题目信息
If K is a positive integer less than 10 and N = 4,321 + K, what is the value of K ?
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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正确答案：
B:Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
Arithmetic Computation with integers
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. Dividing 4,321 by 7 gives a quotient of 617 and a remainder of 2, so 4,321 = 7(617) + 2. It follows that N = [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.
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. Dividing 4,321 by 7 gives a quotient of 617 and a remainder of 2, so 4,321 = 7(617) + 2. It follows that N = [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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