Playing with Numbers Test

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Playing with Numbers Test - 18

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following numbers is divisible by $$9$$?

A
$$8576901$$

B
$$96345210$$

C
$$67594310$$

D
none of these

Solution

We use a rule to check whether the number is divisible by 9 or not.
A number is divisible by 9 if the sum of the digits is evenly divisible by 9.
Since sum of its digits $$ = 8 + 5 + 7 + 6 + 9 + 0 + 1 = 36$$
$$36$$ is divisible by $$9$$
Option (a) is the correct answer
Question 2
1 / -0

The expanded form of the number $$9578$$ is

A
$$9\times 10000+5\times 1000+7\times 10+8\times 1$$

B
$$9\times 1000+5\times 100+7\times 10+8\times 1$$

C
$$9\times 1000+57\times 10+8\times 1$$

D
$$9\times 100+5\times 100+7\times 10+8\times 1$$

Solution

Expanded form of $$9578$$
$$=9\times 1000+5\times 100+7\times 10+8\times 1$$
Hence, B is the correct answer.
Question 3
1 / -0

By using dot $$(.)$$ patterns, which of the following numbers can be arranged in all the three ways namely a line, a triangle and a rectangle ?

A
$$9$$

B
$$10$$

C
$$11$$

D
$$12$$

Solution

Option $$B$$ is right
As we know that every number can be arranged as a line.
The number $$10$$ can be shown as
$$..........$$
Also, it can show a triangle Given below
And, the number cam show as a rectangle. Given below
Question 4
1 / -0

Evaluate: $$3\times 10000+7\times 1000+9\times 100+0\times 10+4$$

A
$$3794$$

B
$$37940$$

C
$$37904$$

D
$$379409$$

Solution

Consider, $$3\times 10000+7\times 1000+9\times 100+0\times 10+4$$
$$=30000+7000+900+0+4$$
$$=37904$$
Hence, option C is right.
Question 5
1 / -0

Which of the following numbers is divisible by $$ 9 $$ ?

A
$$ 972063 $$

B
$$ 730542 $$

C
$$ 785423 $$

D
$$ 561284 $$

Solution

We use a rule to check whether the number is divisible by 9 or not.
A number is divisible by 9 if the sum of the digits is evenly divisible by 9.
Sum of digits $$ = 9 + 7 + 2 + 0 + 3 = 27 $$ which is divisible by $$ 9 $$
Question 6
1 / -0

Which of the following numbers is divisible by $$ 3 $$ ?

A
$$ 50762 $$

B
$$ 42063 $$

C
$$ 52871 $$

D
$$ 37036 $$

Solution

We use a rule to check whether the number is divisible by 3 or not.
A number is divisible by 3 if the sum of the digits is evenly divisible by 3.
Sum of digits is $$ = 4 + 2 + 0 + 6 + 3 = 15 $$ which is divisible by $$ 3 $$
Question 7
1 / -0

A four-digit number $$aabb$$ is divisible by $$55$$. Then possible value(s) of $$b$$ is/are

A
$$0$$ and $$2$$

B
$$2$$ and $$5$$

C
$$0$$ and $$5$$

D
$$7$$

Solution

If the number is divisible by $$55$$,
It must also be divisible by $$5$$.
Therefore the number ends with $$0$$ or $$5$$.
Question 8
1 / -0

If $$5A\times A=399$$, then the value of $$A$$ is

A
$$3$$

B
$$6$$

C
$$7$$

D
$$9$$

Solution

Given,
$$\ \ \ \ 5\ A$$
$$\times\ \ \ \ A$$
$$\overline{ \ \ 3\ 9\ 9\ \ }$$

Here,
$$A\times A=$$ a number whose unit digit is $$9$$
The number from $$0$$ to $$9$$ whose product with itself is a number having its unit's digit $$9$$ is $$7$$.

Hence, $$A=7$$
And the option (C) is correct.
Question 9
1 / -0

Let $$abc$$ be a three digit number. Then $$abc+bca+cab$$ is not divisible by

A
$$a+b+c$$

B
$$3$$

C
$$37$$

D
$$9$$

Solution

We have,
$$abc+bca+cab=(100a+10b+c)+(100b+10c+a)+(100c+10a+b)$$
$$=111a+111b+111c$$
$$=111(a+b+c)$$
$$=3\times 37(a+b+c)$$
Therefore the number $$abc+bca+cab$$ is divisible by$$3,37$$ and $$(a+b+c)$$ but not by $$9$$.
Question 10
1 / -0

A six-digit number is formed by repeating a three-digit number. For example $$256256, 678678$$, etc. Any number of this form is always divisible by

A
$$7$$ only

B
$$11$$ only

C
$$13$$ only

D
$$1001$$

Solution

Let
A six-digit number formed by repeating a three-digit number be $$abcabc$$
Then,
$$abcabc=100000a+10000b+1000c+100a+10b+c$$
$$=a(100000+100)+b(10000+10)+c(1000+1)$$
$$=(100100)a+(10010)b+(1001)c$$
$$=1001(100a+10b+c)$$

Therefore, the six-digit number formed by repeating a three-digit number is always divisible by $$1001$$.

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Re-Attempt Weekly Quiz Competition

Playing with Numbers Test - 18

Result

Playing with Numbers Test - 18

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SHARING IS CARING

Question 1

$$8576901$$

$$96345210$$

$$67594310$$

none of these

Solution

Question 2

$$9\times 10000+5\times 1000+7\times 10+8\times 1$$

$$9\times 1000+5\times 100+7\times 10+8\times 1$$

$$9\times 1000+57\times 10+8\times 1$$

$$9\times 100+5\times 100+7\times 10+8\times 1$$

Solution

Question 3

$$9$$

$$10$$

$$11$$

$$12$$

Solution

Question 4

$$3794$$

$$37940$$

$$37904$$

$$379409$$

Solution

Question 5

$$ 972063 $$

$$ 730542 $$

$$ 785423 $$

$$ 561284 $$

Solution

Question 6

$$ 50762 $$

$$ 42063 $$

$$ 52871 $$

$$ 37036 $$

Solution

Question 7

$$0$$ and $$2$$

$$2$$ and $$5$$

$$0$$ and $$5$$

$$7$$

Solution

Question 8

$$3$$

$$6$$

$$7$$

$$9$$

Solution

Question 9

$$a+b+c$$

$$3$$

$$37$$

$$9$$

Solution

Question 10

$$7$$ only

$$11$$ only

$$13$$ only

$$1001$$

Solution

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