Playing with Numbers Test

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Playing with Numbers Test - 29

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Weekly Quiz Competition

Question 1
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 2
1 / -0

Sum of factors of $$78$$ are ________.

A
$$168$$

B
$$170$$

C
$$167$$

D
$$189$$

Solution

Factors of $$78$$ are $$1, 2, 3, 6, 13, 26, 39$$ and $$78$$.

Required sum $$= 1 + 2 + 3 + 6 + 13 + 26 + 39 + 78 $$
$$= 168$$.
Question 3
1 / -0

The number which have only two factors $$(1$$ and the number itself) are called as ________.

A
Composite

B
Even

C
Prime

D
None of these

Solution
Question 4
1 / -0

Which of the following pair of numbers is co-prime?

A
$$(17, 15)$$

B
$$(10, 16)$$

C
$$(20, 24)$$

D
$$(31, 62)$$

Solution

In number theory, Co-prime numbers are those numbers if the only positive factor that divides them is $$1$$.
Here,
Option A: $$(17,15)$$ Factor that divides both of them is $$1$$.
Option B: $$(10,16)$$ Factors that divides both oh them are $$1,2.$$
Option C: $$(20,24)$$ Factors that divide both of them are $$ 1,2,4.$$
Option C: $$(31,62)$$ Factors that divide both oh them are $$1,31.$$
In reference to above definition $$(17,15)$$ are co-prime numbers.
Hence Option A is correct.
Question 5
1 / -0

Which of the following is a prime number?

A
$$161$$

B
$$221$$

C
$$373$$

D
$$437$$

Solution

A prime number is a whole number greater than $$1$$ whose only factors are $$1$$ and itself.

$$\Rightarrow$$ $$\sqrt{437} > 22$$

$$\Rightarrow$$  All prime numbers less than $$22$$ are $$: 2, 3, 5, 7, 11, 13, 17, 19.$$

$$\Rightarrow$$  $$161$$ is divisible by $$7$$, and $$221$$ is divisible by $$13$$.

$$\Rightarrow$$  $$373$$ is not divisible by any of the above prime numbers.

$$\therefore$$ $$373$$ is prime number
Question 6
1 / -0

Which of the following is a pair of co-primes?

A
$$(14, 35)$$

B
$$(18, 25)$$

C
$$(31,93)$$

D
$$(32, 62)$$

Solution

If the H.C.F of two numbers are $$1$$ they are said to be co-prime
Factors of $$14=1,2,7$$
Factors of $$35=1,5,7$$
$$\Rightarrow$$ Common factor $$=1,7$$
$$\therefore$$ $$(14,35)$$ is not pair of co-prime.

Factors of $$18=1,2,3,6,9$$
Factors of $$25=1,5$$
$$\Rightarrow$$ Common factor $$=1$$
$$\therefore$$ $$(18,25)$$ is pair of co-prime.

Factors of $$31=1,31$$
Factors of $$93=1,3,31$$
$$\Rightarrow$$ Common factor $$=1,31$$
$$\therefore$$ $$(31,93)$$ is not pair of co-prime.

Factors of $$32=1,2,4,8,16$$
Factors of $$62=1,2,31$$
$$\Rightarrow$$ Common factor $$=1,2$$
$$\therefore$$ $$(32,62)$$ is not pair of co-prime.
Question 7
1 / -0

Which of the following is perfect number ?

A
$$6$$

B
$$7$$

C
$$8$$

D
$$9$$

Solution

A number is called a perfect number if by adding all the positive divisors of the number (except itself), the result is the number itself.

$$(a)6$$ is the first perfect number. Its divisors (other than the number itself: $$6$$) are $$1, 2,$$ and $$3$$ and $$1 + 2 + 3=6$$.

$$(b)7$$ is the not a perfect number. Its divisors (other than the number itself: $$7$$) are $$1$$ and $$1\neq\,7$$.

$$(c)8$$ is the not a perfect number. Its divisors (other than the number itself: $$8$$) are $$1,2$$ and $$4$$ and $$1+2+4=7\neq 8$$.

$$(d)9$$ is the not a perfect number. Its divisors (other than the number itself: $$9$$) are $$1$$ and $$3$$ and $$1+3=4\neq9$$.
Question 8
1 / -0

Find the HCF of $$25$$ and $$30$$.

A
$$25$$

B
$$6$$

C
$$1$$

D
$$5$$

Solution

$$\Rightarrow$$$$25=5\times5$$
$$\Rightarrow$$$$30=5\times6$$
Hence the Highest common factor is 5
Therefore HCF is $$5$$
Question 9
1 / -0

The number of prime numbers between $$1 \ and \ 10$$ is

A
$$12$$

B
$$4$$

C
$$3$$

D
$$2$$

Solution

The prime numbers between $$1$$ to$$ 10$$ is,
$$2,3,5,7,$$
There are four prime numbers in between $$1 $$ to $$10$$.
Question 10
1 / -0

Choose the composite numbers from the following numbers $$87, 67, 45, 34, 23, 27, 33$$.

A
$$45, 87, 34, 27, 33$$

B
$$45, 87, 67, 33$$

C
$$33, 27, 23, 34$$

D
All the above

E
None of these

Solution

$$87, 45, 34, 33, 27$$ are composite numbers
[A composite number define as except own and one which are divisible by any numbers such that (4,6,8,9,....)]

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Playing with Numbers Test - 29

Result

Playing with Numbers Test - 29

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SHARING IS CARING

Question 1

$$1$$

$$4$$

$$5$$

$$6$$

Solution

Question 2

$$168$$

$$170$$

$$167$$

$$189$$

Solution

Question 3

Composite

Even

Prime

None of these

Solution

Question 4

$$(17, 15)$$

$$(10, 16)$$

$$(20, 24)$$

$$(31, 62)$$

Solution

Question 5

$$161$$

$$221$$

$$373$$

$$437$$

Solution

Question 6

$$(14, 35)$$

$$(18, 25)$$

$$(31,93)$$

$$(32, 62)$$

Solution

Question 7

$$6$$

$$7$$

$$8$$

$$9$$

Solution

Question 8

$$25$$

$$6$$

$$1$$

$$5$$

Solution

Question 9

$$12$$

$$4$$

$$3$$

$$2$$

Solution

Question 10

$$45, 87, 34, 27, 33$$

$$45, 87, 67, 33$$

$$33, 27, 23, 34$$

All the above

None of these

Solution

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