Playing with Numbers Test

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Playing with Numbers Test - 33

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Weekly Quiz Competition

Question 1
1 / -0

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

A
$$96354142$$

B
$$ 37450176$$

C
$$57064214 $$

D
none of these

Solution

To check if a number is divisible by $$ 8 $$, we check if the last three digits of the number is divisible by $$ 8 $$ .
Since the number formed by hundreds tens and one’s digits is divisible by $$8$$ i.e. $$176$$
$$176 \div 8 = 22$$
Option (b) is the correct answer
Question 2
1 / -0

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

A
$$8576901$$

B
$$96345210$$

C
$$67594310$$

D
none of these

Solution

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.
Since sum of its digits $$ = 8 + 5 + 7 + 6 + 9 + 0 + 1 = 36$$
$$36$$ is divisible by $$9$$
Option (a) is the correct answer
Question 3
1 / -0

Which of the following are co-primes?

A
$$39,91$$

B
$$161,192$$

C
$$385,462$$

D
none of these

Solution

If the H.C.F of two numbers are $$1$$ they are said to be co-prime.
$$\therefore$$ $$(14,35)$$ is not pair of co-prime.
a) $$39, 91$$
Since $$39, 91$$ have common factor $$13$$
Hence $$39, 91$$ are not co-primes
b) $$161, 192$$
Since $$161, 192$$ have no common factor other than $$1$$ itself
Hence $$161, 192$$ are co-primes
c) $$385, 462$$
Since $$385, 462$$ have common factors $$7$$ and $$11$$
Hence $$385, 462$$ are not co-primes
Option (b) is the correct answer
Question 4
1 / -0

Which of the following is a composite number?

A
$$23$$

B
$$29$$

C
$$32$$

D
none of these

Solution

(a) $$23$$
Since it cannot be broken into factors
Hence $$23$$ is not a composite number
(b) $$29$$
Since it cannot be broken into factors
Hence $$29$$ is not a composite number
(c) $$32$$
Since it can be broken into factors i.e.$$2 \times 2 \times 2 \times 2 \times 2$$
Hence $$32$$ is a composite number
Option (c) is the correct answer
Question 5
1 / -0

Which of the following number is divisible by $$6$$?

A
$$8790432$$

B
$$98671402$$

C
$$85492014$$

D
none of these

Solution

We know that the divisibility test of $$6$$ states that a number is divisible by $$6$$ if the number is even and the sum of the digits is divisible by $$3$$.
Since its one digit is divisible by $$2$$ and
Sum of its digits $$= 8 + 7 + 9 + 0 + 4 + 3 + 2 = 33$$
$$33$$ is divisible by $$3,$$ hence divisible by $$6$$
Option (a) is the correct answer
Question 6
1 / -0

Which of the following pairs is not co prime ?

A
$$8, 10$$

B
$$11, 12$$

C
$$1, 3$$

D
$$31, 33$$

Solution

If the H.C.F of two numbers are $$1$$ they are said to be co-prime.

Common factors of the numbers $$(11,12)$$ si $$1$$.

Common factors of the numbers $$(1,3)$$ si $$1$$.

Common factors of the numbers $$(31,33)$$ si $$1$$.

Common factors of the numbers $$8$$ and $$10$$ are $$2$$ and $$1$$. Hence $$8$$ and $$10$$ are not the prime numbers.

Hence option (A) is correct
Question 7
1 / -0

The largest number which always divides the sum of any pair of consecutive odd numbers is

A
$$2$$

B
$$4$$

C
$$6$$

D
$$8$$

Solution

Option B is right
The sum of any pair of consecutive odd number comes in the form of multiple of $$4$$.
$$\therefore$$ the required largest number is $$4$$.
Question 8
1 / -0

All factors of $$ 6 $$ are

A
$$ 1, 6 $$

B
$$ 2 , 3 $$

C
$$ 1, 2 , 3 $$

D
$$ 1 , 2 , 3 , 6 $$

Solution

The factors of $$ 6 $$ are $$ 1 , 2 , 3 , 6 $$
Question 9
1 / -0

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

A
$$ 972063 $$

B
$$ 730542 $$

C
$$ 785423 $$

D
$$ 561284 $$

Solution

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.
Sum of digits $$ = 9 + 7 + 2 + 0 + 3 = 27 $$ which is divisible by $$ 9 $$
Question 10
1 / -0

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

A
$$ 503786 $$

B
$$ 505268 $$

C
$$ 305678 $$

D
$$ 703568 $$

Solution

To check if a number is divisible by $$ 8 $$, we check if the last three digits of the number is divisible by $$ 8 $$ .
Since, the number formed by hundreds, tens and ones digit is divisible by $$ 8 $$ i.e. $$ 568 \div 8 = 71 $$.
Hence, D will be correct answer.

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Re-Attempt Weekly Quiz Competition

Playing with Numbers Test - 33

Result

Playing with Numbers Test - 33

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Rank

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SHARING IS CARING

Question 1

$$96354142$$

$$ 37450176$$

$$57064214 $$

none of these

Solution

Question 2

$$8576901$$

$$96345210$$

$$67594310$$

none of these

Solution

Question 3

$$39,91$$

$$161,192$$

$$385,462$$

none of these

Solution

Question 4

$$23$$

$$29$$

$$32$$

none of these

Solution

Question 5

$$8790432$$

$$98671402$$

$$85492014$$

none of these

Solution

Question 6

$$8, 10$$

$$11, 12$$

$$1, 3$$

$$31, 33$$

Solution

Question 7

$$2$$

$$4$$

$$6$$

$$8$$

Solution

Question 8

$$ 1, 6 $$

$$ 2 , 3 $$

$$ 1, 2 , 3 $$

$$ 1 , 2 , 3 , 6 $$

Solution

Question 9

$$ 972063 $$

$$ 730542 $$

$$ 785423 $$

$$ 561284 $$

Solution

Question 10

$$ 503786 $$

$$ 505268 $$

$$ 305678 $$

$$ 703568 $$

Solution

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Question Analysis

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