Question 12 Marks
Find two numbers whose product is a $1-$digit number and the sum is a $2-$digit number.
Answer$1$ and $9$ are two numbers whose product is a single digit numbr.
$\therefore 1 × 9 = 9$
Sum of the numbers is a two digit number.
$\therefore 1 + 9 = 10$
View full question & answer→Question 22 Marks
Replace $A, B, C$ by suitable numerals:
AnswerHere,
$A - 6 = 6$
$⇒ A = 2 ($with $1$ bieng borrowed$)$
$B = 3$
Since $7 × 9 = 63, C = 9$
$\therefore A = 2, B = 3$ and $C = 9$
View full question & answer→Question 32 Marks
Test the divisibility of the following numbers by $11: 7531622$
AnswerA given number is divisible by $11,$ If the difference between the sum of its digitals at odd places and the sum of its digits at even places, is either $O$ or a number divisible by $11. 7531622$ Sum of digit at odd places $= 7 + 3 + 6 + 2 = 18$ Sum of digit at even places $= 5 + 1 + 2 = 8 $ Difference of the above sum $= (18 - 8) = 10$ Which is divisible by $11\ 7531622$ is divisible by $11$
View full question & answer→Question 42 Marks
Replace $A, B, C$ by suitable numerals. $\underline{ \ \ \ \ 4 \ \text{C B } \ 6\\+3 \ \ 6\ \ 9\text{ A}}\\ \ \ \ \ 8\ \ 1\ \ 7\ \ 3$
Answer$A + 6 = 13$
$\Rightarrow A = 16 - 6$
$= 7$ So, $1$ is carried over. $1 + B + 9 = 17$
$\Rightarrow B = 17 - 10 = 7,$
$B = 7$ and $1$ is carried over. $1 + C + 6 = 11$
$\Rightarrow C = 11 - 7 = 4$
$\therefore A = 7, B = 7$ and $C = 4.$
View full question & answer→Question 52 Marks
Replace $A, B, C$ by suitable numerals. $\underline{ \ \ \text{ A}\\\text{+A}\\\text{+A }}\\\underline{ \text{ BA } }$
Answer$A + A + A = A, 1$ is carried over. When, $A = 5 A + A +A = 15 (1$ carried over$) \Rightarrow B = 1$
$\therefore A = 5, B = 1$
View full question & answer→Question 62 Marks
Find all possible values of $y$ for which the $4-$digit number $64y3$ is divisible by $9.$ Also, find the numbers.
AnswerFor a number to be divisible by $9,$
the sum of the digits must also be divisible by $9.$
$6 + 4 + y + 3 = 13 + y$ For this to be divisible by $9: y = 5$ The number will be $6453.$
View full question & answer→Question 72 Marks
Test the divisibility of the following numbers by $11: 6543207$
AnswerA given number is divisible by $11,$ If the difference between the sum of its digitals at odd places and the sum of its digits at even places, is either $O$ or a number divisible by $11. 6543207$ Sum of digit at odd places $= 6 + 4 + 2 + 7 = 19$ Sum of digit at even places $= 5 + 3 + 0 = 8$ Difference of the above sum $= (19 - 8) = 11,$ Which is not divisible by $11\ 6543207$ is not divisible by $11$
View full question & answer→Question 82 Marks
Test the divisibility of the following numbers by $7: 693$
AnswerFor testing the divisibility of us of a number by $7,$ we proceed according to the Following steps:
Step I: Double the unit digit of the given number.
Step II: Substract the above number from the number formed by excluding the unit digit of the given number.
Step III: IF the number so obtained is divisible by $7$ then the given number is divisible is $7. 693$ Now, $69 - (2 × 3) = 63,$ which is divisible by $7. 693$ is divisible by $7.$
View full question & answer→Question 92 Marks
Find the value of $z$ for which the number $471z8$ is divisible by $9.$ Also, find the number.
AnswerThe number $471z8$ is divisible by $9$ The sum of its digits is also divisible by $9$
$471z8 = 4 + 7 + 1 + z + 8$
$\Rightarrow 20 + z$ is divisible by $9$ Value of $z$ can be $7$ The numbers will be $47178.$
View full question & answer→Question 102 Marks
Find all possible values of $y$ for which the number $53y1$ is divisible by $3.$ Also, find each such number.
