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题库 / Prep2007E1-DS-154
The sum of positive integers x and y is 77. What is the value of xy ?
(1) x = y + 1
(2) x and y have the same tens digit.
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.
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Given that x+y=77x+y=77 find the value of xyxy.
(1) x = y + 1 --> (y+1)+y=77(y+1)+y=77 --> y=38y=38 and x=39x=39 --> xy=39∗38xy=39∗38. Sufficient.
(2) x and y have the same tens digit. In order the sum to be 77 the tens digit of of x and y must be 3, thus x=38x=38 and y=39y=39 or vise-versa, in either case xy=39∗38xy=39∗38. Sufficient.