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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?
10 Answers
- Anonymous1 decade agoFavorite 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.
- Hammed SanusiLv 46 years ago
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.
- Anonymous1 decade ago
194
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