NCERT Solutions Ganita Prakash Chapter 5 Jump Jackpot — In-text Questions

Book page 110 Updated on2026-09-05

Q1.

What jump size can reach both 15 and 30? There are multiple jump sizes possible. Try to find them all.

Answer

Jumpy starts at 0 and lands only on multiples of his jump size. So a jump size works for a number only if it is a factor of that number. To reach both treasures, the jump size must be a common factor of 15 and 30.

Factors of 15 → 1, 3, 5, 15
Factors of 30 → 1, 2, 3, 5, 6, 10, 15, 30

The numbers in both lists are

1, 3, 5 and 15

Answer: jump sizes 1, 3, 5 and 15 — four in all.

Jump 3 → 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 ✔
Jump 5 → 5, 10, 15, 20, 25, 30 ✔
Jump 15 → 15, 30 ✔

Why every factor of 15 works here: 15 is itself a factor of 30, so anything that divides 15 also divides 30. That is why all four factors of 15 make it.

Q2.

Look at the table below. What do you notice? In the table, 1. Is there anything common among the shaded numbers?

Answer

The shaded numbers in the table (31 to 70) are

33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69

Yes — every one of them is in the 3 table.

33 = 3 × 11    36 = 3 × 12    39 = 3 × 13    42 = 3 × 14    45 = 3 × 15
48 = 3 × 16    51 = 3 × 17    54 = 3 × 18    57 = 3 × 19    60 = 3 × 20
63 = 3 × 21    66 = 3 × 22    69 = 3 × 23

All the shaded numbers are multiples of 3. They also step up by 3 each time — 33, 36, 39, … — so they sit in a slanting pattern in the table.

Tip: a number is a multiple of 3 exactly when the sum of its digits is a multiple of 3. Check 57 → 5 + 7 = 12, and 12 is in the 3 table. ✔

Q3.

2. Is there anything common among the circled numbers?

Answer

The circled numbers are

32, 36, 40, 44, 48, 52, 56, 60, 64, 68

Each one goes up by 4 from the previous one, and each is in the 4 table.

32 = 4 × 8 36 = 4 × 9 40 = 4 × 10 44 = 4 × 11 48 = 4 × 12
52 = 4 × 13 56 = 4 × 14 60 = 4 × 15 64 = 4 × 16 68 = 4 × 17

All the circled numbers are multiples of 4.

Tip: a number is a multiple of 4 exactly when the number made by its last two digits is a multiple of 4. You will prove this yourself on page 124.

Q4.

3. Which numbers are both shaded and circled? What are these numbers called?

Answer

Only three numbers wear both marks:

36, 48 and 60

They are common multiples of 3 and 4.

36 = 3 × 12 = 4 × 9 48 = 3 × 16 = 4 × 12 60 = 3 × 20 = 4 × 15

Why they are the multiples of 12: a number that is a multiple of 3 and also of 4 must be a multiple of 3 × 4 = 12 (because 3 and 4 have no common factor other than 1). The multiples of 12 lying between 31 and 70 are 36, 48 and 60 — exactly the three we found. ✔

Try This: if the table went on to 100, the next number that is both shaded and circled would be 72, then 84, then 96.

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