Playing with Numbers Test

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Playing with Numbers Test - 19

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following numbers are co-prime?
a) $$18$$ and $$35$$
b) $$15$$ and $$37$$
c) $$30$$ and $$415$$
d) $$17$$ and $$68$$
e) $$216$$ and $$215$$
f) $$81$$ and $$16$$

A
a,b and f

B
a,b,e and f

C
ab,c and f

D
b,d and f

Solution

Two numbers are co-prime, if the only positive integer that divides both of them is $$1$$. That is, their H.C.F. $$=1$$

(a)
$$18=1\times 2\times 3\times 3$$

$$35=1\times 5\times 7$$

$$H.C.F.=1$$
So, the numbers are co-prime.

(b)
$$15=1\times 3\times 5$$

$$37=1\times 37$$

$$H.C.F.=1$$
So, the numbers are co-prime.

(c)
$$30=1\times 2\times 3\times 5$$

$$415=1\times 5\times 83$$

$$H.C.F.=5$$
So, the numbers are not co-prime.

(d)
$$17=1\times 17$$

$$68=1\times 2\times 2\times 17$$

$$H.C.F.=17$$
So, the numbers are not co-prime.

(e)
$$216=1\times 2\times 2\times 2\times 3\times 3\times 3$$

$$215=1\times 5\times 43$$

$$H.C.F.=1$$
So, the numbers are co-prime.

(f)
$$16=1\times 2\times 2\times 2\times 2$$

$$81=1\times 3\times 3\times 3\times 3$$

$$H.C.F.=1$$
So, the numbers are co-prime.
Question 2
1 / -0

The total number of factors for $$50$$ are

A
$$16$$

B
$$6$$

C
$$4$$

D
$$10$$

Solution

No. of factors for $$50$$

$$50=5\times 5\times 2=5^2\times 2^1$$

Total no. of factors are $$=(2+1)\times (1+1)=6$$
Question 3
1 / -0

How many two-digit prime numbers are there having the digit $$3$$ in their units place?

A
$$10$$

B
$$8$$

C
$$6$$

D
$$5$$

Solution

$$2$$ digit prime nos. having $$3$$ in their units place are-

$$13,23,43,53,73$$

$$\therefore$$ There are $$5$$ such nos.
Question 4
1 / -0

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

A
$$3792$$

B
$$5634$$

C
$$9832$$

D
$$3684$$

Solution

The sum of the digits of the number should be divisible by $$3$$ and the number should be even.

For option A:
$$3 + 7+ 9+ 2 =21$$ which is divisible by $$3$$ and number is even. so answer A is right.
Question 5
1 / -0

The factor of 252 is:

A
2

B
5

C
11

D
10

Solution

$$252 = 2 \times 2 \times 3 \times 3 \times 7$$.
The prime factors of $$252$$ are $$2,3,7$$.
Thus the answer will be A.
Question 6
1 / -0

Which of the following is divisible by $$9$$?

A
$$75636$$

B
$$89321$$

C
$$75637$$

D
$$75632$$

Solution

Number are divisible by $$9 $$ if sum of the all the digits present in it , is divisible by $$9 $$.

$$(a)75636$$
$$\Rightarrow 7+5+6+3+6=27$$ and $$27 $$ is divisible by 9.
Hence, $$75636 $$ is divisible by $$9 $$

$$(b)89321$$
$$\Rightarrow 8+9+3+2+1=23$$ and $$23 $$ is not divisible by $$9 $$.
So, $$ 89321 $$ is not divisible by $$9 $$.

$$(c)75637$$
$$\Rightarrow 7+5+6+3+7=28$$ and $$28 $$ is not divisible by $$9 $$.
So, $$75637 $$ is not divisible by $$9 $$.

$$(c)75632$$
$$\Rightarrow 7+5+6+3+2=26$$ and $$26 $$ is not divisible by $$9 $$.
So, $$75632 $$ is not divisible by $$9 $$
Question 7
1 / -0

The sum of prime numbers, out of the numbers $$17, 8, 21, 13, 41, 2, 27, 31, 51$$ is:

A
$$125$$

B
$$102$$

C
$$104$$

D
$$155$$

Solution

Prime numbers out of $$17,8,21,13,41,2,27,31,51$$ are $$17,13,41,2,31$$.
Sum of prime numbers $$= 17+13+41+2+31=104$$.
Question 8
1 / -0

Which of the following is a prime number?

A
$$117$$

B
$$171$$

C
$$179$$

D
none of these

Solution

$$179$$
Since $$179$$ have no factors other than $$1$$ and itself
Option (c) is the correct answer
Question 9
1 / -0

Which of the following is a prime number?

A
$$323$$

B
$$361$$

C
$$263$$

D
none of these

Solution

a) $$323$$ can be written as $$17 \times 19$$
Hence $$323$$ is not a prime number
b) $$361$$ can be written as $$19 \times 19$$
Hence $$361$$ is not a prime number
c) $$263$$ is a prime number
Option (c) is the correct answer
Question 10
1 / -0

If the sum of digits of a number is divisible by three then the number is always divisible by

A
$$2$$

B
$$3$$

C
$$6$$

D
$$9$$

Solution

If the sum of digits of a number is divisible by three, then the number is always divisible by $$3$$.
This is the test for divisibility by 3.
Hence, (B) is the correct option.

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Re-Attempt Weekly Quiz Competition

Playing with Numbers Test - 19

Result

Playing with Numbers Test - 19

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SHARING IS CARING

Question 1

a,b and f

a,b,e and f

ab,c and f

b,d and f

Solution

Question 2

$$16$$

$$6$$

$$4$$

$$10$$

Solution

Question 3

$$10$$

$$8$$

$$6$$

$$5$$

Solution

Question 4

$$3792$$

$$5634$$

$$9832$$

$$3684$$

Solution

Question 5

2

5

11

10

Solution

Question 6

$$75636$$

$$89321$$

$$75637$$

$$75632$$

Solution

Question 7

$$125$$

$$102$$

$$104$$

$$155$$

Solution

Question 8

$$117$$

$$171$$

$$179$$

none of these

Solution

Question 9

$$323$$

$$361$$

$$263$$

none of these

Solution

Question 10

$$2$$

$$3$$

$$6$$

$$9$$

Solution

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