The telephone company wants to add an area code composed of 2 letters to every phone number. In order to do so, the company chose a special sign language containing 424 different signs. If the company used 422 of the signs fully and two remained unused, how many additional area codes can be created if the company uses all 424 signs? Choices
A) 246  B) 248  C) 1692  D) 15,128  E) 30,256

Rationale: "# of 2 - letter codes possible from 424 different signs = 424 * 424 . # of 2 - letter codes possible from 422 different signs = 422 * 422 . the difference = 424 ^ 2 - 422 ^ 2 = ( 424 - 422 ) ( 424 + 422 ) = 1692 . answer : c ."
Answer: C