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# How many 3 digit numbers leave a remainder of 2 when divided by 7 ?

$\begin{array}{1 1} 100 \\ 996 \\ 128 \\ 129 \end{array}$

Can you answer this question?

Answer : (d) 129
Explanation : 3 digit numbers are between 100 and 999. First 3 digit number to leave a remainder of 2 when divided by 7 is 100.
Last 3 digit number to leave a remainder of 2 when divided by 7 is 996. it is an AP with
$a=100\;,d=7\;,t_{n}=996$
$t_{n}=996=100+7(n-1)$
$896=7(n-1)$
$128=n-1$
$n=129.$
answered Jan 5, 2014 by