SHSAT Math Problems
So I`m gonna go ahead and post another life support request let`s take a look at question number 59 from practice test two please ignore this practice test one on the screen it`s actually practice test two it`s a typo so question 59 bernard is now y years old okay fantastic so Bernard is y years old Louis is eight years older than Bernard in terms of Y how old was Louis five years ago okay so how old was Louis five years ago right so what information already given at the moment Louis is eight years older than Bernard okay so I`m going to say that L is equal to a plus B but Bernard is now Y years old so instead of B I can go ahead and just say this as eight plus y.
So Lenora ll is sorry so Louis is eight plus y now it`s saying in terms of Y how old was Louis five years ago right so this is not asking for the present time right so it`s asking for five years ago how old was Louis well you know what Louis was still 8 plus y but subtract minus five it because five years ago therefore Louis is well eight minus five is simply three plus y so it`s three plus y or y plus 3 which is answer choice C let`s like a look at question number 60. So in the figure above a b c DB e e f g and c f8 are straight line segments what is the value of x right so what is this value over here looking at the diagram you should automatically realize that DB angles DBA which is what you`re looking for an angle CBE are vertical angles that means that whatever this angle is equal to it means that this angle the same thing and if you look at the other side of the diagram over here angles gah and angle CF e are also a vertical angles meaning that this angle the same as this angle and actually in this case we`re given this angle over here and this angle is 65 degrees if this angle 65 degrees that means that angle CFE which is over here is also 65 degrees so let`s go ahead and write that down 65 degrees now on this side we don`t know what the value of x is and we don`t know what this side is so now we`re you know some sort of predicament but we`re actually not because you know what we know the value of this angle
We know the value of this angle we know the value of this angle and we`re missing this fourth angle over here and this is a four-sided figure and that means that the sum of all the interior angles should equal to 360 degrees so therefore we can set up a simple equation and write x plus 110 degrees plus 110 degrees plus 65 degrees should give us 360 degrees and if we add that all up we have 110 plus 110 which is 220 plus 65 5/8 – and then I can subtract 360 minus 285 and I`ll get five I`ll get a fiber here 15 this becomes a 2 and this becomes a 7 so I have 75 degrees so I know that this angle now is 75 degrees and because this angle and this angle are vertical angles that means that this is 75 degrees but this also is 75 degrees therefore the answer choice is K this X or this of the value of x is 75 degrees question number 61 which of the following shows a fraction 13 337 over 8 and 19 4 and order from the greatest to the least so first of all don`t make that mistake okay the answer is going to be from the order of greatest to least and now we have stuck with these three ugly fractions but how can we go ahead and figure out which one of these fractions has the greatest value right so right away what I`m going to go ahead and do is actually I`m going to go ahead and convert these fractions into mixed fractions so how do I convert 3 and 13 over 3 so this will become into a mixed fraction which three goes into 13 four times and then we`re left with one-third right I hope that in this video you already know how to convert improper fractions to mixed fractions.
I`m going to assume that you know that in this fraction we can convert this and this 8 goes into 37 4 times and we are left with 5 over 8 and then over here for 19 over 4 well 4 goes into 19 4 times and we`re left with 3 over 4 ok so now right off the back you should be able to work with these these mixed numbers 4 so let`s take a look at 3 over 4 is equal to 0.75 right so this is basically 4.75 and 4 over 1/3 well I hope you know that 1/3 is just point 3 3 3 3 3 3 or 3 right so this is 4 point 3 3 3 and then the only freshman that you might have trouble with is 5/8 and if you don`t know that you can simply go ahead and divide with 8 divided by 5 and you get 1 sorry point 1 this becomes a 80 it becomes point 16 so it`s for point 16 and now if you arrange these fractions from the greatest to the least this will be your first fraction
So this is 19 over 4 so if you scroll down your answer key you`ll see that answer choice a is incorrect automatically and so choice B is incorrect answer choice C may be an answer answer choice C answer choice D may be an answer and choice choice E is automatically incorrect and now we can move on to our next one 4.33 happens to be the second greatest fraction which is 13 over 3 and automatically you`ll see that 13 over 3 happens to be the second one to answer choice C is correct so the correct answer choice for number 61 is answer choice C okay so let`s go ahead look at question number 62 if x and y are integers which is always even okay so and these kinds of problems
