Is there a fast way to answer these questions without using too much algebra? it took me 10 minutes to solve these.
At a certain college, the number of freshmen is three times the number of seniors. If 1/4 of the freshmen and 1/3 of the seniors attend a football game, what fraction of the total number of freshmen and seniors attends the game?
A.) 5/24
B.) 13/48
C.) 17/48
D.) 11/24
E.) 23/48
ANSWER: B
At Jones College, there are a total of 100 students. If 30 of the students have cars on campus, and 50 have bicycles, and 20 have both cars and bicycles, then how many students have neither a car nor a bicycle on campus?
A.) 80
B.) 60
C.) 40
D.) 20
E.) 0
Answer: C
At a certain college, the number of freshmen is three times the number of seniors. If 1/4 of the freshmen and 1/3 of the seniors attend a football game, what fraction of the total number of freshmen and seniors attends the game?
A.) 5/24
B.) 13/48
C.) 17/48
D.) 11/24
E.) 23/48
ANSWER: B
At Jones College, there are a total of 100 students. If 30 of the students have cars on campus, and 50 have bicycles, and 20 have both cars and bicycles, then how many students have neither a car nor a bicycle on campus?
A.) 80
B.) 60
C.) 40
D.) 20
E.) 0
Answer: C
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1.) F = freshman
S = seniors
F = 3S
(F/4 + S/3)/(F + S) = (3S/4 + S/3)/(4S) = 3/16 + 1/12 = 13/48
2.) 10 have only cars
30 have only bicycles
Students that have neither cars/bicycles = 100 - 40 - 20 = 40
S = seniors
F = 3S
(F/4 + S/3)/(F + S) = (3S/4 + S/3)/(4S) = 3/16 + 1/12 = 13/48
2.) 10 have only cars
30 have only bicycles
Students that have neither cars/bicycles = 100 - 40 - 20 = 40
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Since you know how to do this, here's a quicker way to do them:
(1) Suppose there are x seniors and 3x freshmen. 3x/4 freshmen come and x/3 seniors come, so the required fraction is:
(3x/4 + x/3)/(x + 3x) = (3/4 + 1/3)/(1 + 3)
= 13/48.
(2) Not considering the students that have both a car and a bicycle, there are 100 - 30 - 50 = 20 students that don't have a car nor a bicycle. This over-counts the actual number by 20 since the people that have both a car and bicycle are counted twice. Thus, the actual number is 20 + 20 = 40.
I hope this helps!
(1) Suppose there are x seniors and 3x freshmen. 3x/4 freshmen come and x/3 seniors come, so the required fraction is:
(3x/4 + x/3)/(x + 3x) = (3/4 + 1/3)/(1 + 3)
= 13/48.
(2) Not considering the students that have both a car and a bicycle, there are 100 - 30 - 50 = 20 students that don't have a car nor a bicycle. This over-counts the actual number by 20 since the people that have both a car and bicycle are counted twice. Thus, the actual number is 20 + 20 = 40.
I hope this helps!
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1/4(3x) + 1/3(x)
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4/4(3x) + 3/3(x)
= 13/48 = B.
x-no. of seniors
this is done as they want to know what fractions attends the game, which is the number attending the game over the total amount. those attending the game equal the top, and total number of freshman and seniors equal the bottom line.
C and B = 20
C only = 30 - 20 = 10
B only = 50 - 20 = 30
have neither a car nor bicycle = 100 - (20 + 10 + 30)
= 100 - 60
= 40 = C.
the trick to this question is to always work with the terms that have things in common first, in this case, cars and bikes would be the first term you should focus on.
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4/4(3x) + 3/3(x)
= 13/48 = B.
x-no. of seniors
this is done as they want to know what fractions attends the game, which is the number attending the game over the total amount. those attending the game equal the top, and total number of freshman and seniors equal the bottom line.
C and B = 20
C only = 30 - 20 = 10
B only = 50 - 20 = 30
have neither a car nor bicycle = 100 - (20 + 10 + 30)
= 100 - 60
= 40 = C.
the trick to this question is to always work with the terms that have things in common first, in this case, cars and bikes would be the first term you should focus on.
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Answer for the last question:
30+50-20=60
students have carson campus+ students have bicycles- students have both cars and bicycles, cause you count them twice
100-60=40
the total of the students-students have bicycles, cars or both= students have neither a car nor a bicycle on campus
30+50-20=60
students have carson campus+ students have bicycles- students have both cars and bicycles, cause you count them twice
100-60=40
the total of the students-students have bicycles, cars or both= students have neither a car nor a bicycle on campus