Question

Question 29
If the number 7254*98 is divisible by 22, the digit at * is

(A) 1
(B) 2
(C) 6
(D) 0

Answer 1

We know that, if a number is divisible by two coprime numbers, then it is divisible by the product of these co-prime numbers too.
If 7254*98 is divisible by 22, then it must be divisible by 2 and 11 both. Since the last digit is 8. so it is divisible by 2. Now, for divisible by 11, the difference of the sum of digits on even and odd places must be either zero or divisible by 11.
Sum of digits at even places=9+4+2=15
Sum of digits at odd places=8+(*)+5+7
= 20+(*)
Required difference=(20+*)-15=5+(*)
For divisibility by 11, 5+(*)=11
$\therefore$ *=6
Hence, the required digit at * is 6.