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How many integers between 1 and 2,000 will be the square of an integer and also be the cube of an integer?
How many integers between 1 and 2,000 will be the square of an integer and also be the cube of an integer?
admin
2022-12-19
18
问题
How many integers between 1 and 2,000 will be the square of an integer and also be the cube of an integer?
选项
A、8
B、4
C、6
D、9
E、3
答案
E
解析
我们首先来看一下哪个数的立方小于2,000,这样能把数的范围确定下来,10的3次方是1,000,13
3
稍微大于2,000,因此从1到12这12个数的立方小于2,000。题目条件是这个数既是一个数的平方,又是一个数的立方。也就是:x
3
=y
2
<2,000,(x,y都是正整数)。由此我们得y=
,既然y是正整数,那么x就必然是完全平方数,在1到12这12个数中只有1,4,9是完全平方数,所以在1~2,000中只有3个数既是一个数的平方,又是一个数的立方。它们分别是:1=1
3
=1
2
,64=4
3
=8
2
,729=9
3
=27
2
,选择E。
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本试题收录于:
GMAT QUANTITATIVE题库GMAT分类
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