Playing with Numbers Test

Result

Playing with Numbers Test - 27

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Weekly Quiz Competition

Question 1
1 / -0

What is the largest $$3$$ digit number exactly divisible by $$4$$?

A
$$124$$

B
$$846$$

C
$$984$$

D
$$996$$

Solution

We know the divisibility rule for $$4$$:
Check the last two digits are a multiple of $$4$$ or if the last two digits are $$00$$
Here, $$996$$ is divisible by $$4$$ because the last two digits are multiple of $$4$$.
So, $$996$$ is the largest $$3$$ digit number exactly divisible by $$4$$.
So, option D is correct.
Question 2
1 / -0

How many numbers are divisible by $$8$$?
$$1264, 288, 163, 268, 2364, 1328$$

A
$$3$$

B
$$4$$

C
$$5$$

D
$$6$$

Solution

We know the divisibility rule for $$8$$:
If the last three digits are divisible by $$8$$ or last three digits of the given number are zeros, then the number is divisible by $$8$$.
Here, $$1264, 288$$ and $$1328$$ are divisible by $$8$$, because the last three digits are divisible by $$8$$.
So, option A is correct.
Question 3
1 / -0

Find the number divisible by $$3$$.

A
$$602$$

B
$$563$$

C
$$991$$

D
$$753$$

Solution

We know the divisibility rule for $$3$$:
If the sum of the digits of a number is divisible by $$3$$, then the number is also divisible by $$3$$.
Here, $$7 + 5 + 3 = 15$$ is divisible by $$3$$.

So, option D is correct.
Question 4
1 / -0

Check the numbers which are divisible by $$6$$?

A
$$23,456$$

B
$$12,345$$

C
$$98,765$$

D
$$33,516$$

Solution

We know the divisibility rule for $$6$$:
If the number is exactly divisible by both $$2$$ and $$3$$, then the given number is also divisible by $$6$$.
Here, $$3 + 3 + 5 + 1 + 6 = 18$$
So, $$33516$$ is divisible by $$6$$, because the last digit ends with even and the sum of digits of number is multiple of $$3$$.
So, option D is correct.
Question 5
1 / -0

What is the largest $$3$$ digit number exactly divisible by $$3$$?

A
$$972$$

B
$$990$$

C
$$996$$

D
$$993$$

Solution

We know the divisibility rule for $$3$$:
If the sum of the digits of a number is divisible by $$3$$, then the number is also divisible by $$3$$.
Here, $$9 + 9 + 6 = 24$$ is multiple of $$3$$.
So, $$996$$ is the largest number divisible by $$3$$.

So, option C is correct.
Question 6
1 / -0

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

A
$$12764$$

B
$$28643$$

C
$$2976$$

D
$$1286$$

Solution

We know the divisibility rule for $$8$$:
If the last three digits are divisible by $$8$$ or last three digits of the given number are zeros, then the number is divisible by $$8$$.
Here, $$2976$$ is divisible by $$8$$, because the last three digits $$296$$ are divisible by $$8$$.
So, option C is correct.
Question 7
1 / -0

Which number is divisible by $$3$$?

A
$$68$$

B
$$45$$

C
$$20$$

D
$$65$$

Solution

$${\textbf{Step  -  1 : Describe the rules of divisibility test of 3}}{\text{.}}$$

$${\text{As per the rule , any number can divisible by 3 if and only if}}$$
$${\text{ the last sum of the digits of this number is a multiple of 3,itself}}{\text{.}}$$

$${\textbf{Step  -  2 : Check with divisibility test for the options}}{\text{. }}$$

$${\text{For option A, The sum of digits of 68 is}}=6+8=14{\text{.}}$$

                      $${\text{So obviously 14 is not a multiple of 3.So 68 is not divisible by 3.}}$$

$${\text{For option B, The sum of digits of 45 is}}=4+5=9{\text{.}}$$

                      $${\text{So 9 ist a multiple of 3.So 45 is divisible by 3.}}$$

$${\text{For option C, The sum of digits of 20 is}}=2+0=2{\text{.}}$$

                      $${\text{So obviously 2 is not a multiple of 3.So 20 is not divisible by 3.}}$$

   $${\text{For option D, The sum of digits of 65 is}}=6+5=11{\text{.}}$$

                      $${\text{So obviously 11 is not a multiple of 3.So 65 is not divisible by 3.}}$$

$${\textbf{Hence, The number which is divisible by 3 is 45(B)}}{\text{.}}$$
Question 8
1 / -0

What is the number that should be added to $$27549$$ to make it exactly divisible by $$3$$?

A
$$0$$

B
$$2$$

C
$$4$$

D
$$5$$

Solution

If sum of digits of a number is divisible by $$3$$ then that number is also divisible by $$3$$.
Here, $$2 + 7 + 5 + 4 + 9 = 27$$, which is a multiple of $$3$$.
Hence, no addition is required to make this number to be divisible by $$3$$.

So, option A is correct.
Question 9
1 / -0

Which one is the largest $$5$$ digit number among the given numbers which is exactly divisible by $$8$$?

A
$$98642$$

B
$$99878$$

C
$$99864$$

D
$$99872$$

Solution

We know the divisibility rule for $$8$$ is given by:
If the last three digits of a number is divisible by $$8$$ or last three digits of the given number are zeros, then the number is divisible by $$8$$.

Checking the options, we can say $$99864$$ and $$99872$$ both are divisible by $$8$$ because the last three digits are divisible by $$8$$.

And the largest between them is $$99872$$
So, option $$D$$ is correct.
Question 10
1 / -0

Find the number that should be added to $$452671$$ to make it exactly divisible by $$8$$?

A
$$5$$

B
$$6$$

C
$$1$$

D
$$8$$

Solution

To check if a number is divisible by $$ 8 $$, we check if the last three digits of the number is divisible by $$ 8 $$ .
When we divide the number formed by the last three digits from the given number, $$671$$, by $$8$$, we get a remainder $$7$$.
Hence, if we add $$1$$ to the number, it will be exactly divisible by $$8$$.
So, option C is correct.

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Re-Attempt Weekly Quiz Competition

Playing with Numbers Test - 27

Result

Playing with Numbers Test - 27

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SHARING IS CARING

Question 1

$$124$$

$$846$$

$$984$$

$$996$$

Solution

Question 2

$$3$$

$$4$$

$$5$$

$$6$$

Solution

Question 3

$$602$$

$$563$$

$$991$$

$$753$$

Solution

Question 4

$$23,456$$

$$12,345$$

$$98,765$$

$$33,516$$

Solution

Question 5

$$972$$

$$990$$

$$996$$

$$993$$

Solution

Question 6

$$12764$$

$$28643$$

$$2976$$

$$1286$$

Solution

Question 7

$$68$$

$$45$$

$$20$$

$$65$$

Solution

Question 8

$$0$$

$$2$$

$$4$$

$$5$$

Solution

Question 9

$$98642$$

$$99878$$

$$99864$$

$$99872$$

Solution

Question 10

$$5$$

$$6$$

$$1$$

$$8$$

Solution

User

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