Also, make sure you also try to ask questions and reply to your peers on the POTW thread as well. Maybe someone obtained a different final answer or showed a different process than you, and you'd like to know more about how they did it.
The answers for POTW #1 are in the thread to POTW #1. New POTW #2 (Gr. 7 and Grade 8) are below:
POTW #2 Grade 7
POTW #2 Grade 8
No this isn't possible. First of all I found the amount of students that can be in class meaning that the class number has to divide by 4. That's because in the things that Mr. Jay Fann noticed about his class he mentioned that the probability of asking a baseball fan a question was 3/4. This means that the amount of kids in class has to divide by 4. Then there is the rule that more than half of his class was present. Using these 2 rules there are 4 different amounts of kids that can be in his class. These are 28(28 / 4 = 7 and 28 > 15), 24(24 / 4 = 6 and 24 > 15), 20(20 / 4 = 5 and 20 > 15) and 16 (16 / 4 = 4 and 16 > 15). First 28, 28 is 2 less than 30 which means that 1 baseball fan and 1 non baseball fan are absent. So subtracting 1 from each of then fans and non fans we get 20/28 baseball fans and 8/28 non baseball fans. This doesn't work because 28 / 4 is 7 and 3/4 of 28 is 21 being 7x3 is 21. So 20 is not 3/4 of the class which is why 28 doesn't work. Second 24, 24 does work because if you take away 24 from 30 you get 6 which is the amount of students missing. When you divide 6 by 2 you get 3 which is amount you can take away from each group, and 21 fans minus 3 is 18 which is 3/4 of 24. If you take away 3 from the 9 non fans you get 6 which is 1/4 from 24 which is why 24 works. Third 20, there are many combinations of absent kids if 10 kids are absent so I will show the one that follows the rules. Since there are 10 kids absent we can divide that into a lot of combinations and the one that works is 6 fans and 4 non fans. 21 fans minus 6 is 15 which is 3/4 and if you take away 4 from the 9 non fans we get 5 which is 1/4 of 20 so this also works. Finally 16, 16 also works. This because 30 - 16 is 14 kids absent and to get 3/4 fans we need 9 fans to be absent which would result in (21 - 9) 12 fans being present. 12 is 3/4 from 16 so the fan side is good. If 9 fans are absent that would leave 5 more absent kids, 9 non fans minus 5 is 4 non fans that are present and 4 is 1/4 of 16 which would make 16 present kids also work. Since there are 3 different possibilities it is impossible to determine how many absent kids there are.
ReplyDeleteWho art thou?
DeleteI am not sure but I think but it was posted during the DRA/Memoir part of school.
Deletenvm its Yoav, I think its a glitch because if you click on unknown(the user) it will say YoavYoav.
DeleteGrade 7 POTW: 12 baseball fans were present and 4 non-fans were present. I figured this out by looking at 3 quarters and finding the answer above 15. This means 16 students were still present. Of course there is probably another way... Please inform me if there is.
ReplyDeleteGrade 8 POTW: Club:7 Spade:5 Heart:4 Diamond:3 Just...no words here. I can't explain this.
Luke I think there are 4 different ways.
DeleteGrade 7 POTW:
ReplyDeleteWhat I know:
- There are 9 non-baseball fans and 21 baseball fans. I have to make sure that I don't go over the limit of non-baseball fans for different answers.
- If there is more than one possible answer, there is not enough information to figure out how many students were absent.
- If out of all different possibilities there is only one answer, then the answer is possible.
- There has to be at least 15 students at the practice, since 30*0.5(or 50%) = 15
- The amount of students also has to be an integer after being divided by 4, since we cannot have anyone who is in a fraction
Solving:
Now, I find all of the numbers that are smaller than 30, but larger than 15. These numbers also have to be divisible by 4.
The numbers are 16, 20, 24, 28.
When I divide it by 4, as long as I get a quotient that is smaller than 9, the number would be counted as an answer since it would meet all of the needs of the question. I will start from the largest numbers.
28 / 4 = 7
Since the number is smaller than 9, it would count as an answer. The actual case is having one baseball fan and one non-baseball fan absent, which meets the needs of the question.
24 / 4 = 6
This answer would also work, as the quotient is smaller than 9, and the case would be 2 baseball fans and 2 non-baseball fans absent, with some other possibilities.
