Tricky Interview Questions on Test Divisibility

x

Option: D

Explanation

split 12 into co-primes

i.e. 12 = 3 x 4, 3 & 4 are co-primes

the number should be divisible by both 3 & 4. Clearly the number 3252 is divisible by 4

so 9P2 must be divisible by 3

so (9 + P + 2) = 11 + P, least value of P is 1

the number 12 is divisible by 3

i.e. value of P = 1

x

Option: A

Explanation

split 6 into co-primes

i.e. 6 = 2 x 3,2 & 3 are co-primes

the number should be divisible by both 2 & 3. clearly the number 4#4 is divisible by 2

(4 + # + 4) = 8 + #, which is divisible by 3

the least value of # is 1,such that the number is divisible by 3

the value of X = 1

x

Option: B

Explanation

split 24 into co-primes

i.e. 24 = 3x8, 3 & 8 are co-primes

the number should be divisible by both 3 & 8

(3 + 1 + 2 + 5 + 7 + 3 + 6) = 27, which is divisible by 3

last three digits 736 is also divisible by 8

3125736 is divisible by 24

x

Option: C

Explanation

split 132 into co-primes

i.e. 132 = 3x4x11, 3,4 & 11 are co-primes

the number must divisible by 3, 4 & 11

968 not divisible by 3

462 & 2178 not divisible by 4

5184 not divisible by 11

264, 396, 792, 6336 are divisible by 3, 4 & 11

so total numbers divisible by 3, 4 & 11 are 4

x

Option: C

Explanation

the number must be divisible by both 3 & 11

(4 + 7 + 6 + X + Y + 0) = X + Y + 17, which is divisible by 3

(0 + X + 7) - (Y + 6 + 4) = X - Y - 3, which is divisible by 11

take X + Y + 17 as equation 1

take X - Y - 3 as equation 2

solving two equations we get respective values of X & Y

after solving the value of X = 8 and Y = 5