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CBSE Questions for Class 6 Maths Playing With Numbers Quiz 11 - MCQExams.com
CBSE
Class 6 Maths
Playing With Numbers
Quiz 11
Which of the following is a composite number?
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$$23$$
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$$29$$
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$$32$$
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none of these
Explanation
(a) $$23$$
Since it cannot be broken into factors
Hence $$23$$ is not a composite number
(b) $$29$$
Since it cannot be broken into factors
Hence $$29$$ is not a composite number
(c) $$32$$
Since it can be broken into factors i.e.$$2 \times 2 \times 2 \times 2 \times 2$$
Hence $$32$$ is a composite number
Option (c) is the correct answer
If the sum of the digits of a number is divisible by $$3$$, then the number itself is divisible by $$9$$.
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True
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False
Explanation
According to the divisibility Test for $$9$$, for a number to be divisible by $$9$$ the sum of digits of the number should be divisible by $$9$$.
And not all the numbers divisible by $$3$$ are divisible by $$9$$.
For example: $$15$$ is divisible by $$3$$ but not $$9$$.
$$\textbf{Therefore the given statement is False}.$$
State true of false:
Two prime numbers are always co-prime numbers.
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True
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False
Explanation
Given statement is true.
Any two prime numbers are coprime as they do not have common factor other tham 1.
A number with three or more digits is divisible by $$6$$ if the number formed by its last two digits (i.e., ones and tens) is divisible by $$6$$.
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True
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False
Explanation
We know that according to the divisibility test of $$6$$ if a number is divisible by
both $$2$$ and $$3$$ then it is divisible by $$6$$, it does not have to do anything with the last
two digits of the number.
For example
$$112$$ is not divisible by $$6$$ although the last two digits of $$112$$ are divisible
by $$6$$.
$$\therefore\ \textbf{The given statement is False}.$$
Which of the following are not co-primes?
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$$8,12$$
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$$9,10$$
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$$6,8$$
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$$15,18$$
Explanation
If the H.C.F of two numbers are $$1$$ they are said to be co-prime
.
(a) $$8, 12$$
Here they have a common factor $$4$$
Hence $$8, 12$$ are not co- primes
(b) $$9, 10$$
Here they don’t have a common factor
Hence $$9, 10$$ are co- primes
(c) $$6, 8$$
Here they have a common factor $$2$$
Hence $$6, 8$$ are not co- primes
(d) $$15, 18$$
Here they have a common factor $$3$$
Hence $$15, 18$$ are not co- primes
State whether the following statements are true (T) or false (F) :
There are infinitely many prime numbers.
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True
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False
State whether the following statement is true or false.
HCF of an even number and an odd number is always $$ 1.$$
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True
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False
Explanation
Let us consider an even number $$ 6 $$ and an odd number $$9$$
The HCF of $$ 6 $$ and $$ 9 $$ is $$ 3 $$
Hence the statement "
HCF of an even number and an odd number is always $$1$$
" is false.
Which of the following is an odd composite number ?
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$$ 7 $$
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$$ 9 $$
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$$ 11 $$
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$$ 12 $$
Explanation
$$ 9 = 3 \times 3 $$ , is an odd composite number.
Which of the following pairs is not co prime ?
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$$8, 10$$
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$$11, 12$$
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$$1, 3$$
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$$31, 33$$
Explanation
We know that Numbers which have only $$1$$ as a common factor are called co-prime.
In the given options,
Common factors of $$8$$ and $$10$$ are $$1, 2$$.
Therefore $$8$$ and $$10$$ are not co-prime numbers
$$\therefore$$ $$\textbf{Correct option is A}$$.
The largest number which always divides the sum of any pair of consecutive odd numbers is
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$$2$$
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$$4$$
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$$6$$
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$$8$$
Explanation
$$\textbf{Step 1: Recall Odd numbers}$$.