AnswerThe given number $53y1$ is divisible by $3$ The sum of its digits is divisible by $3$ I.e., $5 + 3 + y + 1$ or $9 + y$ is divisible by $3$ Value of y can be $0, 3, 6, 9$ Then The numbers can be $5301, 5331, 5361,5391$
View full question & answer→Question 112 Marks
Find the value of $x$ for which the number $x806$ is divisible by $9.$ Also, find the number.
Answernumber $x806$ is divisible by $9$ The sum of its digits is also divisible by $3$ or $x + 8 + 0 + 6$ or $14 + x$ is divisible by $3$ Value of $x$ can be $4$ The numbers will be $4806.$
View full question & answer→Question 122 Marks
Find all possible values of $x$ for which the number $7x3$ is divisible by $3,$ Also find each such number.
AnswerThe given number $7x3$ is divisible by $3$
The sum of its digits is divisible by $3 7 + x + 3$
$⇒ 10 + x$ is divisible by $3$
Value of $x$ can be $2, 5, 8$
The number can be $723, 753, 783$
View full question & answer→Question 132 Marks
Which of the following numbers are divisible by $9?$
$i. 524618$
$ii. 7345845$
$iii. 8987148$
AnswerA number is divisible by $9$ if the sum of the digits is divisible by $9.$
| Number |
Sum of the digit |
Divisible by 9? |
| $524618$ |
$26$ |
No |
| $7345845$ |
$36$ |
Yes |
| $8987148$ |
$45$ |
Yes |
View full question & answer→Question 142 Marks
Test the divisibility of the following numbers by $7:$
$88777$
AnswerFor testing the divisibility of us of a number by $7$, we proceed according to the Following steps:
Step I: Double the unit digit of the given number.
Step II: Substract the above number from the number formed by excluding the unit digit of the given number.
Step III: IF the number so obtained is divisible by $7$ then the given number is divisible is$ 7.$
$88777$
Now,
$8877 - (7 × 2) = 8863,$ which is divisible by $7.$
$88777$ is divisible by $7.$
View full question & answer→Question 152 Marks
Test the divisibility of the following numbers by $7: 65436$
AnswerFor testing the divisibility of us of a number by $7,$ we proceed according to the Following steps:
Step I: Double the unit digit of the given number.
Step II: Substract the above number from the number formed by excluding the unit digit of the given number.
Step III: IF the number so obtained is divisible by $7$ then the given number is divisible is $7. 65436$ Now, $6543 - (6 × 2) = 6531,$ which is divisible by $7. 65436$ is divisible by $7.$
View full question & answer→Question 162 Marks
Test the divisibility of the following numbers by $11:379654$
AnswerA given number is divisible by $11,$ If the difference between the sum of its digitals at odd places and the sum of its digits at even places, is either $O$ or a number divisible by $11.379654$
Sum of digit at odd places $= 7 + 6 + 4 = 17$
Sum of digit at even places $= 3 + 9 + 5 = 17$
Difference of the above sum $ = 17 - 17 = 0,379654$ is divisible by $11$
View full question & answer→Question 172 Marks
Replace $A, B, C$ by suitable numerals.
Answer$(A - 4) = 3$
$\Rightarrow A = 7$
Also, $6 \times 6 = 36$
$\Rightarrow 36 - 36 = 0$
$\Rightarrow B = 6$
$\therefore A = 7$
$B = C =6.$
View full question & answer→Question 182 Marks
Test the divisibility of the following numbers by $11:$
$818532$
AnswerA given number is divisible by $11,$ If the difference between the sum of its digitals at odd places and the sum of its digits at even places, is either $O$ or a number divisible by $11. 818532$ Sum of digit at odd places $= 1 + 5 + 2 = 8$ Sum of digit at even places $= 8 + 8 + 3 = 19$ Difference of the above sum $= (19 - 8) = 11,$ Which is divisible by 11818532 is divisible by $11$
View full question & answer→Question 192 Marks
Test the divisibility of the following numbers by $11: 444444$
AnswerA given number is divisible by $11$, If the difference between the sum of its digitals at odd places and the sum of its digits at even places, is either $O$ or a number divisible by $11. 444444$ Sum of digit at odd places$ = 4 + 4 + 4 = 12$ Sum of digit at even places $= 4 + 4 + 4= 12$ Difference of the above sum $= 12 - 12 = 0, 444444$ divisible by $11$
View full question & answer→Question 202 Marks
Test the divisibility of the following numbers by $7: 98175$
AnswerFor testing the divisibility of us of a number by $7,$ we proceed according to the Following steps: Step I: Double the unit digit of the given number. Step II: Substract the above number from the number formed by excluding the unit digit of the given number. Step III: IF the number so obtained is divisible by $7$ then the given number is divisible is $7. 98175$ Now, $9817 - (5 × 2) = 9807,$ which is divisible by $7. 98175$ is divisible by $7.$
View full question & answer→Question 212 Marks
Test the divisibility of the following numbers by $7:$
$54636$
AnswerFor testing the divisibility of us of a number by $7,$ we proceed according to the Following steps:
step I: Double the unit digit of the given number.
