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SAT模拟考试题:SAT数学练习题(30)

2016-08-11 17:13:45来源:网络

  4. A certain animal in the zoo has consumed 39 pounds of food in six days. If it continues to eat at the same rate, in how many more days will its total consumption be 91 pounds?

  A. 12

  B. 11

  C. 10

  D. 9

  E. 8

  Correct Answer: E

  解析:

  Food consumed per day = 39/6. In the remaining days it will consume 91 - 39 pounds = 52 pounds. Now divide the food by the daily consumption to find the number of days. 52 / (39/6) = 52 x (6 / 39) = 8

  5. A perfect cube is an integer whose cube root is an integer. For example, 27, 64 and 125 are perfect cubes. If p and q are perfect cubes, which of the following will not necessarily be a perfect cube?

  A. 8p

  B. pq

  C. pq + 27

  D. -p

  E. (p - q)6

  Correct Answer: C

  解析:

  A perfect cube will have prime factors that are in groups of 3; for example 125 has the prime factors 5 x 5 x 5 , and 64 x 125 will also be a cube because its factors will be 4 x 4 x 4 x 5 x 5 x 5. Consider the answer choices in turn. 8 is the cube of 2, and p is a cube, and so the product will also be a cube. pq will also be a cube as shown above.pq is a cube and so is 27, but their sum need not be a cube. Consider the case where p =1 and q = 8, the sum of pq and 27 will be 35 which has factors 5 x 7 and is not a cube. -p will be a cube. Since the difference between p and q is raised to the power of 6, this expression will be a cube (with cube root = difference squared).

  更多SAT模拟考试题及备考资料敬请查看SAT真题栏目。


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