Playing with Numbers Test

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Playing with Numbers Test - 17

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Weekly Quiz Competition

Question 1
1 / -0

The general form of $$129$$ is

A
$$100 \times 1 + 10 \times 2 + 9 \times 1$$

B
$$120 \times 1 + 9 \times 1$$

C
$$100 \times 1 + 30 \times 1 - 1$$

D
All of the above

Solution

The general form of any three digits number will be, $$abc = a \times 100 + b \times 10 + c$$
Therefore, $$129$$ can be written as $$1 \times 100 + 2 \times 10 + 9 \times 1$$
Question 2
1 / -0

What are the values of $$A$$ and $$B$$?
$$ A\ 5$$
- $$ B A$$
____
$$ B \ 3$$

A
$$A = 2$$ and $$B = 2$$

B
$$A = 2$$ and $$B = 1$$

C
$$A = 1$$ and $$B = 1$$

D
$$A = 0$$ and $$B = 2$$

Solution

$$ A 5$$
$$-$$$$ B A$$
____
$$ B 3$$
The subtraction of $$5$$ and $$A$$ is giving 3 i.e., $$5 - A = 3$$
The above condition is possible only when digit $$A$$ is $$2$$, because $$5 - 2 = 3.$$
The next step to get the value as B as $$A - B = B$$. This is possible if $$B = 1$$.
Therefore, the subtraction is as follows:
$$ 2 5$$
- $$1 2$$
____
$$ 1 3$$
The value of $$A = 2$$ and $$B = 1$$
So, option B is correct.
Question 3
1 / -0

A $$3$$-digit number 'cba' is divisible by $$9$$ if _____ .

A
$$a+2b+c$$ is divisible by $$9$$

B
$$2a+b+c$$ is divisible by $$9$$

C
$$a+b+2c$$ is divisible by $$9$$

D
$$a+b+c$$ is divisible by $$9$$

Solution

Divisibility Test for $$9$$ :
$$\rightarrow$$ A number is divisible by $$9$$ if the sum of the digits is divisible by $$9$$.

For Example,
$$549$$ is divisible by $$9$$ since the sum of the digits is $$18$$ and $$18$$ is Divisible by $$9$$.

Here,
Given number is 'cba'
For it to be Divisible by $$9$$,
(a+b+c) should be divisible by $$9$$

$$\therefore$$ Answer is 'D'
Question 4
1 / -0

How many one digit numbers are divisible by $$2$$

A
$$1$$

B
$$4$$

C
$$5$$

D
$$6$$

Solution

We know the divisibility rule for $$2$$:
Always check the last digit end with $$0, 2, 4, 6$$ or $$8$$.
So one digit numbers which are divisible by $$2$$ are $$0, 2, 4, 6, 8$$.
Question 5
1 / -0

Evaluate:
$$0 \times 2018=$$ ?

A
$$0$$

B
$$2018$$

C
$$not\ defined$$

D
$$-2018$$

Solution

$$0 \times (2018) = 0$$
Product of zero and any natural number is always zero.
Question 6
1 / -0

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

A
$$561$$

B
$$467$$

C
$$233$$

D
None of these

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.
(a) 561=5+6+1 ___(add the digit)
=12_____(divisible by 3)
(b)467=4+6+7______ (add the digits)
=17______ (not divisible by 3)
(c)233=2+3+3
=8 _______(not divisible by 3)
Question 7
1 / -0

The least number of 4-digits which is exactly divisible by 9 is

A
1008

B
1009

C
1026

D
1018

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 of $$1008$$ is $$1+0+0+8=9$$, which is divisible by 9 hence $$1008$$ is divisible by 9.
Question 8
1 / -0

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

A
$$27326$$

B
$$42356$$

C
$$73545$$

D
$$45326$$

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 divisible by $$3$$
A) $$2 + 7 + 3 + 2 + 6 = 20$$
B) $$4 + 2 + 3 + 5 + 6 = 20$$
C) $$7 + 3 + 5 + 4 + 5 = 24$$
D) $$4 + 5 + 3 + 2 + 6 = 20$$

Only C) $$24$$ is divisible by $$3$$
So, option C is the correct option.
Question 9
1 / -0

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

A
$$9076185$$

B
$$92106345$$

C
$$10349576$$

D
$$95103476$$

Solution

Option $$A$$ is correct.

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.

given numbers are

$$9076185 = 9+0+7+6+1+8+5 = 36$$ and is divisible by $$9$$

$$92106345 = 9+2+1+0+6+3+4+5 = 30$$ is not divisible by $$9$$

$$10349576 = 1+0+3+4+9+5+7+6 = 35$$ is not divisible by $$9$$

$$95103476 = 9+5+1+0+3+4+7+6 = 35$$ is not divisible by $$9$$
Question 10
1 / -0

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

A
$$24357806$$

B
$$35769812$$

C
$$83479560$$

D
$$3336433$$

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.
Since sum of its digits $$= 8 + 3 + 4 + 7 + 9 + 5 + 6 + 0 = 42$$
$$42$$ is divisible by $$3$$
Option (c) is the correct answer

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Playing with Numbers Test - 17

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Playing with Numbers Test - 17

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SHARING IS CARING

Question 1

$$100 \times 1 + 10 \times 2 + 9 \times 1$$

$$120 \times 1 + 9 \times 1$$

$$100 \times 1 + 30 \times 1 - 1$$

All of the above

Solution

Question 2

$$A = 2$$ and $$B = 2$$

$$A = 2$$ and $$B = 1$$

$$A = 1$$ and $$B = 1$$

$$A = 0$$ and $$B = 2$$

Solution

Question 3

$$a+2b+c$$ is divisible by $$9$$

$$2a+b+c$$ is divisible by $$9$$

$$a+b+2c$$ is divisible by $$9$$

$$a+b+c$$ is divisible by $$9$$

Solution

Question 4

$$1$$

$$4$$

$$5$$

$$6$$

Solution

Question 5

$$0$$

$$2018$$

$$not\ defined$$

$$-2018$$

Solution

Question 6

$$561$$

$$467$$

$$233$$

None of these

Solution

Question 7

1008

1009

1026

1018

Solution

Question 8

$$27326$$

$$42356$$

$$73545$$

$$45326$$

Solution

Question 9

$$9076185$$

$$92106345$$

$$10349576$$

$$95103476$$

Solution

Question 10

$$24357806$$

$$35769812$$

$$83479560$$

$$3336433$$

Solution

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