Playing with Numbers Test

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Playing with Numbers Test - 28

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Weekly Quiz Competition

Question 1
1 / -0

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

A
$$1,638$$

B
$$2,648$$

C
$$2,564$$

D
$$3,126$$

Solution

We know the divisibility rule for $$8$$:
The last three digits is divisible by $$8$$ or last three digits of the given number are zeroes then the number is divisible by $$8$$.
Here, $$2648$$ is divisible by $$8$$, because the last three digits are multiple of $$8$$.
So, option B is correct.
Question 2
1 / -0

How many of the prime factors of $$30$$ are greater than $$2$$?

A
One

B
Two

C
Three

D
Four

E
Five

Solution

$$30=2\times 3\times 5$$
So, only $$3$$ and $$5$$ are the two prime factors that are greater than $$2$$.
Question 3
1 / -0

Which number is divisible by $$9$$?

A
$$863$$

B
$$932$$

C
$$752$$

D
$$837$$

Solution

$${\textbf{Step -1: Sum of digits of 863 = 17}}$$

$${\text{17 is not divisble by 9}}$$

$${\textbf{Step -2: Sum of digits of 932 = 14}}$$

$${\text{14 is not divisible by 9}}$$

$${\textbf{Step -3:Sum of digits of 752 = 14}}$$

$${\text{14 is not divisible by 9}}$$

$${\textbf{Step -4: Sum of digits of 837 = 18}}$$

$${\text{18 is divisible by 9}}$$

$${\textbf{Hence, 837 is divisible by 9 .}}$$
Question 4
1 / -0

What is the largest odd number that is a factor of $$860$$?

A
$$143$$

B
$$115$$

C
$$215$$

D
$$243$$

Solution

Factorisation of $$860=$$ $$2\times 430=2\times 2\times 215$$
$$215$$ is an odd number, so the largest odd number factor of $$860$$ is $$215$$.
Question 5
1 / -0

Find the number of prime numbers between 301 and 320?

A
6

B
5

C
4

D
3

Solution

Prime numbers between 301 and 320 are 307, 311, 313, 317. So there are total $$4$$ prime numbers between 301 and 320
So correct answer will be option C
Question 6
1 / -0

Every composite number has _____________.

A
no prime divisor

B
one and only one prime divisor

C
atleast one prime divisor

D
atleast two prime divisor

Solution

A composite number is that has at least one prime divisor other than $$1$$ and itself. For example : $$10$$ is composite number that has $$2, 5$$ as its prime divisors.
Question 7
1 / -0

What smallest number should be added to 4456 so that the sum is completely divisible by 6?

A
$$4$$

B
$$3$$

C
$$2$$

D
$$1$$

E
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, $$4456\div 6$$ (Quotient$$=742,$$ Remainder $$=4$$)
Therefore required number $$=(6-4)=2$$

Hence, $$2$$ is the smallest number that should be added to $$4456$$ so that the sum is completely divisible by $$6$$.
Question 8
1 / -0

Find $$HCF$$ by finding factors : $$75, 79$$ and $$89$$

A
$$2$$

B
$$3$$

C
$$1$$

D
$$4$$

Solution

Factorization of the following
$$75 = 5 \times 5 \times 3\times 1$$
$$79=1 \times 79$$
$$89 = 1 \times 89$$
Since, the common factor is $$1$$ this implies that
$$HCF = 1$$

Hence, the correct option is $$C$$
Question 9
1 / -0

A $$3$$-digit number 'cba' is divisible by $$9$$ if _____ .

A
$$a+2b+c$$ is divisible by $$9$$

B
$$2a+b+c$$ is divisible by $$9$$

C
$$a+b+2c$$ is divisible by $$9$$

D
$$a+b+c$$ is divisible by $$9$$

Solution

Divisibility Test for $$9$$ :
$$\rightarrow$$ A number is divisible by $$9$$ if the sum of the digits is divisible by $$9$$.

For Example,
$$549$$ is divisible by $$9$$ since the sum of the digits is $$18$$ and $$18$$ is Divisible by $$9$$.

Here,
Given number is 'cba'
For it to be Divisible by $$9$$,
(a+b+c) should be divisible by $$9$$

$$\therefore$$ Answer is 'D'
Question 10
1 / -0

Find $$HCF$$ by finding factors:
$$6$$ and $$8$$.

A
$$4$$

B
$$6$$

C
$$2$$

D
$$8$$

Solution

Factorization of the following.
$$6 = 3 \times 2\times 1$$
$$8 = 2 \times 2 \times 8\times 1$$
Since, The common factor is $$2$$.This implies that
$$H.C.F = 2$$
Hence,the correct option is $$C$$

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Playing with Numbers Test - 28

Result

Playing with Numbers Test - 28

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SHARING IS CARING

Question 1

$$1,638$$

$$2,648$$

$$2,564$$

$$3,126$$

Solution

Question 2

One

Two

Three

Four

Five

Solution

Question 3

$$863$$

$$932$$

$$752$$

$$837$$

Solution

Question 4

$$143$$

$$115$$

$$215$$

$$243$$

Solution

Question 5

6

5

4

3

Solution

Question 6

no prime divisor

one and only one prime divisor

atleast one prime divisor

atleast two prime divisor

Solution

Question 7

$$4$$

$$3$$

$$2$$

$$1$$

None of these

Solution

Question 8

$$2$$

$$3$$

$$1$$

$$4$$

Solution

Question 9

$$a+2b+c$$ is divisible by $$9$$

$$2a+b+c$$ is divisible by $$9$$

$$a+b+2c$$ is divisible by $$9$$

$$a+b+c$$ is divisible by $$9$$

Solution

Question 10

$$4$$

$$6$$

$$2$$

$$8$$

Solution

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