题目信息
If x and y are integers between 10 and 99, inclusive, is 
an integer?
an integer?
A:Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B:Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C:BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D:EACH statement ALONE is sufficient.
E:Statements (1) and (2) TOGETHER are NOT sufficient.
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已选答案：
正确答案：
A:Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Algebra Properties of integers
Determine whether
is an integer, where x and y are 2-digit integers.
From (1), if x = 10a + b, then y = 10b + a. It follows that x – y = 9(a – b), so
is an integer; SUFFICIENT.
From (2), if x = 10a + b, then a = b + 2. If y = 10c + d, then c = d – 2. It is possible that 
is an integer (for example, if x = 75 and y = 57), and it is possible that 
is not an integer (for example, if x = 75 and y = 46); NOT sufficient.
The correct answer is A;statement 1 alone is sufficient.
Determine whether
is an integer, where x and y are 2-digit integers.From (1), if x = 10a + b, then y = 10b + a. It follows that x – y = 9(a – b), so
is an integer; SUFFICIENT.
From (2), if x = 10a + b, then a = b + 2. If y = 10c + d, then c = d – 2. It is possible that is an integer (for example, if x = 75 and y = 57), and it is possible that is not an integer (for example, if x = 75 and y = 46); NOT sufficient.The correct answer is A;statement 1 alone is sufficient.
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