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Question 660073: max thinks of an odd number between 41 and 64. the difference between the digits is the same as the ones digit. what is max's number.
Answer by kevwill(135)   (Show Source):
You can put this solution on YOUR website! Because max is thinking of an odd number, the ones digit must be odd. Consequently the difference between the digits is also odd, so the tens digit must be even.
Let x be the 10s digit and y be the ones digit. x is even and y is odd.
We have two cases: (1) the 10s digit is less than the ones digit, or (2) the 10s digit is greater than the ones digit.
In the first case, we subtract the smaller number (x) from the larger number (y) to get the ones digit (y):
y = y - x
Subtracting y-x from both sides:
y - (y - x) = y - x - (y - x)
y - y + x = y - x - y + x
x = 0
But since the number is between 41 and 64, the 10s digit cannot be 0, so the first case is ruled out.
In the second case, we subtract the smaller number (y) from the larger number (x) to get the ones digit (y):
y = x - y
Adding y to both sides:
y + y = x - y + y
2y = x
So we know that the 10s digit is twice the ones digit. Since Max's number is between 41 and 64 and the tens digit is even, then the 10s digit must be 4 or 6. The ones digit is half the 10s digit, so it must be 2 or 3.
Since 42 is an even number, the only solution is 63.
Thus, Max is thinking of the number 63.
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