20 / 4 = 5
This answer would work as well, as the quotient is smaller than 9 and the case would vary. For example, the case could be 5 fans and 5 non-fans.
16 / 4 = 4.
This answer would work too, and one case could be 7 fans and 7 non-fans.
So, since all of the answers are possible, and 4 is more than 1, there is no way to determine the possible answer of how many students were absent.
-Alan
Correction to what I said before:
DeleteI cannot have 28 because the ration would be 21:7 and there would be no baseball fans absent. My answer would still be the same since there are three other possibilities and that still wouldn't be enough to figure out the right amount of people absent.
First, I know that there are 2 less people, 1 who is a baseball fan and the other that is not. That would make the children who liked baseball: 20/28 and the children who did not like baseball at a fraction of: 8/28. That is the maximum amount of students that currently in his class.
ReplyDeleteI also know that more than half the class is present. That means there are at least 16 students here. That would mean there are 16-28 students in the morning.
Next, they given me that the probability of baseball fans is 3/4. This means the number of students have to be divisible by 4, or else it will go into a decimal and that means you will have some fraction of a child, which isn't possible. And the only numbers from 16 to 28 that are divisible by 4 are 16 20 24 and 28.
If you divide 16 by 4, your left with 4, and then you would multiply it by 3 because 3/4 of the children are fans. That also means 1/4 of the children are not. This means that 12 are baseball fans, and 4 or not.
If you divide 20 by 4, your left with 15 of the 20 students are fans and 5 of them are not.
If you divide 24 by 4, your left with 18/24 students that are fans and 6 of them are not.
If you divide 28 by 4, your left with 21/28 that are fans and 7/28 are not.
There are 4 different possibilities of numbers of children in these clues, and each number of children has a different amount of absent children. For example, if there are 16 children, there would be 14 absent because 30(the total number of children)-16(this morning's number of children), would mean 14 are absent. For the other options of the number of children, they all give different amount of absent people.
This means that there is not information to determine the number of absent kids
It can't be a total of 28 students because then the ratio would be 21:7 and then all baseball fans would be present
DeleteNo because since we know that at least 15 students are there and that the amount of students has to go cleanly into 4, we just get all the numbers divisible by 4 between 15 and 30. These are 16, 20, 24 and 28. We then have to get the ratios of fans to non fans which is simple because by dividing each number by 4 and the number it's divisible by is the non fans. Subtract that from the original and get the amount of fans. The ratios become 16-12:4, 20-15:5, 24-18:6 and 28-21:7. Given the ratios it can't be 2 students absent because then all the baseball fans would be there(21). However you can't narrow it down from there so there are 3 possible answers.
ReplyDeleteThe first thing that I saw is 1 fan and 1 non-fan is absent. So that would subtract from out total which is 30.
ReplyDelete30-2=28
So now we know 20/28 students are fans and the other 8 aren't. The next thing Mr.Fann notices is that half of his class is present so 30/2(which is half since 1/2 + 1/2= 1) = 15. And since more than half of his class is present, we have to add 1 more since that is more than half which is 16. So we know the minimum and the maximum. Now, the third clue states that 3/4 of the class are baseball fans so we find all the numbers between 16 and 28 that is dividable by 4. So all numbers between 16 and 28 that have 4 as one of their factors.
These numbers are: 16, 20, 24, 28.
Next, we test the numbers (x/4= y, and if y is lower than 8 or is 8 (since that is that is the maximum of non baseball fans.) then it is correct.
16/4=4 So this is correct since the quotient is less than 8, this is correct.
20/4=5 This is also correct since the answer is lower than 8.
24/4=6 This is also correct since 6<8
28/4=8 The last number is also right because it is okay to have the answer as 8 since that is the maximum.
There are 4 different possibilities therefore, there is not enough information to figure out the number of absent students.
Its 7 not 8 for 28/4.
Deleteooops, my bad, 28/4 is actually 7 ^_^
DeleteGrade 8 POTW:
ReplyDeleteI had to draw this out so...
(1)=Clubs
(2)=Diamonds
(3)=Hearts
(4)=Spades
1st Clue said that the Club and the Spade are right beside each other.
So we can conclude that:
(1) (4) (?) (?)
