A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is _____?
- 22
- 24
- 26
- None of these
Explanation
Let's denote the original two-digit number as 10a + b.
Since the product of the digits is 8:
ab = 8
Possible values for a and b are (1, 8) or (2, 4).
When 18 is added to the number, the digits are reversed:
10a + b + 18 = 10b + a
Simplify the equation:
9a - 9b = -18
a - b = -2
Now, check the possible values:
For (1, 8): 1 - 8 ≠ -2 (not valid)
For (2, 4): 2 - 4 = -2 (valid)
So, the original number is 10(2) + 4 = 24.
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