Question

In some code, letters $a, b, c, d, e$ represent 2, 4, 5, 6, and 10 in some order. Given:
I. $a + c = e$,
II. $b - d = d$,
III. $e + a = b$.
Which is true?

• A. $b = 4, d = 2$
• B. $a = 4, e = 6$
• C. $b = 6, e = 2$
• D. $a = 4, c = 6$

Hint:

When coding number-letter puzzles, convert relational statements into equations and test permissible integer pairs.

Answer 1

The Correct Option is B

From II: $b - d = d \Rightarrow b = 2d$. Possible $(b,d)$ from set: (4,2) or (10,5). From I: $a+c = e$. From III: $e+a = b$. Testing $(b,d)=(10,5)$: $e+a=10$. Also $a+c=e$, so $(a+c)+a=10 \Rightarrow 2a+c=10$. Matching values from set gives $a=4, c=2, e=6$, consistent.