在五天的数学打卡中，一共做了25个数学难题，涉及到知识点包括约数个数定理、圆桌排序、运动问题、均值不等式以及余数问题等GRE和GMAT数学里的难点。
下面把全部题目放出来，并给出其中三个比较有代表性的题目解析。
-
给了一个钟表表盘，现在是09:00，问多少分钟之后分针会和时针第一次重合？
-
周一到周五每天干啥概率是1/2，周六周日是1/5，互相独立。问周五or周六or周日概率。
-
Consider a regular polygon of p sides. The number of values of p for which the polygon will have angles whose values in degrees can be expressed in integers?
-
How many integers from 1 to 900 inclusive have exactly 3 positive divisors?
-
There are 10 people in a room. If each person shakes hands with exactly 3 other people, what is the total number of handshakes?
-
151!的末尾有多少个连续的0？
-
已知在 10 个最小的连续质数中，任意挑选 3 个数。问:这 3 个数的和是奇数的概率是多少?
-
—个小于100的质数，被5除后的余数是2,被7除后的余数是6,问这个质数被8除后余几。
-
5对龙凤胎共10人，要从这5对龙凤胎里面选4个人，2男2女，且每一对龙凤胎最多只能选1个人，问有多少种选法。
-
已知x≤y<0，问x/y+y/x的最小值。
-
Set S consists of numbers 2, 3, 6, 48, and 164. Number K is computed by multiplying one random number from set S by one of the first 10 non-negative integers, also selected at random. If Z=6^K, what is the probability that 678463 is not a multiple of Z?
-
有个墙至少有一种颜色，有六色可选（白，粉，红等）请问肯定有白色的可能性有几种？
-
已知a\b\c都是正数，且a^3+b^3+8c^3=6abc。求a/b+b/c+c/a的值。
-
2≤r<s≤6，r和s都是整数，问(r+s)/rs的最大值是多少？
-
把ABC三个字母填入一个九宫格，每一行不能有同一个字母，每一列也不能有同一个字母，问一共有多少种排法？
-
On a partly cloudy day, Derek decides to walk back from work. When it is sunny, he walks at a speed of s miles/hr (s is an integer) and when it gets cloudy, he increases his speed to (s + 1) miles/hr. If his average speed for the entire distance is 2.8 miles/hr, what fraction of the total distance did he cover while the sun was shining on him?
-
If 55 percent of a group of people have brown hair and 80 percent of the same group do not have red hair, what fraction of those who do not have brown hair have red hair?
-
If an integer n is to be chosen at random from the integers 1 to 96, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 8?
-
已知 0.00678 在 10^−(n+1)到10^−n的范围内。问: n 的值等于多少?
-
已知一个数由 1 到 100 每个数字乘以 3 组成:369121518……297300。问:这个数的第 72 位数是多少?
-
有64个小正方体叠成了一个大正方体，每个小正方体都有一个面被涂成蓝色。问正方体的表面蓝色部分面积与整个正方体表面积的比值最大是多少。
-
At a dinner party, 5 people are to be seated around a circular table. Two seating arrangements are considered different only when the positions of the people are different relative to each other. What is the total number of different possible seating arrangements for the group?
-
If the probability is 0.54 that Stock A will increase in value during the next month and the probability is 0.68 that Stock B will increase in value during the next month, what is the greatest possible value for the probability that neither of these two events will occur?
-
In a room filled with 7 people, 4 people have exactly 1 friend in the room and 3 people have exactly 2 friends in the room (Assuming that friendship is a mutual relationship, i.e. if John is Peter’s friend, Peter is John’s friend). If two individuals are selected from the room at random, what is the probability that those two individuals are NOT friends?
-
If Jessica tosses a coin 3 times, what is the probability that she will get heads at least once?
更多数学难题讲解，
来我们的线上课程～
本文源自微信公众号:LABcircle