Question

In the addition problem shown, different letters represent different digits. If the carry over from adding the units digit is 2, then (A+I) cannot be


DID
+ I
+SAY
______
MATH​

Answer 1

Answer:

With # and & each representing different digits in the problem below, the difference between #&& and ## is 667. What is the value of &?

Image

(A) 3

(B) 4

(C) 5

(D) 8

(E) 9

Solution: The big picture: A two digit number is subtracted from a three digit number to give 667. So the three digit number must be a bit larger than 667. This means that the hundreds digit of #&& must be either 6 or 7. It cannot be 8 because you cannot obtain 800+ by adding a two digit number to 667.

Let’s look at both cases:

# is 6: If you subtract 66 from 6&&, you will not get 667 – the largest value you can get is 699 – 66 = 633. So # cannot be 6.

# must be 7.

Now the question is very simple

7&& – 77 = 667

7&& = 667 + 77 = 744