Answer Choices
150
200
250
300
Explanation for Question 3 From the Math (Calc) Section on the Official Sat Practice Test 8
So question three tells us that we have a random sample of 200 cars 2 of a particular model and three have a manufacturing defect. 3 So three are defected, right? And they want to know at this rate, 4 how many of the 10,000 cars of the same model will have a manufacturing 5 defect? And so this is an example of a proportions problem 6 proportions. And the way that we know this is that first we're given a 7 rate, right? We're given three defects for 8 every 200 cars. That's our first rate. 9 And then in the second part of the problem, they give us only one 10 of the numbers and we have to solve for the other number and the 11 rate, right? And so here, they tell us 10,000 cars, 12 we know how many cars, but we don't know how many 13 defects. And so that's our variable. And the first thing that we need to 14 know when we're sending up proportions is that whatever unit you put on the 15 top needs to be on the top for both fractions and whatever unit 16 you put on the bottom needs to be on the bottom for both fractions. 17 So you don't get the, switch it up and put defects in the numerator 18 for one, and then defects in the denominator. 19 We have to be consistent with that. And so that's the most important thing 20 as far as setup. And then the next step is just the solve the 21 equation. And we can do that first by cross multiplying that 22 way we can get rid of our fractions because the fraction is make it 23 a little more difficult to work with the numbers, right? 24 So three times 10,000 is going to be 30,000 25 and X times 200 is going to be 200 X 26 and now to solve for X. All I have to do is divide both 27 sides by 200, these two hundreds we'll cancel these 28 zeros. We'll cancel 300 divided by two is 150. 29 So our answer is 150 equals X. 30 So a.