NCERT Solutions for Class 7th Maths Chapter 6 In-text Questions — Picking Parity
Book page 129 Updated on2026-09-19
Q1.
Can you figure out which 5 cards add to 30? Is it possible? There are many ways of choosing 5 cards from this collection. Is there a way to find a solution without checking all possibilities?
Kishor’s collection of number cards, page 129.
Answer
It is not possible. No choice of 5 cards from that collection adds up to 30.
Look at the cards Kishor has: 13, 9, 1, 7, 11, 5 and 3 — every card carries an odd number.
odd + odd = even
(odd + odd) + odd = even + odd = odd
5 odd numbers = (odd + odd) + (odd + odd) + odd = even + even + odd = odd
30 is even, so the sum can never be 30.
Why it happens: you do not have to test the hundreds of choices. Odd numbers pair up two at a time to make even sums; with 5 cards one odd number is always left over, so the total is always odd.
Tip: if the target had been an odd number such as 31, it would be easy — for example 13 + 9 + 5 + 3 + 1 = 31.
Q2.
Add a few even numbers together. What kind of number do you get? Does it matter how many numbers are added?
Answer
The sum is always even, and it does not matter how many even numbers you add.
Why it happens: every even number can be laid out as complete pairs of dots with nothing left over. Put many such collections of pairs together and you still have only complete pairs — so the total is even again.
Q3.
Now, add a few odd numbers together. What kind of number do you get? Does it matter how many odd numbers are added?
Answer
Here it does matter how many you add.
How many odd numbers
Example
Parity of the sum
2
3 + 5 = 8
even
3
3 + 5 + 7 = 15
odd
4
3 + 5 + 7 + 9 = 24
even
5
3 + 5 + 7 + 9 + 11 = 35
odd
So: an even count of odd numbers gives an even sum, and an odd count of odd numbers gives an odd sum.
Why it happens: each odd number is a set of pairs with one extra dot. Two extra dots join to make one more pair, so the leftovers cancel two at a time. If the number of odd numbers is even, all leftovers pair up and the sum is even; if it is odd, exactly one dot is left over and the sum is odd.