NCERT Solutions for Class 4th Maths Chapter 3 Even and odd numbers, page numbers and neighbours — In-text Questions
Book page 38 Updated on2026-09-19
Q1.
Identify which of the following numbers are even and which are odd. Explain your reasoning.The eight numbers printed on page 38. Odd numbers : ____________ Even numbers : ____________
Answer
The eight numbers printed on page 38.
Look only at the last digit of each number.
The same eight numbers, each one named.
Odd numbers
67, 415, 99
Even numbers
30, 46, 78, 300, 154
My reason, number by number:
30 ends in 0 — even. 46 ends in 6 — even. 78 ends in 8 — even.
300 ends in 0 — even. 154 ends in 4 — even.
67 ends in 7 — odd. 415 ends in 5 — odd. 99 ends in 9 — odd.
Why it happens: Every ten and every hundred can be split into pairs on its own. So only the ones left over decide whether one is left alone.
Tip: A big number does not have to be an even number. 300 is big and even, 415 is big and odd. Size has nothing to do with it.
Q2.
Make two 2-digit numbers using the digits 1 and 6 without repetition.
Answer
The two numbers are 16 and 61.
Put 1 in the tens place and 6 in the ones place → 16 Put 6 in the tens place and 1 in the ones place → 61
‘Without repetition’ means you may not use the same digit twice. So 11 and 66 are not allowed.
Why it happens: With two different digits there are only two places to fill, so there are only two ways to arrange them.
Tip: 16 and 61 use the very same digits, but they are not the same number. The place of a digit decides its value.
Q3.
Identify the numbers as even or odd. Now choose any two digits and make 2-digit numbers in such a way that the numbers are even.
Answer
First, name the two numbers you made from 1 and 6:
16 ends in 6 → even 61 ends in 1 → odd
Now pick two digits that will give even numbers both ways. Pick two even digits.
Sample answer: take the digits 2 and 4.
2 and 4 → 24 and 42 24 ends in 4 → even 42 ends in 2 → even
Other pairs that work: 4 and 6 give 46 and 64; 6 and 8 give 68 and 86; 2 and 8 give 28 and 82.
Why it happens: A number is even when its ones digit is even. If both digits are even, then whichever one you put in the ones place, the number stays even.
Check it yourself: Try 3 and 5. You get 35 and 53 — both odd. Two odd digits can never make an even 2-digit number.
Q4.
Are there more even or odd numbers between 1 and 100?
Answer
Neither. There are just as many even numbers as odd numbers.
You can see it best by writing the numbers two in a row, as the crayon in the book does.
The crayon in the book, with the numbers 1 to 100 written two in a row.
The left column holds every odd number and the right column holds every even number. Both columns have the same length, so the two kinds are equal in number.
Why it happens: Numbers go odd, even, odd, even … in turn. In any run that starts at 1 and ends at an even number, each odd number has exactly one even partner just after it.
Tip: If you leave out 1 and 100 and take only the numbers strictly between them, you get 49 odd and 49 even — still the same many of each.
Q5.
Shiv wonders if both the numbers, before and after an even number, will be odd. What do you think? Check and discuss.
Answer
Shiv is right. The number just before an even number and the number just after it are both odd.
Check it with a few numbers:
Before
Even number
After
7 (odd)
8
9 (odd)
19 (odd)
20
21 (odd)
45 (odd)
46
47 (odd)
99 (odd)
100
101 (odd)
Shirley had already noticed the other half of the same rule: the numbers before and after an odd number are both even. For example 6, 7, 8.
… 6 7 8 9 10 11 12 … even odd even odd even odd even
Why it happens: Adding one coin to an even group leaves one coin alone, and taking one coin away from an even group also leaves one alone. So both neighbours must be odd.
Check it yourself: Take 10 pebbles and make 5 pairs. Add one pebble — it has no partner. Take two away from 10 — you get 8 again, still all in pairs.
Q6.
Choose any 10 numbers in order without skipping any (consecutive numbers). Write whether they are even or odd below each number. What do you notice? Discuss.The strip of ten circles in the book. The first two are filled in.
Answer
The strip of ten circles in the book. The first two are filled in.
The book has started the strip at 20 and 21. Carry on without skipping any number.
The strip filled in, with each number named below it.
Number
20
21
22
23
24
25
26
27
28
29
Even or odd
even
odd
even
odd
even
odd
even
odd
even
odd
What I notice:
Even and odd come turn by turn — never two evens together and never two odds together.
Out of the ten numbers, 5 are even and 5 are odd.
The same thing happens wherever you start. Begin at 37 and you get odd, even, odd, even …
Why it happens: Adding 1 to a number either gives the lonely coin a partner or leaves a new coin alone. So the kind has to change at every step.
Try This: Start your strip at an odd number, say 45. Now the first, third, fifth … numbers are odd instead of even, but they still take turns.