Playing with Numbers Test

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Playing with Numbers Test - 21

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following numbers have most number of divisors?

A
$$176$$

B
$$182$$

C
$$99$$

D
$$101$$

Solution

$$176 = 2\times 2\times 2\times 2\times 11$$
$$182 = 2\times 7\times 13$$
$$99 = 3\times 11\times 3$$
$$101$$ is a prime so has only 1 and itself as factors.
Hence, clearly, $$176$$ has the greatest number of divisors.
Question 2
1 / -0

What is the H.C.F. of $$4 \times 27 \times 3125, 8 \times 9 \times 25\times 7, 16 \times 81 \times 5 \times 11\times 49?$$

A
$$180$$

B
$$360$$

C
$$540$$

D
$$1260$$

Solution

We have
$$\displaystyle 4\times27\times3125=2\times2\times3\times3\times3\times5\times5\times5\times5\times5$$
$$\displaystyle 8\times 9\times 25\times 7=2\times2\times2\times3\times3\times 5\times5\times 7$$
$$\displaystyle 16\times 81\times 5\times 11\times 49=2\times2\times2\times2\times 3\times3\times3\times3\times 5\times 11\times 7\times7$$
Therefore, H.C.F. $$=$$ $$\displaystyle 2\times2\times 3\times3\times 5=4\times 9\times 5=180$$
Question 3
1 / -0

Among the following numbers, number which is divisible by $$2$$ is

A
$$7,907$$

B
$$63,195$$

C
$$72,028$$

D
$$3,451$$

Solution

A number is divisible by $$2$$ if its last digit is an even number (i.e.$$ 0,2,4,6\ or\ 8$$).

$$\therefore 72,028$$ is divisible by $$2$$ because its last digit is an even i.e $$8$$
Rest all numbers have last digit odd.
So, option C is correct.
Question 4
1 / -0

(i) Every prime number is odd.
(ii) The product of any two prime numbers is odd.
Which of the above statements(s) is/are correct?

A
Statement I alone.

B
Statement II alone.

C
Both statements I and II.

D
Neither statement I nor statement II.
Question 5
1 / -0

Consider the following statements:
A. The sum of two prime numbers is a prime number.
B. The product of two prime numbers is a prime number.
Which of these statements is/are correct ?

A
Neither A nor B

B
A alone

C
B alone

D
Both A and B

Solution

Neither the sum nor the product of two prime numbers is a prime number
Eg.$$3+5=8 $$ not a prime number.
$$3\times 5=15 $$ not a prime number.
Question 6
1 / -0

HCF of the numbers $$24,36$$ and $$92$$ is

A
$$24$$

B
$$36$$

C
$$12$$

D
$$4$$

Solution

Factors of $$ 24 =1,2,3,4,6,8,12,24 $$
Factors of $$36= 1,2,3,4,6,9,12,18,36$$
Factors of $$ 92=1,2,4,23,46,92 $$

Common factors are $$ =1,2,4 $$
$$\therefore $$ HCF $$=4.$$
Question 7
1 / -0

Choose the co-prime numbers from the following pairs:

A
$$7$$ and $$ 63$$

B
$$36$$ and $$25$$

C
$$35$$ and $$21$$

D
$$63$$ and $$81$$

Solution

A set of numbers which do not have any other common factor other than $$1$$ are called co-prime.
HCF of $$ 36 = 2 \times 2 \times 3 \times 3$$ and $$ 25 = 5 \times 5 $$ is 1 so they are co prime numbers.
Question 8
1 / -0

Which of the following statement is true?

A
1 is the smallest prime number

B
Every prime number is an odd number

C
The sum of two prime numbers is always a prime number

D
None of these

Solution

$${\because}$$ All the given statements are false.
Question 9
1 / -0

HCF of the numbers 120, 144 and 216 is __.

A
$$38$$

B
$$24$$

C
$$120$$

D
$$144$$

Solution

Given numbers are $$120,\ 144\ and \ 216$$.
To find out: HCF of the given numbers.

On factorising the given numbers, we get:
$$120=2 \times 2 \times 2 \times 3 \times 5$$
$$144=2 \times 2 \times 2 \times 2 \times 3 \times 3 $$
$$216=2 \times 2 \times 2 \times 3 \times 3 \times 3 $$

The common factors amongst the three numbers are:
$$2 \times 2 \times 2 \times 3 = 24.$$

Hence, the HCF of $$120,\ 144\ and \ 216$$ is $$24$$.
Question 10
1 / -0

Example for co-prime numbers from the below options is ?

A
$$25, 14$$

B
$$18, 16$$

C
$$9, 18$$

D
$$11, 77$$

Solution

The two numbers which have only 1 as their common factor are called co-primes.

Out of the given pair of numbers,
Factors of $$ 25 $$ are $$ 1, 5, 25 $$
Factors of $$ 14 $$ are $$ 1, 2, 7, 14 $$
Their common factor is $$ 1 $$.
Hence $$ 25, 14 $$ are co-prime numbers.

While other options has common factors other than $$1$$.
For option $$B$$ the common factor is $$2$$.
For option $$C$$ the common factor is $$3$$.
For option $$D$$ the common factor is $$11$$.

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Re-Attempt Weekly Quiz Competition

Playing with Numbers Test - 21

Result

Playing with Numbers Test - 21

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SHARING IS CARING

Question 1

$$176$$

$$182$$

$$99$$

$$101$$

Solution

Question 2

$$180$$

$$360$$

$$540$$

$$1260$$

Solution

Question 3

$$7,907$$

$$63,195$$

$$72,028$$

$$3,451$$

Solution

Question 4

Statement I alone.

Statement II alone.

Both statements I and II.

Neither statement I nor statement II.

Question 5

Neither A nor B

A alone

B alone

Both A and B

Solution

Question 6

$$24$$

$$36$$

$$12$$

$$4$$

Solution

Question 7

$$7$$ and $$ 63$$

$$36$$ and $$25$$

$$35$$ and $$21$$

$$63$$ and $$81$$

Solution

Question 8

1 is the smallest prime number

Every prime number is an odd number

The sum of two prime numbers is always a prime number

None of these

Solution

Question 9

$$38$$

$$24$$

$$120$$

$$144$$

Solution

Question 10

$$25, 14$$

$$18, 16$$

$$9, 18$$

$$11, 77$$

Solution

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