How many multiples of 4 lie between 10 and 250?
(Hint: All multiples of 4 form an AP. Find the smallest and largest multiples of 4 between 10 and 250.)

Step-by-step solution

Idea: Find the first and last multiples of 4 in the range, then count the terms of the AP between them.

1. Smallest multiple of 4 above 10 is 12; largest below 250 is 248 (250 = 4 × 62 + 2).1 mark
2. AP: 12, 16, 20, …, 248 with a = 12, d = 4.½ mark
3. 12 + (n − 1) × 4 = 248 ⇒ 4(n − 1) = 236 ⇒ n − 1 = 59 ⇒ n = 60.1½ marks

Check: Multiples of 4 up to 248: 62; up to 10: 2 (4 and 8). 62 − 2 = 60 ✓.

Answer to write in the exam

Common mistakes that cost marks

• Starting at 10 or 8. 10 is not a multiple of 4, and 8 is not between 10 and 250.
• Taking 250 as the last term. 250 ÷ 4 = 62.5, so 250 is not a multiple of 4.
• Counting (248 − 12) ÷ 4 = 59 and forgetting the first term.

How this can come in the exam

Try one yourself

How many multiples of 3 lie between 50 and 300?

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