NCERT Solutions Ganita Prakash (Part 1) Chapter 6 Figure it Out — Picking Parity

Book page 131 Updated on2026-09-05

Q1.

Using your understanding of the pictorial representation of odd and even numbers, find out the parity of the following sums: (a) Sum of 2 even numbers and 2 odd numbers (e.g., even + even + odd + odd) (b) Sum of 2 odd numbers and 3 even numbers (c) Sum of 5 even numbers (d) Sum of 8 odd numbers

Answer

Even numbers bring only complete pairs. Only the odd numbers bring leftover dots, so just count how many odd numbers there are.

	Sum	Number of odd numbers	Leftover dots	Parity
(a)	2 even + 2 odd	2 (even count)	pair up fully	even
(b)	2 odd + 3 even	2 (even count)	pair up fully	even
(c)	5 even	0	none	even
(d)	8 odd	8 (even count)	pair up fully	even

All four sums are even.

(a) 4 + 6 + 3 + 5 = 18 even
(b) 3 + 5 + 2 + 4 + 6 = 20 even
(c) 2 + 4 + 6 + 8 + 10 = 30 even
(d) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 = 64 even

Why it happens: the even numbers never disturb the pairing. The parity of the whole sum depends only on how many odd numbers are added — even count → even sum, odd count → odd sum.

Q2.

Lakpa has an odd number of ₹1 coins, an odd number of ₹5 coins and an even number of ₹10 coins in his piggy bank. He calculated the total and got ₹205. Did he make a mistake? If he did, explain why. If he didn’t, how many coins of each type could he have?

Answer

Yes, Lakpa has made a mistake. With those counts the total can never be ₹205.

Let him have a coins of ₹1 (a odd), b coins of ₹5 (b odd) and c coins of ₹10 (c even).

Value from ₹1 coins = a → odd
Value from ₹5 coins = 5b, and odd × odd = odd
Value from ₹10 coins = 10c → even (10 is even)
Total = odd + odd + even = even + even = even
But ₹205 is odd. So the total is impossible.

Check with an example: 3 coins of ₹1, 5 coins of ₹5, 4 coins of ₹10.

3 × 1 + 5 × 5 + 4 × 10 = 3 + 25 + 40 = ₹68 (even, as expected)

Why it happens: a ₹10 coin can never change the parity, and the ₹1 part and the ₹5 part are each odd. Two odd amounts always add to an even amount, so Lakpa's total must be an even number of rupees.

Check it yourself: ₹204 or ₹206 would be possible, but no odd total ever is.

Q3.

We know that: (a) even + even = even (b) odd + odd = even (c) even + odd = odd. Similarly, find out the parity for the scenarios below: (d) even – even = ___ (e) odd – odd = ___ (f) even – odd = ___ (g) odd – even = ___

Answer

	Operation	Parity	Example
(d)	even – even	even	10 – 4 = 6
(e)	odd – odd	even	9 – 3 = 6
(f)	even – odd	odd	10 – 3 = 7
(g)	odd – even	odd	9 – 4 = 5

Why it happens: subtraction behaves exactly like addition here. Taking away complete pairs from complete pairs leaves complete pairs (even). Taking one leftover dot away from another leftover dot also leaves complete pairs (even). Only when one side has a leftover dot and the other does not is a dot stranded — and the answer is odd.

Tip: a short way to remember all eight facts — the answer is odd exactly when the two numbers have different parity, for both + and –.

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