Explanation for Question 10 From the Math (Calc) Section on the Official Sat Practice Test 9
Question 10 asks us Washington high school randomly selected freshmen, 2 sophomore, junior, and senior students for a survey about potential changes to 3 next year's schedule of students selected for the survey one fourth refreshment, 4 and one third were sophomores. Half of the remaining selected students were juniors. 5 If 336 students were selected for the survey. 6 How many were seniors? Okay. 7 So you can see that I've set up an expression on the left-hand side 8 right here. And that's showing that of all the participants. 9 If you were to add up all the fractions, you'd get one. 10 If you're considering 100% of participants, 11 one fourth of them are freshmen. One third are sophomores and then some unknown 12 fraction are juniors and seniors. 13 So let's figure out what fraction are, 14 juniors and seniors. So to do that, 15 we do one minus one fourth. 16 So subtract one fourth from each side and we would get three fourths 17 and then we'd subtract one third from each side and we would get five 18 over 12. 19 So we know that the fraction of 20 the students survey that were juniors or seniors is five or 12. 21 Then we also know that half of the remain selected students were juniors. 22 So juniors or the fractions can be juniors. 23 Is this going to be five over 12 divided by two? 24 So five or 12 divided by two is going to be equal to five 25 over 24. So now we have two options. 26 We can either go and plug this back in for J and then solve 27 for us. Or knowing that hal...