a*****g
发帖数: 1320 | 1 1.At Marsh Mel Low Middle School 34 students play soccer, 36 students play
football and 29 students play basketball. Of these students 15 play both
soccer and football, 18 play both basketball and football and 13 play both
soccer and basketball. What is the smallest possible number of students that
play all three sports?
2. If x and y are two triangular numbers less than 100 that when added,
produce a sum that is a square number, what is the largest possible value of
x or y?
3. Suppose that six brothers (George, John, Thomas, Fred, Andrew, Martin)
each roll a fair 6-sided die. At least three of them have rolled an even
number. What is the probability that John, Fred and Martin have each rolled
an even number? Express your answer as a common fraction. | B******1
发帖数: 9094 | 2 1.At Marsh Mel Low Middle School 34 students play soccer, 36 students play
football and 29 students play basketball. Of these students 15 play both
soccer and football, 18 play both basketball and football and 13 play both
soccer and basketball. What is the smallest possible number of students that
play all three sports?
Since there are 18 play both basketball and football and 13 play both soccer
and basketball, but there there are 29 students playing basketball, then at
least there are 2 person who play all three sports. | B******1
发帖数: 9094 | 3 2. If x and y are two triangular numbers less than 100 that when added,
produce a sum that is a square number, what is the largest possible value of
x or y?
Triangular numbers less than 100: 1,3, 6, 10,15,21,28,36,45,55,66,78,91
A squre number less than 200: 1, 4, 9, 16,25,36,49,64,81,100,121,144,169,196
Apparently 45 + 55 =100. So we know at least 55 is one possible choice.
Can we go any higher? Let's try 91. 196 is out. 169-91 = 78
Bingo.
The answer is 91. | t***o
发帖数: 1353 | 4 你老要在这里开堂授课吧。。。
of
196
【在 B******1 的大作中提到】
: 2. If x and y are two triangular numbers less than 100 that when added,
: produce a sum that is a square number, what is the largest possible value of
: x or y?
: Triangular numbers less than 100: 1,3, 6, 10,15,21,28,36,45,55,66,78,91
: A squre number less than 200: 1, 4, 9, 16,25,36,49,64,81,100,121,144,169,196
: Apparently 45 + 55 =100. So we know at least 55 is one possible choice.
: Can we go any higher? Let's try 91. 196 is out. 169-91 = 78
: Bingo.
: The answer is 91.
| A******s
发帖数: 292 | 5
play
both
both
students that
2
added,
value of
78 and 91
Martin)
even
8/42
【在 a*****g 的大作中提到】
: 1.At Marsh Mel Low Middle School 34 students play soccer, 36 students play
: football and 29 students play basketball. Of these students 15 play both
: soccer and football, 18 play both basketball and football and 13 play both
: soccer and basketball. What is the smallest possible number of students that
: play all three sports?
: 2. If x and y are two triangular numbers less than 100 that when added,
: produce a sum that is a square number, what is the largest possible value of
: x or y?
: 3. Suppose that six brothers (George, John, Thomas, Fred, Andrew, Martin)
: each roll a fair 6-sided die. At least three of them have rolled an even
| B******1
发帖数: 9094 | 6 3. Suppose that six brothers (George, John, Thomas, Fred, Andrew, Martin)
each roll a fair 6-sided die. At least three of them have rolled an even
number. What is the probability that John, Fred and Martin have each rolled
an even number? Express your answer as a common fraction.
Since "At least three of them have rolled an even number", let's do it one
step at a time.
If all 6 dices are even, there is only one way to do it and there is one way
the three brothers have all even.
If 5 dices are even, there are 6 ways to do it and there are 3 ways the
three brothers have all even.
If 4 dices are even, there are 15 ways to do it and there are 3 ways the
three brothers have all even.
If 3 dices are even, there are 20 ways to do it and only one way the three
brothers have all even.
8/42 = 4/21 is the answer. | a*****g
发帖数: 1320 | | a*****g
发帖数: 1320 | 8
我也苯的可以，花了2小时才想明白第一题。第二，第三还在思考中。
【在 a*****g 的大作中提到】
: Thanks a lot!先顶再好好学习。
| a*****g
发帖数: 1320 | 9 第二题，请问为什么有78？谢谢
【在 A******s 的大作中提到】
:
: play
: both
: both
: students that
: 2
: added,
: value of
: 78 and 91
: Martin)
|
|