The second clue says the Diamond is not the most left card and the heart is not the fourth right card since (1) and (4) are already beside each other, this leaves us with:
(1) (4) (3 (2)
So now the fourth clue says 7 (the number) is somewhere to the left of the heart and 3 is somewhere to the right of the heart. We know the most right card is the three of diamonds, since the diamonds is the only card to the right.
And so we are still not sure until the the fifth clue which states from left to right, the cards are arranged from largest to smallest. I can now conclude:
(1) (4) (3) (2)
7 5 4 3
Even though they did not give us the 2 middle numbers, they say they add to nine and since 5+4 is between 7 and 3 it works. Why you may ask? Well, they say from left to right the cards are from largest to smallest. So we know 7 and 3 are the highest and lowest cards. We then have to put 5 onto the spades since it has to be from largest to smallest which leads to the 4 of hearts.
So in conclusion, these are the cards in order with their value.
(Clubs, 7) (Spades, 5) (Heart, 4) (Diamond, 3)
I will replace the cards (spade, club, etc) with numbers:
ReplyDelete1. Clubs
2. Spades
3. Hearts
4. Diamonds
1 and 2 are beside each other in that specific order left to right.
Additionally, 4 can not be the leftmost card, and 3 can not be the rightmost card.
but since 1 and 2 are beside each other, we cannot put 3 and 4 in the middle. So we will put diamonds to the right, and heart beside it to the right of it, as the heart cannot be leftmost in order to allow for rule 3 to work.
1, 2, 3, 4.
or
Clubs, Spades , Heart, diamond.
Now, we need to find the numbers for each card.
According to 3, the 3 is somewhere to the right of the heart. There is only one card to the right, and it is the diamond, therefore diamond is 3.
Secondly, 5 states that the cards are arranged from largest to smallest, and if there is a 7, which means that 7 is the largest value that we know.
So currently, it is this.
7, blank, blank, 3.
Then, I noticed that rule 4 states that the unknown values left add to nine, and so we only have the numbers 6, 5 and 4, which means the only pair I can think of is 5 and 4.
This means that spades must be 5 and heart must be 4.
This gives me a final answer of:
Club-7, spades-5, heart-4, and diamond-3.
The answer to the grade 8 potw is (from left to right) club 7, spades 5, heart 4, diamond 3. I got this answer by first finding out what the first card can't be. Since it straight up tells us it can't be diamonds. The since it tells us that the spade has to be the left of the clubs and that the 7 is the first card the spade or the heart can't be there so the club goes there. Then the spades goes next to it. Then it tells us the heart can't be last so then it goes heart then diamond. As for the numbers the 2 missing ones they have to be in between 7 and 3 and since it has to add to 9, the numbers are 4 and 5 so then the spades is 5 and the heart is 4.
ReplyDeleteThere is 30 students. 21 baseball fans, 9 who aren't. It says at least one baseball fan wasn't present and one non-fan wasn't present. Because the total students is 30, That brings the max down to 28. It also says more than half the class was present, which means that you divide class total by 2, and +1 because it says MORE than half. This means the minimum number of students is 16, while the maximum is 28. Also, it shows that the probability of asking a baseball fan is 3/4, so you divide all the numbers between 16 and 28 by four, which gives you 4 possible numbers.
ReplyDelete16/4=4
20/4=5
24/4=6
28/4=7
Because there is 4 different outcomes, there is not enough information for the teacher.
Grade 8 POTW:
ReplyDeleteUsing the clues they give me, I can immediately figure out only three ways to put the cards in order, since the club and spades have to be together.
1. Club, Spade, Heart, Diamond
2. Heart, Diamond, Club, Spade
3. Heart, Club, Spade, Diamond
But, using the clue about the numbers, I would see that there has to be a card to the left of the hearts and to the right of the hearts. This would show that the only possible way is the first way.
Since now I have my order of cards, I now find the order of the numbers.
The hearts is the third number, so to the rightest card would end up being the 3 of diamonds. Now, I have to figure out the other three cards.
To the left of the hearts are two cards. So, the cards could be the 7 of clubs or the 7 of spades. Now, we look at the 4th clue, which explains how the other two numbers add up to nine. I can list all possible values.
0, 9
1, 8
2, 7
3, 6
4, 5
The numbers also have to be larger than three because three is the smallest number, according to clue number 5. It also cannot be 7 or 3 because the numbers are all different, stated in the question. So, that leaves me with 5 and 4.
