Explanation for Question 16 From the Math (Calc) Section on the Official Sat Practice Test 10
Now for number 16, we're looking at the question that says in 2015 city, 2 X and city, Y had equal populations. 3 All right. So in 2015, X was equal to Y. 4 And that says from 2010 to 2015 city X increased 5 by 20%. Right? 6 And then it tells us that citywide decreased by 10%. 7 So if they eventually become equal in 2015, 8 this tells us that X must've started out smaller. 9 And why must have started out bigger, right? 10 Since X has to increase and Y has decrease. 11 And then it says, if the population of city X was 120,000 12 in 2010, what is the population of city? 13 Y in 2010? So let's look at city X, 14 first stuff. We don't know what city X was in 2015, 15 we'll call that big X, but we know that in 2010, 16 it was 120,000. And then we know that it increased by 17 20% right now, 18 but increased by 20%, the find the rate you need to 19 do one plus the 0.2, 20 right? 21 So 1.2, 120,000 times 1.2 22 would give us our X in 2015. 23 And the reason you knew 1.2, rather than just 0.2, 24 and you can plug this in your calculator to check is that if you 25 do times 0.2, you get a smaller number. 26 You get 24,000. And if the answer was 24,000, 27 then that would mean the X had decreased not increased. 28 So we put the one because it's like, we're taking the initial value, 29 the one, and then we're adding that 20%. 30 We're increasing it by 20%. So when you do 120,000 31 times, 1.2, you get the X was one 44,000. 32 The reason that's important is because Y was also the same thing in 2015. 33 So why 144,000 was equal to the 34 initial value of Y which we're going to solve for Y in 2010 times 35 a certain rate. And now this one decreased by 10%. 36 So rather than doing one plus, we're going to do one minus to find 37 the rate because we've decreased and 10% is the decimal point 10 38 and one minus point 10 is 0.9, right? 39 So I'll do 144,000 divided by 0.9 so 40 that I can get why I get that. 41 Y is equal to 160,000, 42 which we see here in answer choice C.