Logic Question.

Okay guys so. I took a Bio-Statistics class. But my teacher is Russian or one of those countries, so the way he teaches is eccentric. He teaches crazy stuff that goes along with the textbook, but he does it in a way that reading the textbook won't help you if you don't pay attention and understand HIM, then you won't do well on his tests.

He gave a test last Thursday. And it's Spring Break this week, so I won't see him again till next next Monday (the 14th). There was this one question on the test that had to do kind of with logic, he never taught us anything like it, and it wasn't mentioned in the book. I'm dying to know the answer to this question. I did it on my test, but I'm not sure if the answer is right since I was pressured with time and submitted the first thing I got. Here it goes:

There was a study of 100 sophomores in a school to check how many received financial aid. It was found that 49 people used Government Grants, 55 people used Private Scholarships, and 43 people used Academic Credits; 18 people used both Government Grants and Private Scholarships, 28 people used both Government Grants and Academic Credits, and 8 people used all three. Find out how many students use at least one type of scholarship.

So essentially:
49 A
55 B
43 C
18 A + B
28 A + C
8 A + B + C

I'll say the answer I put after one of you smart people figure out how to do it. Thanks in advance.

For me we are missing one equation here. We don't know the intersection of B and C in order to say how many people are outside of all groups.

We have 8 variables:
-people on A
-people on B
-people on C
-people on AB
-people on AC
-people on BC
-people on ABC
-people on none

And 7 equations:
A+AB+AC+ABC = 49
B+AB+BC+ABC = 55
C+AC+BC+ABC = 43
AB+ABC = 18
AC+ABC = 28
ABC = 8
A+B+C+AB+AC+BC+ABC+none = 100

For me we are missing one or two variables here. We don't know the intersection of B and C in order to say how many people are outside of all groups.

this, the more you would be able to know would be the maximum "possible" number of people that didn't use any scholarships, also:

Find out how many students use at least one type of scholarship.

i c wut he did tharr

Well Shidoshi I just assumed none used both Academic Credits and Private Scholarships at the same time. That's pretty much exactly as the problem came.

Edit: I mean, none used AC + PS beside those poor 8 people who used all three.

You can choose anything from 0 intersection between B and C or 15 people on the intersection.

That changes your answer from 99 to 100.

I'm not sure how you're getting your answers.

BUT WAIT A MINUTE. COULD I HAVE DONE A MATRIX?!

Edit: Nvm on Matrix I saw your equations and got excited.

What is sure:
A = 11
AB = 10
AC = 20
ABC = 8

From that we take that:
C+BC = 15
B+BC = 37
B+C+BC = 51 (we have 51 more sophomores to distribute around)

So either we take BC = 15 and we have B = 12 and C = 0, leaving us with 14 students without scholarships.

Or we take the other extreme at BC = 1, C = 14, B = 36, leaving us with 0 students without scholarships.

Or anything inbetween.

8 ABC

(18-8) = 10 AB
(28-8) = 20 AC
(x-8) = x-8 BC

(49-(18-8)-(28-8)-8) = 11 A
(55-(18-8)-(x-8)-8) = 45-x B
(43-(28-8)-(x-8)-8) = 23-x C

8+10+20+x-8+11+45-x+23-x = 109-x = total students with scholarships

100-(109-x) = x-9 = total students without scholarships

Which also leads me to conclude that BC can be anywhere between 15 and 1... `-`

I like Wob's answer better. The answer I got after rushing was that 85 students had some form of scholarship. I remember getting 11 A, but then after that I rushed and don't remember what I did.

Btw Shidoshi the number 100 is like a max. It doesn't mean 100 people got scholarships.

Btw Shidoshi the number 100 is like a max. It doesn't mean 100 people got scholarships.

What? My answer is pretty much the same as wobbufet's.

ABC=8
JUST AB=10
JUST AC=20
JUST A=11
JUST B=37
JUST C=15
The total is101? how but I know I did that right are you sure the numbers are right? and Wobbufet there IS no students who got both B and C otherwise the problem would have said so or ask how many took just B and C

Or the answer is 55, like it says, and you're overthinking it.

Find out how many students use at least one type of scholarship.
55 people used Private Scholarships
18 people used both Government Grants and Private Scholarships
28 people used both Government Grants and Academic Credits
8 people used all three

18+28+8 = 54 + 1 person who was purely private scholarship = 55.

Never rule out semantic traps. It didn't ask how many received financial aid as worded, it asked how many of them were on scholarships.

Or the answer is 55, like it says, and you're overthinking it.



18+28+8 = 54 + 1 person who was purely private scholarship = 55.

Never rule out semantic traps. It didn't ask how many received financial aid as worded, it asked how many of them were on scholarships.

this, the more you would be able to know would be the maximum "possible" number of people that didn't use any scholarships, also:

Find out how many students use at least one type of scholarship.

i c wut he did tharr

which is the only thing i could really figure xD didn't notice the fact that they only mentioned 55 scholarship, and the rest wasn't scholarships.
so i guess that makes the answer 55? it would truly make this a "logic" question instead of a math one

I asked a very similar problem here once too, it's like a page or 2 back on a thread:

A number of tokens (Red, white and blue) is given among 100 people. 45 people get red tokens, 45 receive white tokens and 60 people get blue ones. 15 people get Red and white, 25 get blue and white, 20 people get red and blue and 5 people get of every color. How many people are left without any tokens?

The simplest way to get it seemed to be a venn diagram. (circles that contain eachother)

I asked a very similar problem here once too, it's like a page or 2 back on a thread:

The simplest way to get it seemed to be a venn diagram. (circles that contain eachother)

Problem for him is that there is one less hint given and one more possible group (none) so the problem does not have only one answer.

I asked a very similar problem here once too, it's like a page or 2 back on a thread:

The simplest way to get it seemed to be a venn diagram. (circles that contain eachother)

Except that thread has drifted into oblivion apparently.

What was the answer to that one again?

Except that thread has drifted into oblivion apparently.

What was the answer to that one again?

5 had no tokens.

NO EOS NO I REFUSE TO ACCEPT THAT. *starts crying*

I don't think it's like that though.

But yeah, this thing is crazy. Don't worry guys you only have 9 days until I can tell you what the teacher said.

Unless someone can figure it out now.