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

Question

Philoid · Accepted Answer

Take the alternating sum of the digits in the number, read from left to right. If that is divisible by 11, so is the original number.

7 – 2 + 5 – 4 + * - 9 + 8 = (5 + *)

For 7254 * 98 to be divisible by 11,

(5 + *) must also be divisible by 11

Hence, 5 + * = 11

∴ * = 11 - 5

= 6