The PSAT/SAT & ACT are notorious for asking complicated questions about seemingly simple concepts; this is one reason the PSAT & SAT Math sections can be so difficult. Following College Compass’ Math Sample Questions will help you understand the concepts behind the questions.
The Baltimore Ravens score a touchdown on 25% of all their possessions and the San Francisco 49ers score a touchdown on 20% of all their possessions. Given that neither team goes for two points after any touchdown and that no point after touchdown field goals are missed, who will win the game and what will the score be if the Baltimore Ravens have 16 total possessions and the San Francisco 49ers have 20 total possessions?
This is a fairly easy statistics questions. The easiest way to approach this kind of problem is to convert the percentages into fractions you can actually use:
25% = 25/100 = 1/4
20% = 20/100 = 1/5
Now that you know the number of touchdowns per possessions, you can figure out how many times each team will score:
Ravens: (1/4) x 16 = (16/4) = 4
49ers: (1/5) x 20 = (20/5) = 4
By now it is obvious that regulation play will end in tie, but for the sake of being complete let’s figure out how many points each team scored:
Ravens: 4 touchdowns x 7 points per TD = 28 points
49ers: 4 touchdowns x 7 points per TD = 28 points
It’s a tie? That can’t be right, looks like we’re going to overtime!
It’s the second possession of overtime and the 49ers have driven down the field to somewhere between the 5 and 50 yard lines. If David Akers, the kicker for the 49ers, starts with an automatic 20% chance of making a field goal from anywhere on the field, and his aggregate chance increases 5% for every 5 yards the 49ers advance beyond the 50 yard line, how many yards must the 49ers advance, beyond the 50 yard line, to give Akers a 50% of completing a field goal?
A little more difficult of a problem, but nothing you can’t handle. The first thing to do is create a formula that reflects the problem you’ve been given.
We know David Akers has an automatic 20% chance of successfully kicking a field from anywhere on the field, and that the likelihood of him making a field goal increases 5% for every 5 yards in he is from the fifty yard line. Now, think about the relationship of 5% for every 5 yards; essentially, for every one yard in David Aker’s chances of making a field goal go up 1%:
20 + (50 – 1x) = 50
50 – x = 30
-x = -20
(-x = -20) (-1)
x = 20
That’s right David Akers has to make it to the 20 yard line to have even a 50% chance of successfully making a field goal! In the funky world of inaccurate and blatantly false sports statistics, that makes him a terrible kicker.