[Video] Q8: If a/b =2 what is the value of 4b/a3

Explanation for Question 8 From the Math (No Calc) Section on the Official Sat Practice Test 1

So number eight tells us the eight divided by B is equal to two. 2 And then we want to figure out what the value of four B over 3 a is. So we can think about this, 4 uh, quantity for B over a is really being four times B over 5 a and so a good strategy here. It would be to find out what 6 B over a is, and then multiply that by four. 7 So now we know that a over B is two, right? 8 So if we want to be over a, we just have to manipulate this 9 equation so that we can flip the variables around. 10 So maybe we can start by multiplying both sides by B that'll get B 11 out of, uh, out of the denominator and into a numerator on the right 12 side of the equation. So a is equal to two times B. 13 Now, if I want a, to be a, my denominator, 14 I need to divide both sides by a, 15 so now I get one is equal to two times B over a right, 16 and here is my B over a, I just need to get rid of 17 that too. 18 I can do that. Oops, by dividing both sides by two. 19 So now I've gotten the B over a is equal to one half. 20 Um, and so that's the math and you can always do that. 21 Math. Another thing you can think about is that they've taken our original order 22 of the fraction and flipped it, right? 23 They've taken the inverse. They've made it the reciprocal. 24 And so you can do the same thing with the two. We can just 25 flip the two, because two is two over one, 26 right? This is really two over one. All we need to do is flip 27 it to get that one over to now, 28 back up here. If we know that B over a is one half, 29 then we can do four times one half, and that gives us two. 30 So our best answer is going to be C.