54Z leaves remainder 2 when divided by 5 , and leaves remainder 1 when

1.	54Z leaves remainder 2 when divided by 5 , and leaves remainder 1 when divided by 3, what is the value of Z?
Answer» If 54Z is divisible by 3 then the sum of the digits of the number is divisible by 3. According to problem 54Z is divisible by 3 and leaves remainder 1. ∴ 5 + 4 + Z = (3 x 4) + 1 = 9 + Z = 13 ∴ Z = 4(or) 9 + Z = (3 x 5) + 1 9 + Z = 16 Z = 7 If 54Z is divisible by 5 then Z should be equal to either ‘0’ or ‘5’. ∴ 54(0 + 2) = 542 (Z = 2) 54(0 + 7) = 547 (Z = 7) ∴ From the above two cases Z = 7 ∵ 547 → 7/5 (R = 2)

54Z leaves remainder 2 when divided by 5 , and leaves remainder 1 when divided by 3, what is the value of Z?

Answer»

If 54Z is divisible by 3 then the sum of the digits of the number is divisible by 3.

According to problem 54Z is divisible by 3 and leaves remainder 1.

∴ 5 + 4 + Z = (3 x 4) + 1

= 9 + Z = 13

∴ Z = 4(or)

9 + Z = (3 x 5) + 1

9 + Z = 16

Z = 7

If 54Z is divisible by 5 then Z should be equal to either ‘0’ or ‘5’.

∴ 54(0 + 2) = 542 (Z = 2)

54(0 + 7) = 547 (Z = 7)

∴ From the above two cases Z = 7

∵ 547 → 7/5 (R = 2)