I always like to use hypothetical numbers so let`s just go ahead and say that X is equal to 1 and Y is equal to 2 let`s take a look at question number F answer choice F X plus y over 2 so that means 1 plus 2 over 2 which is two and three over two is certainly not even it results in 1.5 which is not even therefore f can be automatically crossed out now let`s try to plug into these hypothetical values for G 2 over 1 plus 2 1 plus 2 over 1 is 2 plus 1 which is 3 3 times 2 is 6 and it does result it doesn`t give you an even number but please please just don`t stop there ok you have to use several hypothetical values ok and look at this expression ok I see that I have an X in my denominator so you know what let me make let me let me be evil and say that let`s pick new hypothetical value let`s say X is equal to 5 and let`s say Y is equal to 1 ok because I would like to see what happens when I make my denominator odd ok so I have now 2 times X which is 5 plus y is 1 over 5 and I have two parentheses 6 over 5 so now it`s 6 times 2 is 12 over 5 and automatically you realize that if I do 12 over 5 I do not get a even number I get a decimal okay this is really your under has to do with understanding of number theory ok and if you do if you realize that if I have a add number in my denominator I can`t possibly always result in a even number so G is incorrect H X minus y well this is pretty simple to rule out if well I can simply well x and y are just integers these are the only conditions I`m given I can say that X is equal to 3 and I can say that Y is equal to 2 therefore 3 minus 2 is 1 therefore H does not have to be even how about J two parentheses x plus y two parentheses x plus y ok and if you really understand your number theory you`ll realize that any number multiplied by two will always result in a even number
So I have parentheses around here so it doesn`t matter what these numbers are as long as this as long as this value is being multiplied by two I should always result in an even number okay so automatically this is my answer choice okay you can go ahead and try to plug in any numbers at any number you want for these you can go ahead and put hypothetical values and you`ll always see that J always results in an even number let`s try a real quick well if x squared let`s just say X is equal to 1 and Y is equal to 2 x squared 1 squared is 1 plus 2 squared is 4 4 plus 1 is 5 therefore this is not even so K is also incorrect so correct answer choice for question 62 is J let`s go ahead and connect a look at question number 68 the sum of seven consecutive odd integers is 749 what is the largest of the seven integers you can go ahead and approach this problems two ways I like to use my way which saves a lot more time and I go ahead and use a rule which is the mean is always equal to the median or sorry the yeah the mean is always equal to the median in a consecutive integer series so over here I have the sum of seven consecutive integer is 749 so that means my sum is 7 49 and I have seven numbers what is my average right if you`re confused please refer back to the average formula what is the average formula well the average former is the sum of numbers there are some of numbers over the number of numbers which is equal to the average and if you`re confused please watch my average video an average rule trick`d video
This is a rule over here okay I`m just plugging in the information that I`m given in this problem the sum of seven consecutive integers is 749 therefore my son is 749 and I have seven numbers well then I can go ahead and find out my average well seven 49 divided by 7 is equal to 107 and if I know that my rule is that the mean is equal to the median in a consecutive pattern series I know that a hundred and seven is my middle value how does that help me well guess what I`m looking for seven consecutive odd integers right that means I`m looking for a value that`s one two three four five six set those I don`t know why I did that let me go ahead and erase let me go ahead and rewrite the one two three four five six seven and I know that my middle value is going to be where where`s my middle here`s my middle value right I have three three here on this side three here on this side so my middle value my median value is a hundred and seven okay and I know that they`re asking me that this is a consecutive odd integer series that means that if I if I I know that my next number will be simply plus two which is one oh nine plus two again plus two again right so I have one eleven here one thirteen here and if I want to go backwards I can just subtract by 2 so it`s 105 103-101 and this is my seven consecutive odd integers and if you really would like to please go ahead and add all this up and you should get that the sum of this is 749 but that`s not the point the point is that this is saving me a lot of time okay because what is the question asking what is the largest of the seven integers well the largest is obviously going to be the value in the rightmost section so it`s 113 okay so the answer choice is J what if the answer asked what if the question asked you what is the the lowest value of the seven integers well then in that case the answer would be a hundred and one okay you can go ahead and set this up as a algebraic problem but I think that requires more time if you know this way I think it saves you a significant amount of time and if you really know what you`re doing you can actually do this question in under 30 seconds let`s go ahead and take a look at the next question question number 69 can also be tricky if you`re not careful V is equal to PI R squared times H using the formula above if R is doubled and H is divided what is the ratio of the original volume to the new volume okay fantastic so R is being doubled right so V is equal to PI R squared times H and R is being doubled not R square not pi r-squared nothing just 2 R itself well if I`m doubling are then I can say that basically it will be 2 times or okay and now I can put my square back over here and my PI back over here and if you look at the question again it`s saying that H is being divided by two okay so H is being divided by two so I can say times H over 2 which is equal to V and this is the new volume while this is a very ugly thing let`s go ahead and simplify this down okay I know that 2r squared that means that I have to square both this and this so 2 squared is 4 R squared is simply R square R squared is R squared times pi over a times H over 2 and I can go ahead and simplify that entire thing actually and I can divide this 4 and this 2 and it becomes pi times 2r squared times H or I can go ahead and write 3 I can rewrite that because it doesn`t look so nice I can go ahead and write this as 2 times PI R squared times H and that looks much nicer okay so this is a simplified version and this is my new volume.
