Playing with Numbers Test

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Playing with Numbers Test - 32

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Weekly Quiz Competition

Question 1
1 / -0

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

A
$$27326$$

B
$$42356$$

C
$$73545$$

D
$$45326$$

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 divisible by $$3$$
A) $$2 + 7 + 3 + 2 + 6 = 20$$
B) $$4 + 2 + 3 + 5 + 6 = 20$$
C) $$7 + 3 + 5 + 4 + 5 = 24$$
D) $$4 + 5 + 3 + 2 + 6 = 20$$

Only C) $$24$$ is divisible by $$3$$
So, option C is the correct option.
Question 2
1 / -0

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

A
$$8675231$$

B
$$9843212$$

C
$$1234567$$

D
$$543123$$

Solution

Rule to check whether the number is divisible by 4 or not is as follows:

Suppose we have a number is $$abcde$$,

then if $$de$$ is divisible by $$4$$, then the whole number is divisible by $$4$$.

We work on each option and use above rule to find which of the given options is divisible by 4.

A. $$8675231$$
31 is not divisible by 4. So, $$8675231$$ is also not divisible by $$4$$.

B. $$9843212$$
12 is divisible by 4. So, $$9843212$$ is also divisible by $$4$$.

$$\textbf{So, Option B is correct}$$

C. $$1234567$$
67 is not divisible by 4. So, $$1234567$$ is also not divisible by $$4$$.

D. $$543123$$
23 is not divisible by 4. So, $$543123$$ is also not divisible by $$4$$.
Question 3
1 / -0

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

A
$$1258$$

B
$$61233$$

C
$$901352$$

D
$$1790184$$

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 $$3$$.
$$1790194$$ is divisible by 2 as unit's digit is 4 and it is also divisible by 3 because sum of digits
$$= 1 + 7 + 9 + 0 + 1 + 8 + 4$$
$$= 30$$ is a multiple of 3.
Hence, it is divisible by $$6$$
Question 4
1 / -0

The total number of even prime numbers is?

A
$$0$$

B
$$1$$

C
$$2$$

D
Unlimited

Solution

The number $$2$$ is the only prime number, which is even. So, the number of even primes is equal to $$1$$.
Question 5
1 / -0

Mark the correct alternative of the following.
The smallest number which is neither prime nor composite is?

A
$$0$$

B
$$1$$

C
$$2$$

D
$$3$$

Solution

All primes have two positive divisors. There are only two integers that are neither composite or prime and they are 1 and 0.

The number 1 has only 1 positive divisor, itself. The number 0 has an infinite number of divisors.

1 is neither prime nor composite.
Question 6
1 / -0

If a and b are two co-primes, then which of the following is/are true?

A
LCM(a, b)$$=a\times b$$

B
HCF(a, b)$$=1$$

C
Both (a) and (b)

D
Neither (a) nor (b)

Solution

Given $$a,b$$ are two co-primes then HCF $$(a,b)=1$$ [ Definition of co-primes].
We've,
LCM$$\times$$ HCF $$=a\times b$$
or, LCM $$=a\times b$$. [ Since HCF $$=1$$]
Question 7
1 / -0

Mark the correct alternative of the following.
From the numbers $$2, 3, 4, 5, 6, 7, 8, 9$$ how many pairs of co-primes can be formed?

A
$$19$$

B
$$18$$

C
$$20$$

D
$$21$$

Solution

If the H.C.F of two numbers are $$1$$ they are said to be co-prime
The following are the pairs of co-prime numbers:
$$(2,3), (2,5), (2,7), (2,9), (3,4), (3,5), (3,7), (3,8), (4,5), (4,7), (4,9), (5,6), (5,7), (5,8), (5,9), (6,7), (7,8), (7,9), (8,9).$$
Number of pairs of co-prime numbers are $$19.$$
Question 8
1 / -0

HCF of $$144$$ and $$198$$ is

A
$$9$$

B
$$18$$

C
$$6$$

D
$$12$$

Solution

$$\textbf{Step 1: Calculate Common Factors of 144 and 198}$$
$$\text{Prime Factors of 144 and 198 are:}$$
$$ 198 = 2 \times 3\times3 \times 11$$
$$ 144 = 2\times2\times2\times2 \times 3\times3$$
$$\Rightarrow \text{Common factor of 198 and 144 =}$$ $$(3\times 3)$$
$$\therefore\text{HCF=9}$$
$$\textbf{Thus, HCF of 198 and 144 is 9}$$
Question 9
1 / -0

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

A
$$24357806$$

B
$$35769812$$

C
$$83479560$$

D
$$3336433$$

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.
Since sum of its digits $$= 8 + 3 + 4 + 7 + 9 + 5 + 6 + 0 = 42$$
$$42$$ is divisible by $$3$$
Option (c) is the correct answer
Question 10
1 / -0

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

A
$$78653234$$

B
$$ 98765042$$

C
$$24689602 $$

D
$$87941032$$

Solution

A number is divisible by $$4$$ if the number formed
by the digits in $$\text{units and tens}$$ places
is divisible by $$4$$.
Since the number formed by tens and ones digits is divisible by $$4$$ i.e. $$32$$
$$32 \div 4 = 8$$
Option (d) is the correct answer

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Re-Attempt Weekly Quiz Competition

Playing with Numbers Test - 32

Result

Playing with Numbers Test - 32

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SHARING IS CARING

Question 1

$$27326$$

$$42356$$

$$73545$$

$$45326$$

Solution

Question 2

$$8675231$$

$$9843212$$

$$1234567$$

$$543123$$

Solution

Question 3

$$1258$$

$$61233$$

$$901352$$

$$1790184$$

Solution

Question 4

$$0$$

$$1$$

$$2$$

Unlimited

Solution

Question 5

$$0$$

$$1$$

$$2$$

$$3$$

Solution

Question 6

LCM(a, b)$$=a\times b$$

HCF(a, b)$$=1$$

Both (a) and (b)

Neither (a) nor (b)

Solution

Question 7

$$19$$

$$18$$

$$20$$

$$21$$

Solution

Question 8

$$9$$

$$18$$

$$6$$

$$12$$

Solution

Question 9

$$24357806$$

$$35769812$$

$$83479560$$

$$3336433$$

Solution

Question 10

$$78653234$$

$$ 98765042$$

$$24689602 $$

$$87941032$$

Solution

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