Odd numbers are the numbers which are not divisible by $$2$$.
$$\textbf{Step 2: Find the sum of consecutive odd numbers}$$
Consecutive odd numbers are $$3$$ and $$5, 7$$ and $$9, 11$$ and $$13, 13$$ and $$15$$ etc
Sum of consecutive odd numbers $$3$$ and $$5 = 3 + 5 = 8$$ (Divisible by $$2$$ and $$4$$ and $$8$$)
Sum of consecutive odd numbers $$7$$ and $$9 = 7 + 9 = 16$$ (Divisible by $$2, 4$$ and $$8$$)
Sum of consecutive odd numbers $$13$$ and $$15 = 13 + 15 = 28$$ (Divisible by $$2, 4$$ and $$7$$)
The sum of consecutive odd numbers is always divisible by $$2, 4$$ by taking any consecutive odd numbers
So, we can say that the largest number which always divides the sum of any pair of consecutive odd numbers is $$4$$.
$$\therefore$$ $$\textbf{Option B is correct}$$
Any two consecutive numbers are co-prime.
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True
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False
Explanation
The numbers that have only $$1$$ as common factors are called coprime numbers.
HCF of any two consecutive numbers is always $$1$$
So, two consecutive numbers are always coprime.
For example, $$99$$ and $$100$$ are coprime.
$$\textbf{Therefore the given statement is True}.$$
All factors of $$ 6 $$ are
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$$ 1, 6 $$
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$$ 2 , 3 $$
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$$ 1, 2 , 3 $$
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$$ 1 , 2 , 3 , 6 $$
Explanation
The factors of $$ 6 $$ are $$ 1 , 2 , 3 , 6 $$
Which of the following number is divisible by $$ 8 $$ ?
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$$ 503786 $$
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$$ 505268 $$
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$$ 305678 $$
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$$ 703568 $$
Explanation
To check if a number is divisible by $$ 8 $$, we check if the last three digits of the number is divisible by $$ 8 $$ .
Since, the number formed by hundreds, tens and ones digit is divisible by $$ 8 $$ i.e. $$ 568 \div 8 = 71 $$.
Hence, D will be correct answer.
Which of the following number is divisible by $$ 6 $$ ?
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$$ 560324 $$
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$$ 650374 $$
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$$ 798653 $$
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$$ 750972 $$
Explanation
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, the sum of its digit $$ = 7 + 5 + 0 + 9 + 7 + 2 = 30 $$ which is divisible by $$ 3 $$.
and it ends in $$2.$$
Hence it is divisible by $$ 6 $$
Which of the following is a pair of co-prime numbers ?
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$$ 8 , 15 $$
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$$ 3 , 18 $$
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$$ 5 , 35 $$
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$$ 6 , 39 $$
Explanation
If the H.C.F of two numbers are $$1$$ they are said to be co-prime.
$$\therefore$$ $$(14,35)$$ is not pair of co-prime.
The factors of $$ 8 $$ are $$ 1 , 2 , 4 , 8 $$ .
The factor of $$ 15 $$ are $$ 1 , 3 , 5 , 15 $$ .
The common factor of $$ 8 $$ and $$ 15 $$ is $$ 1 $$
They are co-prime.
Which of the following numbers is divisible by $$ 4 $$ ?
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$$ 308594 $$
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$$ 506784 $$
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$$ 732106 $$
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$$ 9301538 $$
Explanation
A number is divisible by $$4$$ if the number formed
by the digits in $$\text{units and tens}$$
places
is divisible by $$4$$.
Here the number formed by tens and ones digits is $$84$$ and divisible by $$ 4 $$ i.e., $$ 84 \div 4 = 21 $$.
A two-digit number $$ab$$ is always divisible by $$2$$ if $$b$$ is an even number.
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True
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False
Explanation
Rule for divisible by 2.
Any number with the last digit of $$0,2,4,6,8$$ are divisible by 2.
A two-digit number is divisible by $$2$$ if the unit digit of the number is even.
