Math problem SAT?

<p>Is there a fast way to answer these questions without using too much algebra? it took me 10 minutes to solve these.</p>

<p>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

<p>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</p>

<p>F = 3S
F/4 + S/3 = Total number of students at the football game</p>

<p>(F/4 + S/3) / (F + 3S); Plug in 3S for F
(9S/12 + 4S/12) / 4S = 13/48</p>

<p>Or, since the answer choices have the LCD of 48, you can assume that there are 48 total freshmen + seniors.</p>

<p>48 Total;
36 Freshmen; 12 Seniors;
9 Freshmen at the game; 4 Seniors at the game;</p>

<p>13 / 48 = B.</p>

<p>100 students
30 have cars
50 have bicycles
20 have both cars and bicycles;</p>

<p>I find these questions easiest when I draw a venn diagram, but I'll try my best to explain this.</p>

<p>If 30 students have cars, but 20 students have both cars and bicycles, there are 10 students with only cars.</p>

<p>Likewise, if 50 students have bicycles, but 20 students have both cars and bicycles, there are 30 students with only cars.</p>

<p>Therefore, there are 10+30+20=60 students who have some sort of a transportation.
There are 100 - 60 = 40 students without any methods of transportation.</p>

<p>For the first one, to avoid algebra entirely, just make up numbers. To make life easier, pick a number of seniors that divides easily by 3 and also that when tripled, can then be divided evenly by 4. So say there were 12 seniors. That would give you 36 freshman. 12/3 = 4 of the seniors and 36/4 = 9 of the freshman for a total of 13 out of the 48 attending...</p>

<p>If I had chosen a bigger number to start with, it would still work but I would have had to reduce my fraction at the end...</p>

<p>As for the second one: 30 + 50 = 80...but that double-counts the 20 kids with both cars and bikes. So 80 - 20 = 60...leaving 40 with none.</p>