What is the sum of all two-digit numbers whic | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) two-digit number $x$ leaves a remainder of $4$ when divided by $6$ if $x = 6n + 4$ for some integer $n$.For two-digit numbers,$10 \le 6n + 4 \le 9

Vedclass · Accepted Answer

$780$

Vedclass · Answer

(C) two-digit number $x$ leaves a remainder of $4$ when divided by $6$ if $x = 6n + 4$ for some integer $n$.For two-digit numbers,$10 \le 6n + 4 \le 99$.Solving for $n$: $6 \le 6n \le 95$,which gives $1 \le n \le 15.83$.Thus,$n$ can take integer values from $1$ to $15$.The sequence of such numbers is $10, 16, 22, \ldots, 94$.This is an Arithmetic Progression $(AP)$ with first term $a = 10$,last term $l = 94$,and number of terms $n = 15$.The sum $S_n$ of an $AP$ is given by $S_n = \frac{n}{2}(a + l)$.$S_{15} = \frac{15}{2}(10 + 94) = \frac{15}{2}(104) = 15 	imes 52 = 780$.

What is the sum of all two-digit numbers which give a remainder of $4$ when divided by $6$?

Similar Questions

The $7^{th}$ term of an $A.P.$ is $40$,then the sum of the first $13$ terms is:

Find the sum of all integers between $50$ and $500$ which are divisible by $7.$

The four arithmetic means between $3$ and $23$ are

$150$ workers were engaged to finish a piece of work in a certain number of days. $4$ workers dropped out on the second day,$4$ more workers dropped out on the third day,and so on. It takes $8$ more days to finish the work now. The number of days in which the work was completed is:

If $a_1, a_2, a_3, \dots, a_n$ are in $A.P.$ and $a_1 + a_4 + a_7 + \dots + a_{16} = 114$, then $a_1 + a_6 + a_{11} + a_{16}$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module