Answer Choices
a > b
b > a
|a| > |b|
a = - b
Explanation for Question 18 From the Math (Calc) Section on the Official Sat Practice Test 1
So question number 18 says that in the X, 2 Y plane, if zero comma zero is the solution to the system of equation 3 system of inequalities above which of the following relationships between a and B 4 must be true. So let's look at this first, 5 let's look at the top one. It says, Y is less than negative X 6 plus a and zero comma zero is a solution. 7 So what it's saying is zero is less than zero plus a. 8 So whatever this is has to be greater than zero, 9 right? And so that means the a has to be positive and 10 it must be positive because if a was zero, 11 this wouldn't be true, right? Because zero is not less than zero. 12 Zero is equal to zero. And if a were negative, 13 then this side of the equation would actually be less than zero, 14 not greater than zero. So a has to be positive. 15 Now let's look at the bottom equation. Y is greater than X plus B, 16 and now let's plug in the zero comma zero. 17 We got zero, oops. 18 Zero is greater than zero plus B. 19 So now we can see that this equation has kind of been flipped, 20 right, right. Now we're trying to make this less than zero, 21 right? Cause zero greater than whatever this is. 22 And if I want that side of the equation to be less than zero, 23 then I actually need be to be negative. 24 Because if B is negative, this will be smaller than zero, 25 which will make that equation equation true. 26 And now if a is positive and B is negative, 27 then we know the a must always be greater than B. 28 Right? Cause positives will always be bigger than negative numbers. 29 And that's how we land on a correct answer of a.