Yow many three digit number are which leaves reminder2 on division by9
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How many three-digit numbers leave a remainder 2 when divided by 9?
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7
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3 Answers

Girija Warrier
, studied at Sufficiently Educated
Answered February 15, 2017
Least 3 digit number is 100 ,Since divisor is 9, & remainder =2So, 9 x 11 + 2 = 101 is the first 3 digit number which when divided by 9, leaves remainder =2Next no will be 101+9 = 110, & next = 110+9 =119& the last 3 digit no leaving remainder 2, while dividing by 9 is 992So we get an AP series101, 110, 119, 128 ………………992Here, Tn = a + (n-1) *d = 992 ,Where a= 1st term, d= common difference, & n is the term=> 101 + (n-1)*9 = 992=> 9n - 9 = 891=> 9n = 900=> n = 100So, there are 100 such number...
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Rhibhu Chattopadhyay
, A budding numberphile
Answered February 15, 2017
Hello.
We will approach this question logically.
First of all, we see that our number is in the form of 9x + 2.
So we substitute x with 11 first
We get,
9 x 11 +2 = 99 + 2 = 101
So this is our first number: 101
Now if we keep on adding 9 to it then we will get all three digit numbers that will leave a remainder 2 when we divide by 9.
So with a hit and trial approach the last number of the series will be
9 x + 2 = 1001
9x = 999
x = 111 .
So the series starts at x = 11 and ends at x = 111.
So the numbers in between are 101.
So there are 101 three digit numbers that leaves a remainder 2 when divided by 9.
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