Hence, given statement is true.
Number of the form $$3N+2$$ will leave remainder $$2$$ when divided by $$3$$.
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0%
True
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False
Explanation
True
$$3N+2$$ is a number whose sum of its digit is $$2$$ more than multiple of $$3$$.
As $$3N$$ is completly divisible by 3. hence, remainder=2
If $$213x27$$ is divisible by $$9$$, then the value of $$x$$ is $$0$$.
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True
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False
Explanation
A number is divisible by $$9$$ if the sum of its digits is also divisible by $$9$$.
$$2+1+3+x+2+7=0,9,18,27,...$$
$$2+1+3+x+2+7=15+x$$
According to the question $$x$$ is a single digit.
Hence, $$18=15+x$$ $$\Rightarrow x=18-15=3$$
A three-digit number $$abc$$ is divisible by $$5$$ if $$c$$ is an even number.
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0%
True
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False
Explanation
False
A three-digit number is divisible by $$5$$ if the unit digit of the number is $$0$$ or $$5$$.
A four digit number $$abcd$$ is divisible by $$4$$ if $$ab$$ is divisible by $$4$$.
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True
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False
Explanation
False
A four-digit number is divisible by $$4$$ if the number formed by its digit units and $$10's$$ place is divisible by $$4$$.
If $$abc$$ is a three digit number, then the number $$abc-a-b-c$$ is divisible by
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$$9$$
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$$90$$
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$$10$$
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$$11$$
Explanation
Expandin $$abc$$, we get,
$$abc=100a+10b+c$$
$$\therefore abc-a-b-c=100a+10b+c-a-b-c\\=99a+9b\\=9(11a+b)$$
Therefore, $$(abc-a-b-c)$$ is divisible by $$9$$
A three-digit number $$abc$$ is divisible by $$6$$ if $$c$$ is an even number and $$a+b+c$$ is a multiple of $$3$$.
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True
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False
Explanation
True
If a number is divisible by $$6$$ then it is also divisible by $$2$$ and $$3$$.
A number is divisible by $$3$$ if its unit digit is divisible by $$2$$.
A number is divisible by $$3$$ if the sum of its digits is also divisible by $$3$$.
State True or False :
If a number is a factor $$ 16 $$ and $$ 24 $$ , it is a factor of $$ 48 $$
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True
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False
Explanation
Factor of $$48$$ is $$1,2,3,4,6,8,12,16,24$$ and $$48$$
As $$ 16 $$ and $$ 24 $$ are factors of $$ 48 $$
All even numbers are prime numbers.
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True
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False
Explanation
False, $$ 4 $$ is an even number but not prime numbers.
Write all the factors of 24 and 36 and find out the common factors. Which is the highest common factor of these two numbers?
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6
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4
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12
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24
Write all the factors of 16 in circle I and all the factors of 20 in circle II. Write all the common factors in common part of both the circles. Which option shows it correctly?
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0%
0%
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None of these
Explanation
Factors of $$ 16 $$ are $$ 1, 2,4 , 8 , 16$$
Factors of $$ 20 $$ are $$ 1, 2, 4, 5, 10, 20 $$
$$\therefore $$ common factors are $$ 1, 2, 4 $$.
Write all the factors of 5, 8 andFind out all the common factors of these numbers. Which is highest common factor?
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5
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8
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10
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1
HCF of $$95$$ and $$152$$ is:
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$$1$$
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$$19$$
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$$57$$
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$$38$$
Explanation
$$95 = 5 \times 19$$
and $$152 = 2^{3} \times 19$$
H.C.F $$ = 19$$
Using multiplication chart, find all the factors of $$36$$.
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1,2,3,5,7,9,12,15,18,36
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1,2,3,4,6,9,12,18,36
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1,4,7,12,18,36
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1,6,9,18,36
Explanation
Factors of 36 are 1,2,3,4,6,9,12,18,36
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