


Every third of them gives a reminder of 2 when is divided by 3.


They are the numbers 


     101, 104, 107, . . . , 998.


They form an arithmetic progression with the common difference of 3.

Solved,  answered,  explained and completed.


Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
How many 3 digit positive integers exist that when divided by 3 leave a reminder of 2?
9
8
27
40
From 101 to 998, and in INTERVALS of 3, there are: highlight_green%28matrix%281%2C4%2C+300%2C+such%2C+POSITIVE%2C+INTEGERS%29%29 


Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

How many 3 digit positive integers exist that when divided by 3 leave a reminder of 2?
Least 3 digit number is 100.
Since divisor is 3, & remainder 2
.
3%2A33%2B2=101
next number will be 3%2A34%2B2=104+
next will be 3%2A35%2B2=107

the last 3 digit number leaving remainder+2, while dividing by 3 is 998
Sequence : 101, 104,107,.......,998
common difference: d=3
use nth term formula:
a%5Bn%5D=a%5B1%5D%2Bd%28n-1%29
where a%5B1%5D= 1st term, d= common difference, & n+is the term
=> 101+%2B+%28n-1%29%2A3+=+998
=> +%28n-1%29%2A3+=+998-101
=> 3n+-+3+=+897
=> 3n+=+900
=> n+=+300
So, there are 300 such numbers ………..ANS