Just to clarify the question, it is as follows: If X is an integer from 1 to X, then X = ?
(1) The tenth's digit of 1/X is X
(2) The hundredth's digit of 1/X is X
To answer this question, we must refresh our memories on what the tenth's and hundredth's digits are. For an integer of the form A.BC (e.g. 2.34, 4.67 etc), the tenth's digit is B and the hundredth's digit is C.
Consider statement (1) first. For which integers (1 to 10) is the tenth's digit the same as the integer itself? This is true only for the integer 3 (1/3 = 0.333333...). Therefore X can only be 3. Sufficient.
Consider statement (2) next. For which integers (1 to 10) is the hundredth's digit the same as the integer itself? This is true for 3 (1/3 = 0.333333...) as well as for 6(1/6=0.16666....). We can't say which of the two it will be. Insufficient.
The answer is therefore A.
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