Question

Find the value of x if the number 25x368 is divisible by :
(a) 3
(b) 6
(c) 9
(d) 11​

Answer 1

Answer:

(a)3

Step-by-step explanation:

I like to do it in an alternative way using modular arithmetic.

This method/technique works even if u replace 11 with some other number.

8x9784≡0mod118x9784≡0mod11

⟹8x9784−44≡0mod11⟹8x9784−44≡0mod11 (since 44 is also divisible by 11)

⟹8x9740≡0mod11⟹8x9740≡0mod11

⟹8x974≡0mod11⟹8x974≡0mod11 (since 10 and 11 are relatively prime)

⟹8x974−44≡0mod11⟹8x974−44≡0mod11 (since 44 is also divisible by 11)

⟹8x930≡0mod11⟹8x930≡0mod11

⟹8x93≡0mod11⟹8x93≡0mod11 (since 10 and 11 are relatively prime)

⟹8x93−33≡0mod11⟹8x93−33≡0mod11 (since 33 is also divisible by 11)

⟹8x60≡0mod11⟹8x60≡0mod11

⟹8x6≡0mod11⟹8x6≡0mod11 (since 10 and 11 are relatively prime)

⟹800+10x+6≡0mod11⟹800+10x+6≡0mod11

⟹8(100)+10x+6≡0mod11⟹8(100)+10x+6≡0mod11

⟹8(99+1)+10x+6≡0mod11⟹8(99+1)+10x+6≡0mod11

⟹8(1)+10x+6≡0

Answer 2

Answer:

Option a is your answer

hope it helps u