2. 外语
  3. Merle’s spare change jar has exactly 16 U. S. coins, each of which is a 1-cent coin, a 5-cent coin, a 10 cent coin, a 25-cent co

Merle’s spare change jar has exactly 16 U. S. coins, each of which is a 1-cent coin, a 5-cent coin, a 10 cent coin, a 25-cent co

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问题 Merle’s spare change jar has exactly 16 U. S. coins, each of which is a 1-cent coin, a 5-cent coin, a 10 cent coin, a 25-cent coin, or a 50-cent coin. If the total value of the coins in the jar is 288 U. S. cents, how many 1-cent coins are in the jar?
(1) The exact numbers of 10-cent, 25-cent, and 50-cent coins among the 16 coins in the jar are, respectively, 6, 5, and 2.
(2) Among the 16 coins in the jar there are twice as many 10-cent coins as 1-cent coins.
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D
解析 Let a, b, c, d, and e be the number, respectively, of 1-cent, 5-cent, 10-cent, 25-cent, and 50-cent coins. We are given the two equations shown below. Determine the value of a.
a + b + c + d+e=16
a + 5b + 10c + 25d+50e = 258
(1)     We are given that c = 6, d = 5, and e = 2. Substituting these values into the two equations displayed above and combining terms gives a + b = 3 and a + 5b = 3. Subtracting these last two equations gives 4b = 0, and therefore b = 0 and a = 3; SUFFICIENT.
(2)     We are given that c = 2a. Substituting c = 2a into the two equations displayed above and combining terms gives the following two equations.
3a + b + d+e= 16
21a+ 5b + 25d+50e = 288
From the first equation above we have 3a = 16 - b - d- e. Therefore, 3a < 16, and it follows that the value of a must be among 0,1,2, 3,4, and 5. From the second equation above we have 5(b + 5d+ 10e) = 288 - 21a, and thus the value of 288 - 21a must be divisible by 5.

The table above shows that a = 3 is the only nonnegative integer less than or equal to 5 such that 288 - 21a is divisible by 5; SUFFICIENT.
The correct answer is D;
each statement alone is sufficient.
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