Finally, I have 4 numbers and 4 cards. I have to order the numbers now.
The order would be 7,5,4, and 1. This is an order from largest to smallest.
The final answer is
first card: 7 of clubs
second card: 5 of spades
third card: 4 of hearts
fourth card: 3 of diamonds
-Alan
There is not information to determine how many students that are absent. There are 30 students, 21 baseball lovers, and 9 who are not. At least one baseball lover and one non-baseball lover are absent. This gives a maximum of 28 students since more than half of the class is present, divide 30 by 2 and add one because more than half the class is present. That means 16-28 people are present. Since there is a 3/4 chance of a baseball fan, the number of students is a multiple of 4. 16, 20, 24,and 28 are multiples of 4. This gives 4 different outcomes which means that the number of students absent is 2, 6, 10 or 14 and cannot be determined.
ReplyDeleteFor the grade 7 POTW:
ReplyDeleteFirst, it says that AT LEAST one baseball fan and one non-baseball fan. So we must first do 30-2=28. Now we know the maximum number of students that could be inside the class that day. Now, it says that more than 15 people were there that day. Subsequently, it says that the probability of someone being a baseball fan is 3/4 or 75%.
Now the possibilities of how many people being here are:
16
20
24
28
There is not enough information to know how much people are in the class.
Grade 7 POTW:
ReplyDeleteFirst of all we know that at least 1 of each "group"/one baseball fan and one non-baseball fan aren't there. So we know take those two off 30-2=28 would be the maximum people there. Now it also says that there are more then half of the class present, that means that we need at least 16 people (30 divided by 2=15+1 *for more then half the class*) Now the probability of a baseball fan is 3/4 so that means that the number of students present can only be a multiple of 4. That leaves 4 numbers.
16,
20,
24,
28
That means that the 4 outcomes possible for student absent is:
2,
6,
10,
14
Therefore there is not enough info to get an answer. This is because there is not enough information provided to continue to filter the information. Right now you can only filter it down to 4 possibilities with the info provided.
~Michelle
This is how I solved the Grade 7 POTW.
ReplyDeleteFirst, I analyzed the information given.
There are 30 students in total, 21 baseball fans and 9 non-baseball fans.
The other information given is:
More than half of the students are present,
3/4 is the probability of asking a baseball fan,
and at least one person is absent from both groups.
Now, to figure out if this is enough information to determine how much students are absent, I will have to try to find one or more possibilities for how much students are absent.
So, since one person from each group is absent, the maximum amount of people present would be 28.
More than half of the students are present, meaning that there is a minimum of 16 students present.
And, because the chance of asking a baseball fan is 3/4, the number(s) must be divisible by 4.
The numbers that are divisible between 16 and 28 are as follows:
28
24
20
16
I can draw a conclusion that there is not an adequate amount of information to determine how much students were absent in Jay Fann's class that day.
Grade 8 POTW:
ReplyDeleteCARD LOGIC:
I have 4 cards, club, diamond, heart and spade.
I have to find the order of the ards and the number on each card.
This is what each clue gave me in order (s=spade, d=diamond, h=heart, and c=club)
1. c s ✓
2. d - - h x
3. h - - - x and 7 h 3 ✓
4. So I came up with c7 s h d3 ✓
5.6. The answer is c7 s5 h4 d3 ✓
Grade 7 POTW #2:
ReplyDeleteFrom the information, I know that:
The maximum amount of students present is 28, because at least one baseball fan was absent and one non- fan was absent. That means 30 - 2 = 28.
There were more than 16 students present, because more than half his class was present. 30 / 2 = 15, and since the information said more that means 16.
From 16-28, the numbers in between are:
16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, and 28. But according to the last piece of information, the number of students present has to be divisible by 4. That leaves 16, 20, 24, and 28.
But there is no more information. Therefore, there is not enough information to know how many students were present that day.
I Agree with you! ^_^
DeleteBut I believe it isn't possible to have 28 students present, because to get 3/4 to x/28, you have to times by 7, and 7 x 3 is 21, which means all baseball fans are present. Otherwise, I agree with your answer! ^_^
POTW GRADE 8:
ReplyDeleteHere is how I solved it:
Hint one stated that the Club and Spade card are right beside each other in that order, so I wrote down C ( Club) and S ( Spade) on a piece of paper.
