Complete the diagram on page 170 by writing each number in the right place. 90 22 38 30 75 45 66 78 62 40 84 56 25 95 55 Numbers divisible only by 2 Numbers divisible only by 5 Numbers divisible by 2, 5 and 10 Numbers divisible only by 10 Page 170 — the fifteen number cards and the blank sorting dia

Here is the finished diagram, with all fifteen numbers placed. 22, 38, 66 78, 62, 84 56 75, 45, 25 95, 55 90 30 40 None divisible by 2 only divisible by 5 only divisible by 10 only by 2, 5 and 10 All fifteen numbers sorted. The bottom part, for numbers divisible by 10 only, stays empty. Part of the diagram Numbers How many Divisible only by 2 22, 38, 66, 78, 62, 84, 56 7 Divisible only by 5 75, 45, 25, 95, 55 5 Divisible by 2, 5 and 10 90, 30, 40 3 Divisible only by 10 None 0 Check the count: 7 + 5 + 3 + 0 = 15 There were 15 numbers to sort ✓ Why it happens: Sorting like this is really sorting by the last digit. Ends in 0 → the middle, shared part. Ends in 5 → the "5 only" part. Ends in 2, 4, 6 or 8 → the "2 only" part. Check it yourself: Read the numbers off the page one by one — 90, 22, 38, 30, 75, 45, 66, 78, 62, 40, 84, 56, 25, 95, 55 — and tick each one as you place it. Every number should be used exactly once.

NCERT Solutions for Class 5th Maths Chapter 13 Sort 90, 45, 84, 22, 66, 56, 38, 78, 25, 30, 62, 95, 75, 40 and 55 — Let Us Do (Question 11: Sorting)

Book page 170 Updated on2026-09-19

Q1.

11. Sort the following numbers into those that are — (a) divisible by 2 only

Answer

22, 38, 66, 78, 62, 84 and 56 are divisible by 2 only.

A number is divisible by 2 if it is even — that is, if its last digit is 0, 2, 4, 6 or 8. "Divisible by 2 only" means it is even but not divisible by 5, so it must not end in 0.

Number	Last digit	Divisible by 2?	Divisible by 5?
22	2	Yes	No
38	8	Yes	No
66	6	Yes	No
78	8	Yes	No
62	2	Yes	No
84	4	Yes	No
56	6	Yes	No

Why it happens: Jumping 2 at a time from 0 lands you on every even number. None of these seven numbers ends in 0 or 5, so 5-jumps miss them all.

Q2.

11. (b) divisible by 5 only

Answer

75, 45, 25, 95 and 55 are divisible by 5 only.

A number is divisible by 5 if its last digit is 5 or 0. "Divisible by 5 only" means it must not also be even — so it has to end in 5.

75 ÷ 5 = 15 ✓ but 75 is odd, so 2 does not divide it
45 ÷ 5 = 9 ✓
25 ÷ 5 = 5 ✓
95 ÷ 5 = 19 ✓
55 ÷ 5 = 11 ✓

Why it happens: All five numbers end in 5. Numbers ending in 5 are always odd, so they can never be divisible by 2 or by 10.

Q3.

11. (c) divisible by 10 only

Answer

There are none. This box stays empty.

Not one of the fifteen numbers can go here — and in fact no number ever can.

10 = 2 × 5
So every multiple of 10 is also a multiple of 2 and of 5
90 ÷ 10 = 9, and also 90 ÷ 2 = 45, 90 ÷ 5 = 18

Why it happens: A jump of 10 is the same as five jumps of 2, or two jumps of 5. So wherever a 10-jump lands, a 2-jump and a 5-jump have already been. A number can never be divisible by 10 alone.

This is the point of the question. An empty box is a real answer. It shows that 2 and 5 are hidden inside 10, so the three circles of the diagram can never be separate.

Q4.

11. (d) divisible by 2, 5, and 10

Answer

90, 30 and 40 are divisible by 2, by 5 and by 10.

Number	÷ 2	÷ 5	÷ 10
90	45	18	9
30	15	6	3
40	20	8	4

Why it happens: All three numbers end in 0. A number ending in 0 is even, so 2 divides it; it also ends in 0 or 5, so 5 divides it; and ending in 0 is exactly the test for 10. The one digit 0 settles all three tests at once.

Tip: Look only at the last digit. Ends in 0 → divisible by 2, 5 and 10. Ends in 5 → divisible by 5 only. Ends in 2, 4, 6 or 8 → divisible by 2 only. Ends in 1, 3, 7 or 9 → none of the three.

Q5.

Complete the diagram on page 170 by writing each number in the right place.

Page 170 — the fifteen number cards and the blank sorting diagram to be filled in.

Answer

Here is the finished diagram, with all fifteen numbers placed.

All fifteen numbers sorted. The bottom part, for numbers divisible by 10 only, stays empty.

Part of the diagram	Numbers	How many
Divisible only by 2	22, 38, 66, 78, 62, 84, 56	7
Divisible only by 5	75, 45, 25, 95, 55	5
Divisible by 2, 5 and 10	90, 30, 40	3
Divisible only by 10	None	0

Check the count: 7 + 5 + 3 + 0 = 15
There were 15 numbers to sort ✓

Why it happens: Sorting like this is really sorting by the last digit. Ends in 0 → the middle, shared part. Ends in 5 → the "5 only" part. Ends in 2, 4, 6 or 8 → the "2 only" part.

Check it yourself: Read the numbers off the page one by one — 90, 22, 38, 30, 75, 45, 66, 78, 62, 40, 84, 56, 25, 95, 55 — and tick each one as you place it. Every number should be used exactly once.

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