2. 外语
  3. If K is a positive integer less than 10 and N = 4,321 + K, what is the value of K ? (1) N is divisible by 3. (2) N is divisible

If K is a positive integer less than 10 and N = 4,321 + K, what is the value of K ? (1) N is divisible by 3. (2) N is divisible

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问题 If K is a positive integer less than 10 and N = 4,321 + K, what is the value of K ?
(1) N is divisible by 3.
(2) N is divisible by 7.
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B
解析 (1)     Dividing 4,321 by 3 gives a quotient of 1,440 and a remainder of 1, so 4,321 = 3(1,440) + 1. It follows that N= [3(1,440) + 1] + K= 3(1,440) + (1 + K). It is given that N is divisible by 3, from which it follows that 1 + K must be a multiple of 3. Therefore K can be 2, 5, or 8 since K < 10.
Alternatively, a number is divisible by 3 if and only if the sum of its digits is divisible by 3. If K ≠ 9, the sum of the digits of N= 4,321 + K is 4 + 3 + 2 + 1 + K= 10 + K= 1 + K, which is divisible by 3 when K=2,5, or 8;
NOT sufficient.
(2)     Dividing 4,321 by 7 gives a quotient of 617 and a remainder of 2, so 4,321 = 7(617) + 2. It follows that W= [7(617) + 2] + K= 7(617) + (2 + K). It is given that N is divisible by 7 from which it follows that 2 + K must be a multiple of 7. Thus, K= 5 since K < 10; SUFFICIENT.
The correct answer is B;
statement 2 alone is sufficient.
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