and here we go moving right along to CLT math practice test number one uh question number 91 Alexander claims that he has discovered a law of geometry if the side lengths of a square are doubled then its area must increase by at least four square units which of the following is a counter example that disproves the above statement so if the side lengths of a square are doubled then its area must increase by at least four square units and and the question is which is a counter example that disproves the above statement so what makes it false and I've noticed when looking at these practice tests that especially if I'm at the beginning of the test right this is only question number 11 here on the um on the practice test we haven't gotten into where we're supposed to be at super hard questions so for me to check these right I want to check which of these answer choices makes that statement false I'm going to start with the easiest number so a square when its sides are one is the easiest number for me to find the area area of a square equals length time width or side squared which would just be one squared equals 1 * 1 it's just one and now if I double it if I double the sides and my side is now two right then my area of a square with a side of two of two units would be length * width or side squared 2 * 2 2 squared equal four and I went from one to four I only went up one 2 3 four I only went up by three so I immediately did not increase by at least four square units I only increased by three so that disproves our blue and pink statement that I highlighted disproves that it says nope that's false didn't happen so we don't have to check the rest I noticed that quite a few times on CLT if you start with the easier thing often enough that easier thing will be the answer and now number 92 we've got a classic algebra question which value of x does not yield a true statement in the inequality below we've got the absolute value of x - 5 is greater than zero so which of these down here is not true you've got a couple of ways that you could go about about solving this you could plug in numbers for your X and see okay is that true or no um I'm I'm gonna just go ahead and solve this the classic algebra teacher way here and I'm G to say we got an absolute value inequality so we got to split this off into two inequalities where the first one looks just as it is x - 5 is greater than zero and then your other inequality where it splits off is going to be x minus 5 is something to I mean we don't normally write this but I'm going to put it anyway negative Z what do I say in class when we bring a negative to the inequality party what happens to our inequality it's gonna flip around like this so now we have our two inequalities and we can go ahead and solve and how do we get rid of a minus5 that's right we're going to add it on both sides of our inequality and this first step here for this inequality we'll notice is also the first step for this inequality so while I'm writing over there I'll just write it over here as well both sides of the inequality so this gives me that X is greater than five and X is less negative Z or just just zero + five x is less than five is -5 less than five yeah is 0o less than five yes is five less than five no is five greater than five no is six greater than five yes so the only one that's not a value is X is five and if you didn't want if you didn't want to go through this little rule here with your inequality with me and you just wanted to jump straight into guess and check you could try putting them all in here right5 minus 5 would be1 absolute value of -10 would be 10 is greater than zero that would have been true good thing I did the good thing I did the algebra way here because guess and check might have gotten us into trouble oh no 10 it would have gotten 10 10 is greater than zero if I put zero 0 minus 5 Nega five absolute value negative five is positive five positive five is greater than zero put in the five 5 - 5 is zero 0 is not greater than zero so I still would have got that answer okay and 6 - 5 is 1 absolute value of one is 1 1 is greater than zero so I still would have gotten the same answer or you would have gotten the same answer but you know me I'm gonna I'm going to go the algebra teacher way and also solving it this way might help you with a little bit more of a complex inequality question all right number 19 93 if a and b are positive integers and a is a factor of B which of the following must be false so what must be False A and B are positive integers so that's like whole numbers greater than zero um a is a factor of B so what's an ex example I could use a is a factor of B what is a factor a factor is a number that divides into another number so like how five divides into say 35 I just made up numbers right I just put it in numbers for my excuse me for my variables a divide or a divides into B A is a factor of B 5 divided into 35 so five is a factor of 35 a is greater than b five is greater than 35 that is false b equals a * k for some number K so B 35 = 5 * 7 that's true B is a multiple of a 5 10 15 20 25 30 35 boom there it is multiple that's true B / a is an integer 35 / 5 is s that's an integer true so the only one false is a and how are we doing on time we got five minutes okay where' she go okay one more question before I cut this video number 94 which of the following is not a solution of the given equation so there's two ways you can go about doing this this is similar to question number uh 92 where I said I'm G to solve this question that algebra teacher way um number 94 I think I'll go I'll go opposite mode I'm going to go Mrs Cameron the test taker and I'm going to plug in the numbers which is not a solution of the given equation so if I put in zero for my x's 0 cubed minus oops 9 * 0 = 16 * 0 that's 0 0 Z it's all zeros that is true that zero is a solution next I'm going to plug in one 1 cubed - 9 * 1 = 16 * 1 1 cubed is just 1 minus 9 * 1 is 9 equals 16 that is not true not a solution we have found our not solution pretty quickly I can prove that five is a solution really quickly replace my ones with fives five cubed five five 5 to the power of three means 5 * 5 * 5 5 * 5 is 25 * 5 again is 125 - 9 * 5 is 40 5 = 16 * 5 I know that 5 * 10 is 50 and 5 * 6 is 30 so 5 * 16 is 80 and 125 minus 45 is also equal to 80 so that is a solution so no they're not all solutions only a and C are solutions so B is the not solution so we solve that test taker mode and if you're looking for brownie points then you you want to solve this in algebra teacher mode um you would just like factor that out and say x cubed - 9x bring my 16 to The Other Side by subtracting - 16 x = 0 -9 - 16 gives us X cubed minus 25x = 0 both of these got a x so Factor one out x * x^2 - 25 equal 0 and we know from our special case of um multiplying B binomials that this x^2 minus 25 is x * x - 5 * x + 5 = 0 so we went above and beyond and we found that not only is five a solution right because five minus 5 is zero also NE five would have been a solution Nega five plus 5 would have also been zero so we have gone above and beyond and way over proven our answer