In-Text Questions Try These (Textbook Page No. 8, 19) - Chapter 1 Numbers Term 2 6th Maths Guide Samacheer Kalvi Solutions - SaraNextGen [2024-2025]

Updated By SaraNextGen

On April 24, 2024, 11:35 AM

Try These (Textbook Page No. 8)
Question $1 .$
Are the leap years divisible by $2 ?$
Solution:
Leap years are divisible by $4 .$
Leap years are divisible by $2 .$

Question $2 .$
Is the first 4 digit number divisible by 3 ?
Solution:
The first four-digit number is 1000 .
Sum of the digits is $1+0+0+0=1$, not divisible by 3 .
1000 is not divisible by 3 .

Question $3 .$
Is your date of birth (DDMMYYYY) divisible by $3 ?$
Solution:
Date of birth $25.05 .2007$
Sum of digits $=2+5+0+5+2+0+0+7=21$
Again $2+1=3$, divisible by 3 .
My date of birth is divisible by 3 .

Question $4 .$
Identify the numbers in the sequence $2000,2006,2010,2015,2019,2025$ that are divisible by both 2 and $5 .$
Solution:
We know that a number is divisible by both 2 and 5 if it is divisible by $10.2000$ and 2010 are divisible by 10 .
 

Question $5 .$
Check whether the sum of 5 consecutive numbers is divisible by 5 .
Solution:
Take the first five consecutive natural numbers $1,2,3,4$ and 5 .
Their sum $1+2+3+4+5=15$, divisible by 5
Also, $2+3+4+5+6=20$, divisible by 5 .
$3+4+5+6+7=25$, divisible by 5 .
Generally, the sum of 5 consecutive natural numbers is divisible by 5 .

Try These (Textbook Page No. 19)
A small boy went to a town to sell a basket of wood apples. On the way, some robbers grabbed the fruits from him and ate them! The small boy went to the King and complained. The King asked him, "How many wood apples did you bring?". The boy replied, "Your Majesty! I didn't know, but I knew that if you divided my fruits into groups of 2 , one fruit would be left in the basket". He continued saying that if the fruits were divided into groups of $3,4,5$ and 6 , the fruits left in the basket would be $2,3,4$ and 5 respectively. Also, if the fruits were divided into groups of 7 , no fruit would be there in the basket. Can you find the number of fruits, the small boy had initially?
(This problem is taken from the famous Mathematics problems collection book in Tamil called "Kanakkathikaram" under the heading of "Wood Apple Problem")
Solution:
The total number of fruits, when divided by $2,3,4,5$ and 6 , leaves the remainders $1,2,3,4$ and 5 respectively.
Here $(2-1)=(3-2)=(4-3)=(5-4)=(6-5)=1$.
$\therefore$ The required no. of fruits will be $\operatorname{LCM}(2,3,4,5,6)-1$
$\mathrm{LCM}(2,3,4,5,6)=2 \times 3 \times 2 \times 5=60$

Now take the multiples of 60 and subtract 1 from it.
Also checking the conditions, multiplies of 60 are $60,120,180, \ldots \ldots$
The multiple $-1$
$59,119,179, \ldots \ldots$
The required number $=119$
$\therefore$ The total number of fruits $=119$.