C S
Hint two stated that the Heart was not 4th and the Diamond is not 1st,
Hint three states that 7 is somewhere to the left of the heart and that 3 is somewhere to the right,
this confirms the location of the heart and Diamond as the Heart has to have at least one card to both sides, meaning it would have to be 3th while the Diamond would be 4th, and the Diamond being on the right of the heart means that the diamond has the number 3 on it
C S H D ( 3)
Hint 4 states that the two cards who values are unknown add up to nine
Hint 5 states that the values or fro largest to smallest
since 7 is on the left it would have to be on the club due to the fact nothing over 7 pus a number can make Hint 5's statement true meaning the Club is 7
C (7) S H D (3)
The values of the spade and the heart must equal 9 now as they are the only unknowns left, and to make Hint 5 true the only numbers that fit are 5 ( S) and 4( H) Meaning this is the order of the cards and their values:
Club ( 7), Spade ( 5), Heart ( 4), Diamond (3)
POTW GRADE 7
ReplyDeleteHere is how I solved it:
the first hint said that at least one baseball fan was absent and one non baseball fan was absent, meaning at the total people here had to be at least 28/30 from hint one.
Hint 2 states that more than half of the class was present, which means 16+/30 people had to be here.
HInt 3 states that the probability of asking a baseball fan was 3/4, meaning the total number of students is either 24, 20, 16, since there is no other info to narrow down the number, it is unsolvable for now.
Reason why the total number can not be 21:
3/4 x 7 = 21/28
and at least 1 baseball fan had to be absent meaning 21 baseball fans can not be possible due to that being the total number of base ball fans before the absent one.
There has to be 16+ kids and a least one baseball and one non-baseball fan absent. Also, the probability of asking a baseball fan a question was 3/4.
ReplyDeleteThis means that 16, 20 or 24 has to be the total number of students as they are multiples of 4.
16 kids would mean that there is 12 baseball and 4 non-baseball fans.
20 would mean that there are 25 baseball and 5 non-baseball fans.
24 would mean that there are 18 baseball and 6 non-baseball fans.
The reason as to why there can't be 18 kids in the class is that there wouldn't be any baseball fans absent. There would be 21 baseball fans and 7 non-baseball fans. There is 21 baseball fans normally so none would be absent.
There are many results which is why there is not enough information to determine how many students were absent that particular morning.
Avi btw 20 students means that theres 15 baseball fans not 25. Just saying.
Delete25+5 does not equal to 20 Avi Σ（ﾟдﾟlll）
DeleteMy answer is:
ReplyDeleteC7 S5 H4 D3
P.S. I originally explained, but then I clicked something (I actually have no idea what I clicked) but then I had to rewrite my comment, and honestly I'm just too lazy to rewrite it all because I wrote a lot :PP.
That's OK this time Jenny. Great job staying on-top of your work!
DeleteHere is how I went about solving this week's Grade 7 POTW:
ReplyDeleteFirst, I took into account the fact that two students were absent so the number of people in the class would be 28. Therefore, the maximum number of fans would be 20 because we would have to subtract 21 by 1 (due to the absent student). Similarly, we would subtract 9 by 1 which would give us a difference of 8. Since more than half the class was present, at least 16 had to have showed up. Due to the fact that the probability of asking a baseball fan a question was 3/4, the probability of asking a non-baseball fan would be 1/4. We would have to be looking for a number between 16 and 28 so that we don't end up with a decimal. After calculations, you find that the numbers are 16, 20, 24 and 28.
- 16 kids would mean that there are 14 kids absent, 12 baseball fans, and 4 non-baseball fans
- 20 kids would mean that there are 10 kids absent, 15 baseball fans, and 5 non-baseball fans
- 24 kids would mean that there are 6 kids absent, 18 baseball fans, and 6 non-baseball fans
It is not possible for there to be 28 students in class because, 3/4 of 28 is 21, and that would be the amount of baseball fans in the class. But that wouldn't count the absent baseball fan. Therefore, the maximum number of baseball fans there could be are 20.
I first looked at 3/4 to help me find the possible amounts of students. The denominator in 3/4 (in this case 4) means that the total amount of students would have to be a multiple of 4. But we can't go under 16 because more than half the class was present. Also, we can't go over 24 because it wouldn't meet the criteria(I will get to 28 later on). That leaves us with 3 multiples. 16, 20, and finally 24. Now going back to the 3/4. Since we know that 3/4 if the amount of baseball fans present, that means that 1/4 of non baseball fans would have to be present too. So we can now check our multiples to see if it fits within all the criteria.
