Discrete Math
posted by Ajun
A professor gave his 40 students a test with three questions. Every student answered at least one question. Ten didn't answer the first question. 14 didn't answer the second question. 12 didn't answer the third question. If 18 students answered all three questions, how many answered exactly one question?
Thanks for your help

Scott
t = two answers , x = one answer
(3 * 40)  (3 * 18)  10  14  12 = 2 t + x
40  18 = t + x
solve the system for x 
MathMate
Another way to solve.
Let
A=# of students who answered the first question
B=# of students who answered the second question
C=# of students who answered the third question
Then
we are given
B+CB∩C = 10
A+CA∩C = 14
A+BA∩B = 12
Add three equations
2A+2B+2C(A∩B+B∩C+C∩A)=36....(1)
But the total number who answered one OR two question is 4018=22, or
A+B+CA∩B B∩CC∩A=22.....(2)
(1)(2)
A+B+C=3622=14
Respond to this Question
Similar Questions

Math
In a multiplechoice test, each question has five options. Students will get 5 points for each correct answer; lose 2 point for each incorrect answer; and receive no points for unanswered questions. A student does not know the correct … 
Mathprobability
In a multiplechoice test, each question has five options. Students will get 5 points for each correct answer; lose 2 point for each incorrect answer; and receive no points for unanswered questions. A student does not know the correct … 
Math
In a multiplechoice test, each question has five options. Students will get 5 points for each correct answer; lose 2 point for each incorrect answer; and receive no points for unanswered questions. A student does not know the correct … 
Math
I need help with the second question: A student is taking a multiple choice exam. There are five possible answers for each question. What is the probability the student will answer the first question correctly? 
math
Beth Dahlke is taking a ten question multiple choice test for which each question has three answer choice only one of which is correct. Beth decides on answers by rolling a fair die and making the first answer choice if the die shows … 
math
Beth Dahlke is taking a ten question multiple choice test for which each question has three answer choice only one of which is correct. Beth decides on answers by rolling a fair die and making the first answer choice if the die shows … 
math
A professor gave his 40 students a test with three questions. Every student answered at least one question. Ten student did not answer the first question, 14 did not answer the second question, and 12 did not answer the third question. … 
probabilities
A multiple choice test has 16 questions. Each question has 4 possible answers with only one is correct. Assume that all questions are answered and the probability to answer any question correctly is 0.25. Let X be the number of questions … 
English
There are three teams in a classroom. 1. This question is for Team 1. 2. Only Team 2 can answer this question. 22. Only students in Team 2 can answer this question. (Do we have to put 'the' before 'students'? 
MATH
Sally is evaluating some test papers. There are 80 multiple choice questions in the test. Students get two points for every correct answer and for every wrong answer or any question left blank, one point is deducted from the total …