Find a number that leaves a remainder of 2 when divided by 3, a remainder of 3 when divided by 4 Class 8

Find a number that leaves a remainder of 2 when divided by 3, a remainder of 3 when divided by 4 Class 8

Question 1.

Find a number that leaves a remainder of 2 when divided by 3, a remainder of 3 when divided by 4, and a remainder of 4 when divided by 5. What is the smallest such number? Can you give a simple explanation of why it is the smallest? Class 8

Solution:

Here, 3 - 2 = 1, 4 - 3 = 1 and 5 - 4 = 1.

So, required smallest number is LCM of 3, 4 and 5 — 1 = 60-1 = 59. It is smallest due to LCM 60.

Question 2.

Look at each of the following statements. Which are correct and why? Class 8

(i) If a number is divisible by 9, then the sum of its digits is divisible by 9.

(ii) If the sum of the digits of a number is divisible by 9, then the number is divisible by 9.

(iii) If a number is not divisible by 9, then the sum of its digits is not divisible by 9.

(iv) If the sum of the digits of a number is not divisible by 9, then the number is not divisible by 9.

Solution:

(i) Correct

(ii) Correct

(iii) Correct

(iv) Correct

Note : It has been shown in the textbook that a number is divisible by 9 if sum of its digits.is divisible by 9. In view of the above all these four statements are correct.