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 smallest 3 digit prime number is:

A
$$101$$

B
$$103$$

C
$$109$$

D
$$113$$

Solution

The smallest 3-digit number is $$100$$, which is divisible by $$2$$.
$$\therefore$$ $$100$$ is not a prime number.
$$\sqrt{100}< 11$$ and $$101$$ is not divisible by any of the prime numbers $$2,3,5,7,11$$.
$$\therefore$$ $$101$$ is a prime number.
Hence $$101$$ is the smallest 3-digit prime number.
Question 2
1 / -0

What is the value of $$x$$ for which $$x, x + 1, x + 3$$ are all prime numbers?

A
$$0$$

B
$$1$$

C
$$2$$

D
$$101$$

Solution

Option $$A :$$ Substitute $$x=0,$$
$$x,x+1,x+3=0,1,3$$ are not prime numbers.

Option $$B :$$ Substitute $$x=1,$$
$$x,x+1,x+3=1,2,4$$ are not prime numbers.

Option $$C :$$ Substitute $$x=2,$$
$$x, x + 1, x + 3=2,3,5$$ which are all prime numbers.

Hence, option $$C$$ is correct.
Question 3
1 / -0

Which of the following number is a prime?

A
$$667$$

B
$$861$$

C
$$481$$

D
$$331$$

Solution

$$667$$ is divisible by $$23$$
$$861$$ is divisible by $$3$$
$$481$$ is divisible by $$13$$
$$331$$ is divisible only by $$1$$ and $$331$$.
$$\therefore 331$$ is a prime number.
Question 4
1 / -0

Consider the following numbers.
1. $$247$$
2. $$203$$
Which of the above number is/are prime?

A
$$1$$ only

B
$$2$$ only

C
Both $$1$$ and $$2$$

D
Neither $$1$$ nor $$2$$

Solution

A number which is divisible by itself and $$1$$ are prime numbers.
1. $$247 = 13\times 19$$
2. $$203 = 7\times 79$$
Here both the numbers have some divisors.
So, none of the two are prime.
Question 5
1 / -0

Which of the following is a prime number?

A
$$33$$

B
$$81$$

C
$$93$$

D
$$97$$

Solution

Clearly, $$97$$ is a prime number.
Question 6
1 / -0

Which one of the following is a prime number?

A
$$184$$

B
$$171$$

C
$$173$$

D
$$221$$

Solution

$$184 = 23\times 8$$
Therefore, cannot be prime
$$171 = 19\times 9$$
Therefore,cannot be prime
$$221 = 17\times 13$$
Therefore, cannot be prime
Hence, by elimination we have $$173$$ as a prime number.
Question 7
1 / -0

Which one of the following is not a prime number?

A
$$31$$

B
$$61$$

C
$$71$$

D
$$91$$

Solution

$$91$$ is divisible by $$7$$ and $$13$$. So, it is not a prime number.
Rest all the given numbers are prime numbers since they don't have any factors other than $$1$$ and themselves.
Question 8
1 / -0

What is the least positive integer that is the product of $$3$$ different prime numbers greater than $$2$$?

A
$$27$$

B
$$45$$

C
$$63$$

D
$$75$$

E
$$105$$

Solution

Three different prime numbers which are greater than $$2$$ are $$3,5,7$$.
$$\therefore 3,5,7$$ are three least prime numbers above $$2$$.
Therefore, the product of all these is $$3 \times 5 \times 7 = 105$$.
Question 9
1 / -0

Find $$HCF$$ by finding factors:
$$16$$ and $$56$$.

A
$$6$$

B
$$18$$

C
$$8$$

D
$$9$$

Solution

The given numbers are $$16$$ and $$56$$
Factorizing the given numbers,
$$16 = 2 \times 2 \times 2 \times 2$$
$$56 = 2 \times 2 \times 2 \times 7$$
Since, the common factors are $$2,2,2$$, this implies that
$$H.C.F = 2 \times 2 \times 2$$
$$=8$$
Hence, the correct option is $$Op-C$$.
Question 10
1 / -0

Find HCF of $$66$$ and $$88$$.

A
$$21$$

B
$$23$$

C
$$24$$

D
$$22$$

Solution

Factorization of the following
$$66 = 1 \times 3 \times 2 \times 11$$
$$88 = 1 \times 2 \times 2 \times 2 \times 11$$
Since, the common factor is $$1,2,11$$ this implies that
$$HCF=22$$
Hince, the correct option $$D$$

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Playing with Numbers Test - 17

Result

Playing with Numbers Test - 17

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SHARING IS CARING

Question 1

$$101$$

$$103$$

$$109$$

$$113$$

Solution

Question 2

$$0$$

$$1$$

$$2$$

$$101$$

Solution

Question 3

$$667$$

$$861$$

$$481$$

$$331$$

Solution

Question 4

$$1$$ only

$$2$$ only

Both $$1$$ and $$2$$

Neither $$1$$ nor $$2$$

Solution

Question 5

$$33$$

$$81$$

$$93$$

$$97$$

Solution

Question 6

$$184$$

$$171$$

$$173$$

$$221$$

Solution

Question 7

$$31$$

$$61$$

$$71$$

$$91$$

Solution

Question 8

$$27$$

$$45$$

$$63$$

$$75$$

$$105$$

Solution

Question 9

$$6$$

$$18$$

$$8$$

$$9$$

Solution

Question 10

$$21$$

$$23$$

$$24$$

$$22$$

Solution

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