07. KNOWING OUR NUMBERS
Explanation:
1
We know that, if a number is divisible by two coprime numbers, then it is divisible by their product also.
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 divisibility by 11, the difference of 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 * = 6
Hence, the digit at * is 6.