Hi All,
This DS question can be solved with a combination of Number Properties and TESTing VALUES.
We're told that M is a two-digit positive integer. We're asked for the SUM of the two digits.
Fact 1: If the digits of M are reversed, the resulting integer is 27 greater than M.
This Fact is actually based on an 'accounting error' that happens when digits are accidentally reversed. You'll find that it's not too difficult to find a few examples that differ by 27.
IF...
M is 41
41 - 14 = 27
The answer to the question is 4+1=5
IF....
M is 52
52 - 25 = 27
The answer to the question is 5+2=7
Fact 1 is INSUFFICIENT
Fact 2: The difference between the squares of the digits of M is 39.
Since we're dealing with digits, there are a finite number of values that we need to consider:
1^2 = 1
2^2 = 4
3^2 = 9
4^2 = 16
5^2 = 25
6^2 = 36
7^2 = 49
8^2 = 64
9^2 = 81
We have to 'play around' a bit with the values, but for the DIFFERENCE in the digits to = 39, the ONLY values that fit are 8 and 5 (64-25 = 39).
Whether M is 58 or 85, the answer to the question is the SAME: 5+8=13. The answer is ALWAYS 13.
Fact 2 is SUFFICIENT
Final Answer:
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Rich
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