Okay and the question is asking what is the ratio of the original volume of the original volume is this PI R squared times H to the new volume and let`s see if we can cross anything out so we can simplify I have a PI here I have a PI here cancelled out R squared R squared H and H so we`re simply left with or if everything is canceled out here then this simply becomes 1 is equal to well everything is cancelled out here we`re only left with 2 so 1/2 well this is not an equal sign all right this is 1 to 2 right this is a proportion right so this is 1 to 2 and the answer choice is answer choice B let`s take a look at question number 70 a yellow cap has a base fare of $350 $350 that`s very expensive three dollars and fifty cents per ride plus 20 cents for each 1/4 mile event if a yellow cab cost $22.50 how many miles long was a ride well we can set up an equation okay so my total cost is $22.50 and I know that my base fare is going to be three dollars and fifty cents plus 20 for each 1/4 of a mile written that means so 20 cents for 1/4 of a mile that means that for a a whole mile how many cents does it cost me right so if I`m multiplying this side by 4 I have to multiply this side by 4 it`s so it`s 80 cents so I know that for every mile I`m spending 80 cents so I can just do point 8 cents for every mile right and I`m going to represent this mile as an X and so now I can go ahead and solve this equation I have to subtract 350 on both sides and then I will take this value and then I will divide this value by 0.8 and I should get that X is equal to 23 point 75 miles I actually won`t show the map yeah you can go ahead and do the math yourself I actually went over this problem in a previous video so double-check if I`m doing this question correctly and hopefully you get the right answer which would be 23 point 75 miles and so choice F question number 71 please check out my previous video I`ve already actually answered this question on a previous live support request and the answer to this question is answered choice B which is $26 question 63 what is the probability that a point chosen will be in the shaded region
Okay please look at this question carefully okay so this is a probability question then we`re saying what is the probability that point chosen will be in the shaded region and this happens to be our shaded region okay so we are given two different values okay we`re given the radius of this side over here which is actually the unshaded portion and this over here which happens to be the in time this is the diameter of so this is the radius of the entire figure over here which is actually very helpful okay well first of all let`s see what you know let`s see how we can duplicate well I know that well this is a probability question so I know that my denominator has to be the entire region okay and how do I find out the area of my entire region well I have to figure out what is my radius right so my radius for this entire thing is why so if my radius is why I can find out I can actually use the formula a is equal to PI R squared so R is simply y so Y squared times pi so the area of this entire figure is PI y squared okay so I can say that my denominator is PI y squared and the probability that the point will be landed in this entire region will be what well it would be pi times y squared minus the white area right – the unshaded region okay and how do I find out the area of my unshaded region well I know that the radius of the unshaded region happens to be X so I can say that my radius is equal to X so I can once again use my formula a is equal to PI R squared or is simply X so it`s x squared times pi so the over here I would subtract it by PI x squared and this would essentially give me the probability of a point that a point could land in a shaded region if I look at my answer key I see nothing that resembles this so I will try to go ahead and further simplify it down and I can pencil out pi right so I can actually rewrite let`s rewrite this equation I can rewrite this as pi y squared over pi Y squared minus PI x squared over pi Y squared and you`ll notice that I can cancel out PI`s over here so I`m left with Y well I could technically cross out Y squared + y squared and this answer becomes 1 minus x squared over Y squared but if you look very carefully there`s actually not any answer choice that resembles that so I can another way to rewrite this is y squared minus x squared over Y squared which happens to be answer choice t but actually actually actually the specialized high school exam I believe simplifies every single question down so you wouldn`t actually see an answer choice like this you would actually see the correct answer choice being like this so my apologies for not simplifying this answer key at the answer all the way down so this is something that you would definitely see on the exam however in this case this is the correct answer to this problem
Let`s go ahead and take a look at the next question question 64 if Q is equal to X plus y so Q is equal to X plus y and X is equal to y plus Z what is Z in terms of Y and Q automatically you should understand that you have to you see you`re given this value over here for a reason okay you want to go ahead and plug this value into this right we know that X is equal to y plus Z therefore let`s go ahead and substitute that entire value into this equation over here so it becomes Q is equal to y plus Z right I`m getting it from here plus y okay this is the same thing it`s U is equal to X plus y so what happens here so Q is equal to y plus y is 2y plus Z and now it sings what is Z in terms of Y and Q so you`re isolating for Z only right so you`re going to go ahead and isolate Z so if I do that I can go ahead and subtract 2y on both sides and it becomes Q minus 2y is equal to Z and we can see that the answer choice is F Q – oh sorry not F that`s Q minus 2x I mean answer choice G Q – – I apologize for that so they correct answer choice G thanks for watching the videos please be sure to check out our book on Amazon to specialize high school test prep books since book comes with five full-length exam with answer explanations along with a manual to go ahead and better prepare you for the exams you will find the link on the video or in the description above have fun studying