2012-03-12 09:00:39

In the correctly worked out addition problem below, each symbol represents a different digit. What is the value of #?

   4#

 + #4

  !^!

A) 4
B) 5
C) 6
D) 7
E) 8

The correct answer is D

Explanation: In this prompt, each symbol represents one integer, but each symbol represents one number throughout the prompt (i.e. if # = 0, then #4 would be 04 and 4# would be 40). There is no way of figuring out what numbers are represented on sight alone, but you can use the answer choices to your advantage. For two two-digit numbers to sum to a three-digit one, the two must sum to something greater than 100. This would mean that if one of the numbers starts with 4 (as is the case of 4#), then the other would have to start with a number greater than 5 (because 50 + 40 is only 90). Thus, you can eliminate choices (A) and (B). Now, simply plug in the remaining choices for # in the problem.

(C) 46 + 64 = 110. This does not work, since !^! cannot be 110, as 110 could only be expressed as !!^.
(D) 47 + 74 = 121. This works, since !^! could be 121 if ! = 1 and ^ = 2.
(E) 48 + 84 = 132. This does not work, since !&! cannot be 132, since 132 lacks a repeating integer.

Therefore, choice D is the correct answer.