Question
In the following numbers, replace * by the smallest number to make it divisible by $11:$
$86*72$
$86*72$
✓
Answer
86*72Sum of the digits at odd places $2 + * + 8 = 10 + *$
Sum of the digits at even places $6 + 7 = 13$
Difference = sum of odd terms - sum of even terms.
$= 10 + * - 13$
$= * - 3$
Now, $(* - 3)$ will be divisible by $11$ if $* = 3.$
i.e., $3 - 3 = 0$
$0$ is divisible by $11.$
$\therefore$ * $= 3$
Hence, the number is $86372.$
Sum of the digits at even places $6 + 7 = 13$
Difference = sum of odd terms - sum of even terms.
$= 10 + * - 13$
$= * - 3$
Now, $(* - 3)$ will be divisible by $11$ if $* = 3.$
i.e., $3 - 3 = 0$
$0$ is divisible by $11.$
$\therefore$ * $= 3$
Hence, the number is $86372.$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Find the perimeter of the figure:
In an election, the successful candidate registered $5, 77,570$ votes and his nearest rival secured $3,48,685$ votes. By what margin did the successful candidate win the election?
→Find the prime factors of $1729$. Arrange the factors in ascending order, and find the relation between two consecutive prime factors.
→Write the smallest and the largest six digit numbers. How many numbers are between these two.
Write the name of:
$a.\ $Vertices.
$b.\ $Edges, and
$c.\ $Faces of the prism shown in Fig.
→$a.\ $Vertices.
$b.\ $Edges, and
$c.\ $Faces of the prism shown in Fig.
Determine if the ratio form a proportion. Also, write the middle term and extreme term where the ratio form a proportion:
$200\ ml:$ $2.5$ litre and $₹4 : ₹50.$
→$200\ ml:$ $2.5$ litre and $₹4 : ₹50.$
The ratio of the length of a field to its width is $5 : 3.$ Find its length if the width is $42$ metres.
→Rohit earns $Rs. 15300$ and saves $Rs. 1224$ per month. Find the ratio of: His income and savings.
→Show that the following numbers are in continued proportion:
$16, 84, 441$
→$16, 84, 441$
Study the following pattern:
$
\begin{array}{ll}
1+3 & =2 \times 2 \\
1+3+5 & =3 \times 3 \\
1+3+5+7 & =4 \times 4 \\
1+3+5+7+9 & =5 \times 5
\end{array}
$
By ohserving the above pattern, find:
(i) $...+3+5+7+9+11$
(ii) $1+3+5+7+9+11+13+15$
(iii) $21+23+25+\ldots \ldots+51$
→$
\begin{array}{ll}
1+3 & =2 \times 2 \\
1+3+5 & =3 \times 3 \\
1+3+5+7 & =4 \times 4 \\
1+3+5+7+9 & =5 \times 5
\end{array}
$
By ohserving the above pattern, find:
(i) $...+3+5+7+9+11$
(ii) $1+3+5+7+9+11+13+15$
(iii) $21+23+25+\ldots \ldots+51$