Playing with Numbers Test

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Playing with Numbers Test - 31

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following pairs are always co-primes?

A
Two prime numbers

B
One prime and one composite number

C
Two composite numbers

D
None of the above

Solution

Two prime numbers whose difference is two are called twin primes or we can say consecutive prime numbers are the twin primes and hence their HCF will be 1.
So answer will be A.
Question 2
1 / -0

Choose a perfect number:

A
$$16$$

B
$$8$$

C
$$24$$

D
$$28$$

Solution

The proper divisors of $$28$$ are $$, 2, 4, 7, 14 $$
Now their sum $$1+2+4+7+14 = 28 $$
Hence, $$28$$ is a perfect number.
Question 3
1 / -0

Which of the following are co-primes?

A
$$8, 10$$

B
$$9, 10$$

C
$$6, 8$$

D
$$15, 18$$

Solution

If the H.C.F of two numbers are $$1$$ they are said to be co-prime
Factors of $$9=1,3$$
Factors of $$10=1,2,5$$
$$\Rightarrow$$ Common factor $$=1$$
$$\therefore$$ $$(9, 10)$$ is pair of co-prime.
Question 4
1 / -0

Mark the correct alternative of the following.
Which of the following is a prime number?

A
$$263$$

B
$$361$$

C
$$323$$

D
$$324$$

Solution

The option (a) is correct answer.
We know that 263 = 1 x 263 = 263 has two factors, 1 and 263
Therefore, it is a prime number
Question 5
1 / -0

Choose the perfect number:

A
$$4$$

B
$$12$$

C
$$8$$

D
None of these

Solution

A perfect number is a positive integer that is equal to the sum of its positive divisors.
Question 6
1 / -0

Mark the correct alternative of the following.
Which of the following numbers is prime?

A
$$23$$

B
$$51$$

C
$$38$$

D
$$26$$

Solution
Question 7
1 / -0

Which of the following is a prime number?

A
$$203$$

B
$$139$$

C
$$115$$

D
$$161$$

Solution
Question 8
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 9
1 / -0

Which of the following numbers is divisible by $$8$$?

A
$$87653234$$

B
$$78956042$$

C
$$64298602$$

D
$$98741032$$

Solution

To check if a number is divisible by $$ 8 $$, we check if the last three digits of the number is divisible by $$ 8 $$ .
Last $$3$$ digits of the given numbers are:
A. $$234$$
B. $$042$$
C. $$602$$
D. $$032$$
We see that the only number divisible by $$8$$ is $$032$$.
$$\therefore \ 98741032$$ is the only number divisible by $$8$$.

Hence, option D is correct.
Question 10
1 / -0

The least prime is?

A
$$1$$

B
$$2$$

C
$$3$$

D
$$5$$

Solution

The number $$2$$ is the least prime. It is the only even prime also.

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Re-Attempt Weekly Quiz Competition

Playing with Numbers Test - 31

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Playing with Numbers Test - 31

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Question 1

Two prime numbers

One prime and one composite number

Two composite numbers

None of the above

Solution

Question 2

$$16$$

$$8$$

$$24$$

$$28$$

Solution

Question 3

$$8, 10$$

$$9, 10$$

$$6, 8$$

$$15, 18$$

Solution

Question 4

$$263$$

$$361$$

$$323$$

$$324$$

Solution

Question 5

$$4$$

$$12$$

$$8$$

None of these

Solution

Question 6

$$23$$

$$51$$

$$38$$

$$26$$

Solution

Question 7

$$203$$

$$139$$

$$115$$

$$161$$

Solution

Question 8

$$9076185$$

$$92106345$$

$$10349576$$

$$95103476$$

Solution

Question 9

$$87653234$$

$$78956042$$

$$64298602$$

$$98741032$$

Solution

Question 10

$$1$$

$$2$$

$$3$$

$$5$$

Solution

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