[B].
[C].
[D].
Answer: Option C
Explanation:
Unit digit in 34 = 1 Unit digit in (34)16 = 1
Unit digit in 365 = Unit digit in [ (34)16 x 3 ] = (1 x 3) = 3
Unit digit in 659 = 6
Unit digit in 74 Unit digit in (74)17 is 1.
Unit digit in 771 = Unit digit in [(74)17 x 73] = (1 x 3) = 3
Required digit = Unit digit in (3 x 6 x 3) = 4.
[B].
[C].
[D].
Answer: Option A
Explanation:
80 = 2 x 5 x 8
Since 653xy is divisible by 2 and 5 both, so y = 0.
Now, 653x is divisible by 8, so 13x should be divisible by 8.
This happens when x = 6.
x + y = (6 + 0) = 6.
[B].
[C].
[D].
Answer: Option C
Explanation:
72 = 9 x8, where 9 and 8 are co-prime.
The minimum value of x for which 73x for which 73x is divisible by 8 is, x = 6.
Sum of digits in 425736 = (4 + 2 + 5 + 7 + 3 + 6) = 27, which is divisible by 9.
Required value of * is 6.
[B].
[C].
[D].
Answer: Option D
Explanation:
99 = 11 x 9, where 11 and 9 are co-prime.
By hit and trial, we find that 114345 is divisibleby 11 as well as 9. So, it is divisible by 99.
[B].
[C].
[D].
Answer: Option C
Explanation:
45 = 5 x 9, where 5 and 9 are co-primes.
Unit digit must be 0 or 5 and sum of digits must be divisible by 9.
Among given numbers, such number is 202860.
[B].
[C].
[D].
Answer: Option C
Explanation:
Then number 6×2 must be divisible by 8.
x = 3, as 632 is divisible 8.
[B].
[C].
[D].
Answer: Option A
Explanation:
Given number = 97215×6
(6 + 5 + 2 + 9) – (x + 1 + 7) = (14 – x), which must be divisible by 11.
x = 3
[B].
[C].
[D].
Answer: Option D
Explanation:
Sum of digits = (4 + 8 + 1 + x + 6 + 7 + 3) = (29 + x), which must be divisible by 9.
x = 7.
[B].
[C].
[D].
Answer: Option C
Explanation:
Sum of digits = (5 + 1 + 7 + x + 3 + 2 + 4) = (22 + x), which must be divisible by 3.
x = 2.
[B].
[C].
[D].
Answer: Option C
Explanation:
Unit digit in 7105 = Unit digit in [ (74)26 x 7 ]
But, unit digit in (74)26 = 1
Unit digit in 7105 = (1 x 7) = 7