题目信息
What is the number of integers that are common to both set S and set T ?
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.
参考答案及共享解析
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本题耗时：
已选答案：
正确答案：
C:BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
Arithmetic Sets
In standard notation,
and 
represent the intersection and union, respectively, of sets S and T, and |S| represents the number of elements in a set S. Determine 
.
It is given that |S| = 7 and |T| = 6. If, for example, S = {1, 2, 3, 4, 5, 6, 7} and T = {1, 2, 3, 4, 5, 6}, then
= 6. However, if S = {1, 2, 3, 4, 5, 6, 7,} and T = {11, 12, 13, 14, 15, 16}, then 
= 0; NOT sufficient.
It is given that 
= 10. If, for example, S = {1, 2, 3, 4, 5, 6, 7} and T = {1, 2, 3, 8, 9, 10}, then 
= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, 
= 10, and 
= 3. However, if S = {1, 2, 3, 4, 5, 6, 7} and T = {11, 12, 13}, then 
= {1, 2, 3, 4, 5, 6, 7, 11, 12, 13}, 
= 10, and 
= 0; NOT sufficient.
Taking (1) and (2) together along with the general addition rule for two sets A and B
(
= |A| + |B| – 
) applied to sets S and T gives 10 = 7 + 6 – 
, from which 
can be determined.
The correct answer is C;both statements together are sufficient.
In standard notation,
and represent the intersection and union, respectively, of sets S and T, and |S| represents the number of elements in a set S. Determine .It is given that |S| = 7 and |T| = 6. If, for example, S = {1, 2, 3, 4, 5, 6, 7} and T = {1, 2, 3, 4, 5, 6}, then
= 6. However, if S = {1, 2, 3, 4, 5, 6, 7,} and T = {11, 12, 13, 14, 15, 16}, then = 0; NOT sufficient.
It is given that = 10. If, for example, S = {1, 2, 3, 4, 5, 6, 7} and T = {1, 2, 3, 8, 9, 10}, then = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, = 10, and = 3. However, if S = {1, 2, 3, 4, 5, 6, 7} and T = {11, 12, 13}, then = {1, 2, 3, 4, 5, 6, 7, 11, 12, 13}, = 10, and = 0; NOT sufficient.Taking (1) and (2) together along with the general addition rule for two sets A and B
(
= |A| + |B| – ) applied to sets S and T gives 10 = 7 + 6 – , from which can be determined.The correct answer is C;both statements together are sufficient.
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