Playing with Numbers Test

Result

Playing with Numbers Test - 34

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following is an odd composite number ?

A
$$ 7 $$

B
$$ 9 $$

C
$$ 11 $$

D
$$ 12 $$

Solution

$$ 9 = 3 \times 3 $$ , is an odd composite number.
Question 2
1 / -0

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

A
$$ 560324 $$

B
$$ 650374 $$

C
$$ 798653 $$

D
$$ 750972 $$

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, the sum of its digit $$ = 7 + 5 + 0 + 9 + 7 + 2 = 30 $$ which is divisible by $$ 3 $$.
and it ends in $$2.$$
Hence it is divisible by $$ 6 $$
Question 3
1 / -0

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

A
$$ 8 , 15 $$

B
$$ 3 , 18 $$

C
$$ 5 , 35 $$

D
$$ 6 , 39 $$

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.
The factors of $$ 8 $$ are $$ 1 , 2 , 4 , 8 $$ .
The factor of $$ 15 $$ are $$ 1 , 3 , 5 , 15 $$ .
The common factor of $$ 8 $$ and $$ 15 $$ is $$ 1 $$
They are co-prime.
Question 4
1 / -0

Which of the following numbers is divisible by $$ 4 $$ ?

A
$$ 308594 $$

B
$$ 506784 $$

C
$$ 732106 $$

D
$$ 9301538 $$

Solution

A number is divisible by $$4$$ if the number formed
by the digits in $$\text{units and tens}$$ places
is divisible by $$4$$.
Here the number formed by tens and ones digits is $$84$$ and divisible by $$ 4 $$ i.e., $$ 84 \div 4 = 21 $$.
Question 5
1 / -0

Which of the following numbers is divisible by $$ 3 $$ ?

A
$$ 50762 $$

B
$$ 42063 $$

C
$$ 52871 $$

D
$$ 37036 $$

Solution

We use a rule to check whether the number is divisible by 3 or not.
A number is divisible by 3 if the sum of the digits is evenly divisible by 3.
Sum of digits is $$ = 4 + 2 + 0 + 6 + 3 = 15 $$ which is divisible by $$ 3 $$
Question 6
1 / -0

A four-digit number $$aabb$$ is divisible by $$55$$. Then possible value(s) of $$b$$ is/are

A
$$0$$ and $$2$$

B
$$2$$ and $$5$$

C
$$0$$ and $$5$$

D
$$7$$

Solution

If the number is divisible by $$55$$,
It must also be divisible by $$5$$.
Therefore the number ends with $$0$$ or $$5$$.
Question 7
1 / -0

If $$abc$$ is a three digit number, then the number $$abc-a-b-c$$ is divisible by

A
$$9$$

B
$$90$$

C
$$10$$

D
$$11$$

Solution

Expandin $$abc$$, we get,
$$abc=100a+10b+c$$

$$\therefore abc-a-b-c=100a+10b+c-a-b-c\\=99a+9b\\=9(11a+b)$$

Therefore, $$(abc-a-b-c)$$ is divisible by $$9$$
Question 8
1 / -0

Write all the factors of 25 in blue circle, all the factors of 35 in green circle and all the common factors in yellow circle. Which is highest common factor?

A
5

B
7

C
2

D
1

Solution
Question 9
1 / -0

Write all the factors of 24 and 36 and find out the common factors. Which is the highest common factor of these two numbers?

A
6

B
4

C
12

D
24

Solution
Question 10
1 / -0

Write all the factors of 16 in circle I and all the factors of 20 in circle II. Write all the common factors in common part of both the circles. Which option shows it correctly?

A

B

C

D
None of these

Solution

Factors of $$ 16 $$ are $$ 1, 2,4 , 8 , 16$$
Factors of $$ 20 $$ are $$ 1, 2, 4, 5, 10, 20 $$
$$\therefore $$ common factors are $$ 1, 2, 4 $$.