Question

Find the number between 225 and 300, when divided by 8, 9, 24 gives 5 as remainder in each case?
1. 245
2. 275
3. 235
4. 293

Answer 1

Correct Answer - Option 4 : 293

Given:

Numbers = 8, 9, 24

Remainder = 5

Concept Used:

If remainder in each case is same then find LCM of given numbers and then multiply the LCM by appropriate number and then add the remainder in that number so we can get the required number between the required range.

Calculation:

8 = 2³

9 = 3²

24 = 2³ × 3¹

LCM of 8, 9, 24 = 2³ × 3²

⇒ 72

Now, we have to multiply LCM 72 by an an appropriate number so we can get the resultant between 225 and 300

⇒ 72 × 4 = 288 

Add 5 so we can get equal remainder as 5

⇒ 288 + 5

⇒ 293 

∴ The number between 225 and 300 is 293 when divided by 8, 9, 24 in each case it gives equal remainder 5