Playing with Numbers Test

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Playing with Numbers Test - 13

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following numbers are divisible by $$2$$?

A
$$10$$

B
$$100$$

C
$$1000$$

D
All of the above

Solution

Since all the options contain an even digit i.e. $$0$$ in the units place,
all the numbers are divisible by $$2$$.

So, option D is correct.
Question 2
1 / -0

$$21$$ is co-prime with

A
$$3$$

B
$$7$$

C
$$22$$

D
all of the above

Solution

$$21 = 3\times 7\times 1$$
$$22 = 1\times 2\times 11$$
Only $$1$$ is common, so option $$C$$ is correct.
Question 3
1 / -0

The product of $$2 \times 7 \times 3 \times 5$$ is a .........

A
composite number

B
prime number

C
negative number

D
none of the above

Solution

Composite numbers are numbers which have more then $$2$$ factors. They have at least $$1$$ factor more than $$1$$ and the number itself.
The given expression has more than $$2$$ factors. So, it is a Composite number.
Therefore, $$A$$ is the correct answer.
Question 4
1 / -0

Which of the following numbers are divisible by $$5$$ ?

A
$$10$$

B
$$100$$

C
$$1000$$

D
All of the above

Solution

A number is divisible by $$5$$, if it contains $$0$$ or $$5$$ in the units place.
Since all the numbers have $$0$$ in the units place,
therefore all are divisible by $$5$$.

So, option D is correct.
Question 5
1 / -0

Fundamental theorem of arithmetic is when any .......... greater than $$1$$ is either a prime number or can be written as a unique product of prime numbers.

A
decimal number

B
fraction

C
irrational number

D
integer

Solution

Let us take an example, $$15$$ is not a prime number.
$$15 = 3 \times 5$$, where $$3$$ and $$5$$ are prime numbers.
We cannot get the number $$15$$ by multiplying any other prime numbers.
$$15 \neq 2 \times 5 \times 7.$$
It is only with one particular set of prime numbers.
Hence, it is said integers greater than $$1$$ are prime numbers or unique product of prime numbers.
Therefore, $$D$$ is the correct answer.
Question 6
1 / -0

Every ........ number can be expressed as a product of prime numbers.

A
composite

B
prime

C
natural

D
irrational

Solution

For example, $$6 = 2\times 3$$, where $$2$$ and $$3$$ are prime numbers.
When we multiply two or more prime numbers we get the product as a composite number.
Therefore, $$A$$ is the correct answer.
Question 7
1 / -0

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

A
$$81$$

B
$$99$$

C
$$108$$

D
All of the above

Solution

A number is divisible by $$9$$, if the sum of the digits is also divisible by $$9$$.
Sum of digits of $$81$$ is $$8+1=9$$
Sum of digits of $$99$$ is $$9+9=18$$
Sum of digits of $$108$$ is $$1+0+8=9$$
Thus, all given numbers are divisible by $$9$$

So, option D is correct.
Question 8
1 / -0

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

A
$$12$$

B
$$14$$

C
$$20$$

D
None of the above

Solution

The sum of the digits of $$12$$ is $$1+2 =3$$.
$$3$$ is divisible by $$3$$
Therefore, $$12$$ is divisible by $$3$$.

So, option A is correct.
Question 9
1 / -0

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

A
$$111$$

B
$$121$$

C
$$131$$

D
None of the above

Solution

A number is divisible by $$3$$, if the sum of its digits is divisible by $$3$$.
$$\therefore 111 = 1+1+1= 3 $$
$$3$$ is divisible by $$3$$, so option A is correct.
Question 10
1 / -0

Which of the following numbers are divisible by $$2$$ ?

A
$$76$$

B
$$84$$

C
$$64$$

D
All of the above

Solution

Divisibility by 2:
If the number contains an even number (0, 2, 4, 6, 8) in the units place,
then the number is completely divisible by $$2$$.

All the options given here are even numbers i.e $$76$$ ends with $$6$$
$$84$$ and $$64$$ ends with $$4$$

So, option D is correct..

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Playing with Numbers Test - 13

Result

Playing with Numbers Test - 13

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SHARING IS CARING

Question 1

$$10$$

$$100$$

$$1000$$

All of the above

Solution

Question 2

$$3$$

$$7$$

$$22$$

all of the above

Solution

Question 3

composite number

prime number

negative number

none of the above

Solution

Question 4

$$10$$

$$100$$

$$1000$$

All of the above

Solution

Question 5

decimal number

fraction

irrational number

integer

Solution

Question 6

composite

prime

natural

irrational

Solution

Question 7

$$81$$

$$99$$

$$108$$

All of the above

Solution

Question 8

$$12$$

$$14$$

$$20$$

None of the above

Solution

Question 9

$$111$$

$$121$$

$$131$$

None of the above

Solution

Question 10

$$76$$

$$84$$

$$64$$

All of the above

Solution

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