一道GRE数学题,OG上的,没明白,
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一道GRE数学题,OG上的,没明白,
Let S be the set of all positive integers n such that n^2 is a multiple of both 24 and108.Which of the following integers are divisors of every integer n in Indicate all such integers.
A.12 B.24 C.36 D.72
Let S be the set of all positive integers n such that n^2 is a multiple of both 24 and108.Which of the following integers are divisors of every integer n in Indicate all such integers.
A.12 B.24 C.36 D.72
![一道GRE数学题,OG上的,没明白,](/uploads/image/z/6696862-70-2.jpg?t=%E4%B8%80%E9%81%93GRE%E6%95%B0%E5%AD%A6%E9%A2%98%2COG%E4%B8%8A%E7%9A%84%2C%E6%B2%A1%E6%98%8E%E7%99%BD%2C)
先理解题目:S是所有正整数n的集合,n的特点是n^2是24和108的公倍数.问选项里哪些数是S里所有n的公约数.
24和108的公倍数是12×2×9×a,a是一个正整数.
所以n^2=12×2×9×a,n = sqrt(12×2×9×a) = 6×sqrt(6×a),a应该等于6,6×4,6×9,6×16,6×25,6×m^2(m是整数)之类的,这样才能保证sqrt(6×a)能开根号得到整数.所以n=36,72,108,36×m.n最小是36.
所以答案是AC.
24和108的公倍数是12×2×9×a,a是一个正整数.
所以n^2=12×2×9×a,n = sqrt(12×2×9×a) = 6×sqrt(6×a),a应该等于6,6×4,6×9,6×16,6×25,6×m^2(m是整数)之类的,这样才能保证sqrt(6×a)能开根号得到整数.所以n=36,72,108,36×m.n最小是36.
所以答案是AC.