题目信息
Exactly 3 deposits have been made in a savings account and the amounts of the deposits are 3 consecutive integer multiples of $7. If the sum of the deposits is between $120 and $170, what is the amount of each of the deposits?
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 Properties of integers
If k represents the least of the multiples of 7, then the three deposits, in dollars, are represented by 7k, 7(k + 1), and 7(k + 2). The sum, in dollars, of the deposits is 21k + 21, where 120 < 21k + 21 < 170. It follows that the value of the integer k is 5, 6, or 7. If k = 5, then the deposits could be 35, 42, 49, with a sum of 126, which is between 120 and 170. If k = 6, then the deposits could be 42, 49, 56 with a sum of 147, which is between 120 and 170. If k = 7, then the deposits could be 49, 56, 63 with a sum of 168, which is between 120 and 170.
It is given that one of the deposits, in dollars, is 49. Since 49 is one of the amounts for each value of k in the remarks above, the amounts of the three deposits cannot be determined; NOT sufficient. It is given that one of the deposits, in dollars, is 63. Since 63 occurs for exactly one value of k in the remarks above, the amounts, in dollars, of the deposits are 49, 56, and 63; SUFFICIENT.
The correct answer is B;statement 2 alone is sufficient.
If k represents the least of the multiples of 7, then the three deposits, in dollars, are represented by 7k, 7(k + 1), and 7(k + 2). The sum, in dollars, of the deposits is 21k + 21, where 120 < 21k + 21 < 170. It follows that the value of the integer k is 5, 6, or 7. If k = 5, then the deposits could be 35, 42, 49, with a sum of 126, which is between 120 and 170. If k = 6, then the deposits could be 42, 49, 56 with a sum of 147, which is between 120 and 170. If k = 7, then the deposits could be 49, 56, 63 with a sum of 168, which is between 120 and 170.
It is given that one of the deposits, in dollars, is 49. Since 49 is one of the amounts for each value of k in the remarks above, the amounts of the three deposits cannot be determined; NOT sufficient. It is given that one of the deposits, in dollars, is 63. Since 63 occurs for exactly one value of k in the remarks above, the amounts, in dollars, of the deposits are 49, 56, and 63; SUFFICIENT.
The correct answer is B;statement 2 alone is sufficient.
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