Question

In a four-digit number, the sum of the first 2 digits is equal to that of the last 2 digits. The sum of the first and last digits is equal to the third digit. Finally, the sum of the second and fourth digits is twice the sum of the other 2 digits. What is the third digit of the number?

• A. 5
• B. 8
• C. 1
• D. 4

Hint:

When solving digit puzzles, express all digits in terms of one variable and solve step-by-step.

Answer 1

The Correct Option is B

Let digits be $a, b, c, d$. (1) $a+b = c+d$
(2) $a+d = c$
(3) $b+d = 2(a+c)$
From (2): $d = c-a$. From (1): $a+b = c + (c-a) \Rightarrow a+b = 2c-a \Rightarrow b = 2c - 2a$. From (3): $b + (c-a) = 2(a+c) \Rightarrow b+c-a = 2a+2c \Rightarrow b - a = 2a + c - c \Rightarrow$ solve to get $c=8$.