单选题 If x and y are integers such that x3 = y2, which of the following could not be the value of y?
Indicate all such values.
  • A. -1
  • B. 1
  • C. 8
  • D. 12
  • E. 16
  • F. 27
【正确答案】 D、E
【答案解析】Test each choice until you find all the correct answers.
(A) Could y = -1? Is there an integer x such that x3 = (-1)2 = 1? Yes, x = 1.
(B) Similarly, if y = 1, x = 1.
(C) Could y = 8? Is there an integer x such that x3 = (8)2 = 64? Yes, x = 4.
(D) Could y = 12? Is there an integer such that x3 = 122 = 144? No, 53 = 125, which is too small, and 63 = 216, which is too big.
(E) Could y = 16? Is there an integer x such that x3 = 162 = 256? No, 63 = 216, which is too small; and 73 = 343, which is too big.
(F) Could y = 27? Is there an integer x such that x3 = 272 = 729? Yes, 93 = 729. The answer is D and E.