Answer Choices
|x − 1| − 1
|x + 1| + 1
|1 -x| +1
|x − 1| + 1
Explanation for Question 1 From the Math (No Calc) Section on the Official Sat Practice Test 4
So here for number one, we're told that, 2 um, we have some value of X and we need to figure out which 3 of these equations is equal to zero. 4 Right? So all of these equations out of all of them, 5 only one will always be zero. 6 Um, and so what we need to do here right, 7 is first figure out what would that sum value of X be? 8 That's one way we can think about this problem, or we can think a 9 little bit logically about what the absolute value means. 10 Now, if we're taking the absolute value of anything, 11 it's always going to be positive, 12 right? So if I'm starting with something positive and I want to get to 13 zero, right, that means I'm going to have to subtract. 14 And so the only possible answer choice that I can choose here is a, 15 because everything else is taking something positive and adding more to it that just 16 gets us further away from zero. 17 So since B, C, and D are all positive numbers, 18 um, then they can't possibly be the answer because zero is not positive. 19 Now, if we look at a, we can think about how, 20 if X is equal to two, right? I do the absolute value of two 21 minus one, minus one to minus one. 22 That's going to be one. The absolute value of positive one is one and 23 one minus one is zero. So one possible case where a is equal to 24 zero is one X is equal to two, but we have no possible cases 25 where, um, this expression is equal to zero for BC or D.