Question

I am thinking of a 4 digit number. The sum of the digits is 25. The largest digit is used twice but not did by side. The smallest digit is in the largest place. The smallest digit is 1/4 as large as the largest digit. What is the number?

Answer 1

2878

Explanation:

Let "abcd" represent the digits of the number.

a ≠ 0

"The sum of the digits is 25"

a+b+c+d = 25

"The smallest digit is in the largest place"

a < b, c, d

"The largest digit is used twice but not side by side"

The digits of the number are "abcb"

b > a, c

"The smallest digit is ¼ as large as the largest digit"

a = b/4

b = 4 or 8

If b = 4, then a = 1 and c = 25 - a - 2b = 16, which is not a single digit. ∴ b ≠ 4

b = 8

a = b/4 = 2

2+8+c+8 = 25

c = 7

The number is 2878.