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  3. If x and y are integers between 10 and 99, inclusive, is [img]2022m10x/ct_ve0120

If x and y are integers between 10 and 99, inclusive, is [img]2022m10x/ct_ve0120

游客2025-02-27  0
问题 If x and y are integers between 10 and 99, inclusive, is an integer?
(1) x and y have the same two digits, but in reverse order.
(2) The tens’ digit of x is 2 more than the units’ di git, and the tens’ digit of y is 2 less than the units’ digit.
选项 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.
答案 A
解析 Determine whether is an integer, where x and y are 2-digit integers.
(1)     From (1), if x = 10a + b, then y =10b + a. It follows that x-y= 9(a - b), so is an integer; SUFFICIENT.
(2)     From (2), if x = 10a + b, then a = b + 2. If y = 10r + 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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