Question

Question 1 Which of the following statements are true? (a) If a number is divisible by 3, it must be divisible by 9. (b) If a number is divisible by 9, it must be divisible by 3. (c) A number is divisible by 18, if it is divisible by both 3 and 6. (d) If a number is divisible by 9 and 10 both, then it must be divisible by 90. (e) If two numbers are co-primes, at least one of them must be prime. (f) All numbers which are divisible by 4 must also be divisible by 8. (g) All numbers which are divisible by 8 must also be divisible by 4. (h) If a number exactly divides two numbers separately, it must exactly divide their sum. (i) If a number exactly divides the sum of two numbers, it must exactly divide the two numbers separately.

Class 6 - Math - Playing with Numbers Page 61

Answer 1

Divisibility test:


Divisibility of numbers by 2:
A number that has 0, 2, 4, 6 or 8 in its ones place is divisible by 2.


Divisibility of numbers by 3:
A number is divisible by 3 if the sum of its digits is divisible by 3.


Divisibility of numbers by 4:
A number is divisible by 4 if the number formed by its last two digits (i.e. ones and tens) is divisible by 4.


Divisibility of numbers by 5:
A number that has either 0 or 5 in its ones place is divisible by 5.


Divisibility of numbers by 6:
A number is divisible by 6 if that number is divisible by both 2 and 3


Divisibility of numbers by 8:
A number is divisible by 8 if the number formed by its last three digits (i.e. ones, tens and hundreds) is divisible by 8.


Divisibility of numbers by 9:
A number is divisible by 9 if the sum of its digits is divisible by 9.

Divisibility of numbers by 10:
A number that has 0 in its ones place is divisible by 10.

Divisibility of numbers by 11:
If the difference between the sum of the digits at the odd and even places in a given number is either 0 or a multiple of 11, then the given number is divisible by 11.

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Solution:

a)
FALSE

Because there are many numbers which are divisible by 3 but not divisible by 9.

For e.g
15 is divisible by 3 but not divisible by 9.

b)
TRUE

Because if a number is divisible by any number then it is divisible by each factor of that number .
Here 3 is a factor of 9.

For e.g
27/9= 3, & 27/3= 9

c)
FALSE

For e.g
Number 30 is divisible by 3 and 6 both but not divisible by 18.

d)
TRUE

Because if a number is divisible by 2 coprime numbers then it is divisible by their product also.

e)
FALSE

We know that two prime numbers having only one as a common factor are called co- prime numbers so it is not necessary that one of them must be Prime.

For e.g
8 and 15 are coprime numbers since both have only 1 as a common factor but no one is a prime number.

f)
FALSE

For e.g
36 is divisible by 4 but not divisible by 8.

g)
TRUE

If a number is divisible by any number then it is divisible by each factor of that number .
Here 4 is a factor of 8 so all the number divisible by 8 must also be divisible by 4.

For e.g
56 is divisible by 8 as well divisible by 4.

h)
TRUE

If two given numbers are divisible by a number then their sum is also divisible by that number.

For e.g
13 is exactly divides number 52 and 65 also divide their sum 117.

i)
FALSE

5 is exactly divide the sum of the numbers 2 and 3 but not exactly divide two numbers.

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Hence, statement b, d, g, h are true..

Hope this will help you.....

Answer 2

Answer:

a)False

b)True

c)False

d)True

e)False

f)True

g)True

h)True

i)False