2.I am a three digit number. My tens digit is five more than my ones digit. My hundreds digit is eight less t?

2. I am a three digit number.
My tens digit is five more than my ones digit.
My hundreds digit is eight less than my tens digit.
What number am I?

Anonymous2009-05-08T09:00:57Z

Favorite Answer

Let the number be abc.

Then we have 4 statements:
(1) b = c + 5
(2) a = b - 8
(3) 0 =< b,c < 10 (since they are each single digits)
(4) 0 < a < 10 (since it is a 3 digit number, hence a is non-zero)

From (1), (2), we get:
(5) a = b - 8 = c + 5 - 8 = c - 3

From (4), (5):
c - 3 > 0 => c > 3

From (1), (3):
c + 5 < 10 => c < 5

Since 3 < c < 5, hence c = 4.

Using (1), (5), we get:
b = 4 + 5 = 9
a = 4 - 3 = 1

Hence the number is 194.

Nice riddle/question.

0 0

Hammed Sanusi2015-09-27T08:27:52Z

Let the number be xyz.

From the given statement: I deduce the fact below.

(1) y = z + 5
(2) x = y - 8
(3) 0 = < y,z < 10 (Because they are single digit each)
(4) 0 < x < 10 (so far the numbers is a 3 digit, hence it is a non - zero numbers)

From (1), (2), we get:

y = z + 5 ........ (1)
x = y - 8 ......... (2)

From (2)
x = y - 8
y = x + 8 ............. equation(5)

By equating equation (1) and equation (5)
y = y
z + 5 = x + 8
x = z + 5 - 8
x = z - 3 ........................ equation (6)

From (4), (6):

z - 3 > 0
∴ z > 3
Hence, z > 3

From (1), (3):
z + 5 < 10
z = < 10 - 5
∴ z < 5

Since 3 < z < 5, hence z = 4.

Using (1), (2), we get:

y = 4 + 5 = 9
x = 9 - 8 = 1

∴ x = 1, y = 9, z = 4

Since the number is xyz

Hence the number is 194.