When you reverse the digits of the number 13, the number increases by 18. How many other two-digit numbers increase by 18 when their digits are reversed?
- 5
- 6
- 7
- 8
Explanation
We are solving:
(Reversed number) - (Original number) = 18
Let the original two-digit number be 10x + y
Reversed = 10y + x
So:
(10y + x) - (10x + y) = 18
→ 9y - 9x = 18
→ y - x = 2
Now we find how many two-digit numbers satisfy:
Units digit = Tens digit + 2
Possible values for x (tens digit): 1 to 7
Since y = x + 2 must still be a digit (i.e., ≤ 9)
Let’s list them:
- x = 1 → y = 3 → 13
- x = 2 → y = 4 → 24
- x = 3 → y = 5 → 35
- x = 4 → y = 6 → 46
- x = 5 → y = 7 → 57
- x = 6 → y = 8 → 68
- x = 7 → y = 9 → 79
That's 7 total, including 13.
But your question was:
"How many *other two-digit numbers increase by 18 when reversed?"*
So, exclude 13 itself.
Answer: 6 other numbers.
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