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题库 / GMATAdvanced-DS-26
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.
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.
（2）21x+5a+25b+50c=288, 3x+a+b+c=16
根据尾数，21x的尾数是3或8时，288-21x的值才可能等于5a+25b+50c，凑3和8，8的话3x已经大于16了，不行；凑3，a,b,c有解，所以x=3。
Statement 2- the total value of the coins in the jar is 288
Value of 5-cents, 10-cent, 25-cent, and 50-cent coins must be a multiple of 5
Hence value of 1-cent
= 288-5k
= 285-5k +3
= 5(57-k) +3
= 5X+3
Hence number of 1-cent can be 3, 8, 13.....so on
正确D 错误A
2可以的理由：列方程21x + 5a + 25b + 50c = 288
5a + 25b + 50c 必定是5的倍数，所以21x的尾数必须是3或8
x= 3，8，13，18...一个一个试，最后x只能是3
条件2，可以根据所列式子的尾数求出
看到尾数8，表示1 cent必从3起跳，且一定是3+5k
条件2表示 1 cent 和 5 cent 的硬币数量一样多，从1 cent 最小的可能数字开始代3，可以得出唯一解 1cent的数量就是3，因为再往上代8就无法满足题目的等式
1： 能求出1cents是3枚。5cents是0枚。
2： 5cents是0枚，20cents的币是5枚，50的是2枚时，条件成立有且只有一种答案。
所以两都能得出结论。 选C
21x+5a+25b+50c=288, 3x+a+b+c=16 根据尾数，21x的尾数是3或8时，288-21x的值才可能等于5a+25b+50c，凑3和8，8的话3x已经大于16了，不行；凑3，a,b,c有解，所以x=3。
2)11a+10c+25d+50e=288
3a+c+d+e=16
看尾數 288-11a a必須是3or8 8不合2.因此a=3有唯一解
又是凑数题，mark
（2）A=3
根据（2）方程组有条件（小于等于16）整数解只有一组
答案有误？应该是C吧？