【正确答案】 A

【答案解析】Let a b, c, and d be the number, respectively, of 5-cent, 10-cent, 25-cent, and 50-cent coins. We are given that a + b + c+d= 50 and Sa + 10b + 25c + 50d = 1,000, or a + 2b + 5 c + 10d= 200. Determine the value of a.a + b + c+d=50 a + 2b + 5c+10d=200(1) We are given that c = 10 and d = 10. Substituting c = 10 and d=10 into the two equations displayed above and combining terms gives a + b = 30 and a + 2b = 50. Subtracting these last two equations gives b = 20, and hence it follows that a = 10; SUFFICIENT.(2) We are given that b = 2a. Substituting b -2a into the two equations displayed above and combining terms gives a +2a+ c+d= 50 and a + 4a + 5c + 10d= 200, which are equivalent to the following two equations.3a + c + d=50 a + c + 2d=40Subtracting these two equations gives 2a — d= 10, or 2a = d + 10. Since 2a is an even integer, d must be an even integer. At this point it is probably simplest to choose various nonnegative even integers for d to determine whether solutions for a, b, c, and d exist that have different values for a. Note that it is not enough to find different nonnegative integer solutions to 2a = d+ 10, since we must also ensure that c and d are nonnegative integers. If d= 8, then 2a = 8 + 10 = 18, and we have a = 9, b= 18, c= 15, and d=8. However, if d= 10, then 2a = 10 + 10 = 20, and we have a =10,6 = 20, c = 10, and d= 10; NOT sufficient.The correct answer is A; statement 1 alone is sufficient.