Step II: Substract the above number from the number formed by excluding the unit digit of the given number.
Step III: IF the number so obtained is divisible by $7$ then the given number is divisible is $7.$
$54636$
Now,
$5463 - (6 × 2) = 5451,$ which is divisible by $7.$
$54636$ is divisible by $7.$
View full question & answer→Question 222 Marks
Test the divisibility of the following numbers by $11:1057982$
AnswerA given number is divisible by $11,$ If the difference between the sum of its digitals at odd places and the sum of its digits at even places, is either $O$ or a number divisible by $11.1057982$
Sum of digit at odd places $= 1 + 5 + 9 + 2 = 17$ Sum of digit at even places $= 0 + 7 + 8 = 15$ Difference of the above sum $= (17 - 15) = 2,$ Which is not divisible by $11.1057982$ is not divisible by $11$
View full question & answer→Question 232 Marks
Test the divisibility of the following numbers by $7:12873$
AnswerFor testing the divisibility of us of a number by $7,$ we proceed according to the Following steps: Step I: Double the unit digit of the given number. Step II: Substract the above number from the number formed by excluding the unit digit of the given number. Step III: IF the number so obtained is divisible by $7$ then the given number is divisible is $7.12873$
Now, $1287 - (3 × 2) = 1281,$ which is divisible by $7. 12873$ is divisible by $7.$
View full question & answer→Question 242 Marks
Replace $A, B, C$ by suitable numerals. $ \ \ \ \ \ 5\text{ A}\\\underline{+ \ \ 8 \ 7 \ }\\\underline{\text{C} \ \text{ B} \ 3}$
Answer$A + 7 = 13$ So, $1$ is carried over. $(1 + 5 + 8) = 14.$ So, $B = 4$ and $1$ is carried over. And $C = 1.$
$\therefore A = 6, B = 4$ and $C = 1.$
View full question & answer→Question 252 Marks
Test the divisibility of the following numbers by $11:$
$900163$
AnswerA given number is divisible by $11,$ If the difference between the sum of its digitals at odd places and the sum of its digits at even places, is either $O$ or a number divisible by $11. 900163$ Sum of digit at odd places $= 0 + 1 + 3 = 4$ Sum of digit at even places $= 9 + 0 + 6 = 15$ Difference of the above sum $= (15 - 4) = 11,$ Which is divisible by $11.900163$ is divisible by $11$
View full question & answer→Question 262 Marks
Test the divisibility of the following numbers by $7: 3467$
AnswerFor testing the divisibility of us of a number by $7,$ we proceed according to the Following steps: Step I: Double the unit digit of the given number. Step II: Substract the above number from the number formed by excluding the unit digit of the given number. Step III: IF the number so obtained is divisible by $7$ then the given number is divisible is $7. 3467$ Now, $346 - (7 × 2) = 332,$ which is divisible by $7. 3467$ is not divisible by $7.$
View full question & answer→Question 272 Marks
Test the divisibility of the following numbers by $7:7896$
AnswerFor testing the divisibility of us of a number by $7,$ we proceed according to the Following steps:
Step I: Double the unit digit of the given number.
Step II: Substract the above number from the number formed by excluding the unit digit of the given number.
Step III: IF the number so obtained is divisible by $7$ then the given number is divisible is $7.7896$
Now, $789 - (6 × 2) = 777,$ which is divisible by $7. 7896$ is divisible by $7.$
View full question & answer→Question 282 Marks
Give five examples of numbers, each one of which is divisible by $4$ but not divisible by $8.$
AnswerConsider numbers as $36, 44, 52, 60.$ as these numbers are divisible by $4$ not by $8.$
Let the number $39,$ sum of digits $3 + 9 = 12$
Which is divisible by $3$ not by $9.$
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