If the symbols Δ and ◊ each represent digits in the following subtraction operation, what is the value of ◊?

Δ ◊ ◊
- Δ Δ
6 6 7

A. 3
B. 4
C. 5
D. 8
E. 9

Replacing the symbols with alphabets

abb - aa = 667

Expanding LHS

100a + 10b + b - (10a + a) = 667

89a + 11b = 667

Looking at the options:

A: For b=3

89a = 667-33 = 634

If a = 6; then 634 should be divisible by 6.. its NOT; so discard

How I selected 6???

For 89 to be multiplied by "a" & give the result ending with "4"; a should be 6

B: For b = 4

89a = 667 - 44 = 623

If a=7; 623 should be divisible by 7... 623/7 = 89 ......... SUCCESS

Answer = B = 4
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The most difficult part of the first problem is simply getting started. Even though it is a subtraction problem, think of it as addition (667 + ∆∆ = ∆◊◊) and consider the following logic: If you add a two–digit number to 667, you must end up in the high 600s or the 700s. However, if the ∆ symbol is a 6, then you are adding 66 to 667, which will not work out, as the result will be in the 700s but the ∆ symbol has been designated as 6. Therefore the ∆ symbol must be a 7. At this point you can add 7 to 7 and see that the other symbol ◊ must be a 4 (7 plus 7 is 14). Check your work: 744 – 77 does indeed equal 667. The correct answer choice is B.
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