ReplyDelete16 students = 12 baseball fans and 4 non-baseball fans. 12 = 3/4 of 16, 4 = 1/4 of 16
20 students = 15 baseball fans and 5 non-baseball fans. 15 = 3/4 of 20, 5 = 1/4 of 20
24 students = 18 baseball fans and 6 non-baseball fans. 18 = 3/4 of 24, 6 = 1/4 of 24
Now even though 28 is also a multiple of 4 and not over 28, we still can't use it. If we put that into the equation like we did with the other 3 multiples that would not meet the criteria. 28 students = 21 baseball fans. The criteria states that 1 baseball fan and 1 non-baseball fan was absent but in this case that wouldn't be true since 21 was the amount of students of original baseball fans. So 28 wouldn't work out in the situation.
But we still have to other three multiples which fit within all the criteria. We can't single one out and get the exact number. This all means that we can't really pin point how many people exactly were absent.
To solve the grade 8 math problem using the clues I did the following:
ReplyDeleteBecause the Club (C) and Spade (S) are beside each other in that order I started off with CS. Next with the clue that Diamond (D) is not the first and Heart (H) is not the last, I first ignored it because there wasn't enough information to place down D and H. Finally I read the last two hints together and I was able to make an educated guess. Because there were cards to the left and right of H I knew that H was probably between S and D but not C and S because of the first hint. Next after placing the cards in order (C S H D) I know that D is 3 because on the right of H is 3. Also because it is ordered from largest to lowest that meant that C was 7 because if the two unknown numbers were to be adding up to 9 then it had to be in between 4 and 6. So we know that the only way to get 9 from those three numbers were 4+5. Finally the order is C7 S5 H4 and D3.
Test
ReplyDeleteThis is my final answer: No because someone can be sick or go on vacation
ReplyDeleteTo solve this question I first looked at the clues, clue number 1 states that the club and the spade are next to each other which means they cannot have anything in between so it would be so far,
ReplyDeleteClub,Spade
The second clue states that the diamond is not the first to the left, and the heart is not the last card to the right so I put them like this,
Club,Spade,Heart,Diamond
The next clue states that 7 is somewhere left of the heart, and 3 is somewhere on the right of the heart and since the only this to the right of the heart is the Diamond it is the 3. Clue number 5 states that from left to right the cards are arranged from largest to smallest, so seven must be with the Club, as the other clue states that the other unknown cards at up to nine so it can’t be any other number higher than 7. Lastly I though of which 2 numbers at up to nine, two number that would work are 4 and 5 so I used them.
Club(7),Spade(5),Heart(4),Diamond(3)
Since at least one person was absent from each "group", we would subtract 2 from 30 to get 28. Since the chance of asking a baseball fan is 3/4, there would be 21 of them. The problem with this is that there are only 21 baseball fans in the whole class and at least one person needs to be absent. The next possibility is that there are 20 people in the whole class so 15 are baseball fans and 5 are not but another way is 16 people in the whole class with 12 baseball fans and 4 non baseball fans. In conclusion, there are too many possibilities to determine how many people were absent.
ReplyDeleteTo solve this problem, I decided to use the information given and try to deduce how many students were absent. Since at least one baseball fan (BF) and one non-baseball fan (NBF) were absent, there could not be more than 20 BF's and 8 NBF's, and no more than 28 people total in the class. As well, since more than half of the class is present, there could be no less than 16 people in his class. Since we also know that the probability of asking a baseball fan was 3/4, the amount of total people was a multiple of 4.
ReplyDeleteNow, we know that the amount of people is a multiple of 4, and is also between 16 and 28. I decided to then create a chart listing how many people would be BF's and NBF's which each possible amount of total people, and seeing if the amounts met the requirements given. (No more than 8 NBF's and 20 BF's
Amount of people Number of BF's Number of NBF's Meets Requirements?
16 12 4 Yes
20 15 5 Yes
24 18 6 Yes
28 21 7 No (Too many BF's)
Because there are 3 possibilities that meet all of the requirements, we can not figure out exactly how many people are absent.