Playing with Numbers Test

Result

Playing with Numbers Test - 26

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following numbers are divisible by $$5$$ ?

A
$$60$$

B
$$50$$

C
$$120$$

D
All of the above

Solution

A number is divisible by $$5$$ if it contains a $$0$$ or $$5$$ in the units place.
Since all the numbers have $$0$$ in the units place, therefore all are divisible by $$5$$.
So, option D is correct.
Question 2
1 / -0

Which of these numbers are divisible by 6?

A
$$12,453$$

B
$$23,498$$

C
$$56,821$$

D
$$78,324$$

Solution

The divisibility rule for $$6$$ states that:
If the number is exactly divisible by both $$2$$ and $$3$$, then the given number is also divisible by $$6$$.
Since, $$78,324$$ has the last digit ending with an even number and the sum of its digits is a multiple of $$3$$, it is divisible by both $$2$$ and $$3$$, and hence, by $$6$$.

Hence, option D is correct.
Question 3
1 / -0

Among the following, which is the largest $$3$$ digit number exactly divisible by $$2$$?

A
$$340$$

B
$$542$$

C
$$848$$

D
$$921$$

Solution

We know the divisibility rule for $$2$$:
Always check the last digit end with $$0, 2, 4, 6$$ or $$8$$.
Here, $$848$$ is the largest $$3$$ digit number exactly divisible by $$2$$.
So, option C is correct.
Question 4
1 / -0

Among the following numbers, how many numbers are divisible by $$4$$?
$$124, 118, 280, 314, 512$$

A
$$4$$

B
$$3$$

C
$$2$$

D
$$1$$

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, $$124, 280$$ and $$512$$ is divisible by $$4$$ because the last two digits are a multiple of $$4$$ and $$0$$.
So, option B is correct.
Question 5
1 / -0

How many numbers are divisible by $$6$$?
$$234, 346, 248, 348, 684, 580, 329, 125, 376$$

A
$$0$$

B
$$1$$

C
$$2$$

D
$$3$$

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 $$6$$.
Hence, $$2 + 3 + 4 = 9$$ which is divisible by $$6$$.
And $$3 + 4 + 8 = 15$$ which is divisible by $$6$$
And $$6 + 8 + 4 = 18$$ which is divisible by $$6$$.
Because the last digits are ending with even number
and the sum of digits of all numbers are multiple of $$3$$.
So, there are $$3$$ numbers $$234, 348$$ and $$684$$ divisible by $$ 6$$.

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

Among the following numbers, how many numbers are divisible by $$4$$?
$$12, 476, 308, 201, 23, 368$$

A
$$4$$

B
$$3$$

C
$$5$$

D
$$2$$

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, $$12, 476, 308$$ and $$368$$ are divisible by $$4$$ because the last two digits are a multiple of $$4$$.
So, option A is correct.
Question 7
1 / -0

Which of these numbers are divisible by $$2$$?

A
$$211$$

B
$$303$$

C
$$200$$

D
$$101$$

Solution

We know the divisibility rule for $$2$$:
Always check the last digit end with $$0, 2, 4, 6$$ or $$8$$.
Here, $$200$$ is divisible by $$2$$ because the last digit ends with $$0$$.

So, option C is correct.
Question 8
1 / -0

The number of prime factors in $$1955$$ are

A
$$5$$

B
$$8$$

C
$$3$$

D
$$2$$

Solution

Factors of $$1955 = 5\times 17\times 23$$
Number of factors are $$3.$$
Therefore, $$C$$ is the correct answer.
Question 9
1 / -0

The number of even prime factor(s) in $$1955$$ is/are

A
$$5$$

B
$$0$$

C
$$3$$

D
$$2$$

Solution

Factor of $$1955 = 5\times 17\times 23$$
$$1, 5, 17, 23$$ are not even, so there are no even factors.
Therefore, B is the correct answer.
Question 10
1 / -0

How many of the following numbers are divisible by $$6$$?
$$12, 36, 45, 51, 78, 96, 57$$

A
$$4$$

B
$$3$$

C
$$2$$

D
$$1$$

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, $$12, 36, 78$$ and $$96$$ are divisible by $$6$$, because the last digit ends with even number and sum of numbers are multiples of $$3$$.
Therefore, there are $$4$$ numbers which are divisible by $$6$$.
So, option A is correct.

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Re-Attempt Weekly Quiz Competition

Playing with Numbers Test - 26

Result

Playing with Numbers Test - 26

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SHARING IS CARING

Question 1

$$60$$

$$50$$

$$120$$

All of the above

Solution

Question 2

$$12,453$$

$$23,498$$

$$56,821$$

$$78,324$$

Solution

Question 3

$$340$$

$$542$$

$$848$$

$$921$$

Solution

Question 4

$$4$$

$$3$$

$$2$$

$$1$$

Solution

Question 5

$$0$$

$$1$$

$$2$$

$$3$$

Solution

Question 6

$$4$$

$$3$$

$$5$$

$$2$$

Solution

Question 7

$$211$$

$$303$$

$$200$$

$$101$$

Solution

Question 8

$$5$$

$$8$$

$$3$$

$$2$$

Solution

Question 9

$$5$$

$$0$$

$$3$$

$$2$$

Solution

Question 10

$$4$$

$$3$$

$$2$$

$$1$$

Solution

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Question Analysis

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