This is a Value question. We need to be able to determine exactly one and only one value for x to have sufficiency. We are told that x and y are two-digit prime numbers and that if we reverse the digits of x, we’d get y. We’ll jot down a list of the two-digit primes and see which are the reverse of the other. Those primes are: 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 71, 73, 79, 83, 89, and 97.
Whittling this list down to pairs whose digits are reversed, we get the possibilities for x and y: 11 and 11, 13 and 31, 17 and 71, 37 and 73, and 79 and 97.
We need to figure out which pair we are looking at and which number is x.
Evaluate the Statements:
Statement (1): We are given that the difference of x and y is 54. From our list of possible combinations, only 17 and 71 give us a difference of 54. x must be the larger of the pair (if x were the smaller value, then x – y would be negative), so x = 71.
Statement (1) is Sufficient to answer the question. Eliminate choices (B), (C), and (E).
Statement (2): Again, looking at our possibilities, only 17 and 71 add to 88. But we do not know from Statement (2) whether x is the larger or the smaller value. Therefore, Statement 2 is Insufficient. Eliminate choice (D).
Answer Choice (A) is correct.
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