# GRE Quantitative Reasoning

Let`s go ahead and now take a look at practice test one and focus on the quantitative reasoning section of the exam I`m gonna actually go over all the questions of this exam so just in case you`re stuck and of course you can go ahead on YouTube and look at the description below I`m going to go over the entire exam but if you`re stuck on question 7 and question 14 just go ahead and look at the description below and just click on question 7 and 14 to save some time so question number one it`s say X plus y is equal to 16 and y plus 4 is equal to 10 all right so how do you approach this problem right this is what the quantitative comparisons and if I if you remember from the overview video I told you that you should automatically remember what astroids a as choice B C and D already stand for answer choice a is always quantity a or cough sorry column a is always greater than column B and so choice B would always be column B is greater than column a and then as choice C is that both columns are equal or both the values are equal and D is not enough information cannot be determined we don`t know so let`s go ahead and take a look at the first four questions of the exam question 1 again I have two variables at on the first equation over here and I have y plus 4 is equal to 10 with only one variable since it becomes very easy y plus 4 is equal to 10 so let`s go ahead and deal with the second equation and I automatically can tell that I can subtract by both sides right you want to isolate for the variable right this is your front of foundation of algebra if you`re missing this please go back in our test prep book and review the algebra chapter so y is equal to 6 so Y is equal to 6 all right and now this makes this a question very easy I know that Y is equal to 6 so I can plug that in so this equation becomes now X plus 6 is equal to 16 remember the golden rule of algebra you want to isolate the variable how do I do that I want to subtract 6 from both sides so I can have X by itself so I subtract 6 subtract 6 this of course cancels out X is equal to 10 now you`re not done.

What does column a is asking you and look at column a look at column B column a is telling you what is greater column a is X and then column what B is y so what is greater so Y is 6 x is 10 obviously X is greater so the answer choice would be that column a is, in fact, greater than column B let`s take a look at question number 2 a is less than B but B is less than 0.

That means that B has to be a negative number and it must also be a negative number so let`s go ahead and just you know so whenever you`re given a situation like this I like to use hypothetical numbers so what`s a value less than 0 let`s say negative 1 so let`s say B is negative 1 so negative 1 and then a must be lower than negative 1 so let`s just say negative 2.

Now what`s column a after you column a is saying the absolute value of B and then column B is telling you absolute value of a so let`s see a is negative 2 so a is equal to negative 2 however if I do the absolute value sign I`ll get that a is equal to 2 if I take the absolute value sign of V V is over here remember this is B this is a B is negative 1 right B is equal to negative 1 but if I take the absolute value of negative 1 I`m given just 1 so in this scenario over here right because this is what my columns are determining what`s greater is a greater or b greater it turns out that actually a is always greater right because I have positive 2 here compresses to a positive 1, therefore, this is greater since this is in column B the answer choice is a B that column B is greater than column a let`s take a look at question number 3 question number 3 you have x squared is equal to 16.

Column a is saying what`s the value of x or Combes saying negative 4 white what`s greater right are they equal can you not determine the information let`s go and take a look at this right right off the back some people might go you know very very quickly oh this is easy x squared is equal to 16 4 squared is 16 X is equal to 4 right but don`t you know don`t act too quick remember this rule right don`t forget that x squared is equal to 16 if you square both sides X can actually be plus or minus 4 remember that .

It can even plus 4 or negative 4 positive or negative 4 so we have two values we don`t know actually whether it`s 4 or negative 4 so we`re kind of stuck here essentially right we have no idea what the pathway if what if this column is greater than this column right maybe it`s negative 4 maybe it`s 4 and therefore automatically the answer choice is d cannot be determined question number 4 over here I have a circle I`m given that the radius is 10 centimeters.

Column a asks you for the area okay I hope you remember that the area of a circle is PI R squared the radius is 10 so 10 squared times pi which is a hundred pi versus two to the eighth power now here you can go ahead and go to your calculator and plug in two times two times two eight times but hopefully you know you take a look at the chart on our book and you should actually memorize two to the eighth powers to 56 right that shows up economy that`s pretty common two to the eighth you should already have in your head if not go ahead ease your calculator so 256 versus 100 PI once again you don`t really need a calculator for this question I know that pi is equal to 3.14 so what`s a hundred times 3.14 that`s about 314 right 314 versus 256 what`s greater of course the area of the circle over here so the answer is going to be that calm a is greater than column B therefore the answer for this question would be any so now question number five the sum of Q acute angles versus 90 degrees right which column is greater right so the sum of two to tangle well what is an acute angle what is the definition of an acute angle an acute angle defined of any angle less than 90 degrees.

Less than nine degrees versus 90 degrees and you know what I bet a lot of students already are you know drop the gun and say well hey some of two acute angles well less than ninety but if I add two angles less than ninety degrees it must be great at ninety and a lot of students will fall for it very quickly and choose column it`s greater but that`s not true you have no idea what the sum of two acute angles are what if I told you the one angle was five degrees and the other angle was ten degrees right some of that is fifteen degrees and which makes a column B greater right so you have no idea the answer for this question is actually D because we don`t have enough information we don`t know the angles of both of the the two acute angles over here so the answer choice is d hopefully did not go for answer choice a let`s go ahead and take a look at question number six we have a graph over here please don`t mind my poorly written hand-drawn graph over here but column a is asking you it`s giving you the value three-fourths column B is telling you find the slope with you know which value is greater right which column is greater well let`s take a look at slope how do you find slope hopefully you know the slope formula by heart it`s y2 minus y1 over x2 minus x1 and you should certainly find the slope which is noted as M over here so first before you do this go ahead and find the coordinates right the two quarters that were given so hopefully you know how to read an XY coordinate graph the first point let`s pick it over here so we`re going to go along the x axis first so it`s one two three and four so the X is four and then we`re going up two therefore the value of the fruit the place of where the first coordinate is is 4 comma 2 and then we`re given this corner over here so we`re going to go over once again and read along the x-axis go along two places and go down 1 2 3 4 but this is the fourth quad remember this is all negative so this is negative 4 and now once again even if you`re an expert what I`d like to do is always I like to label that this is X 1 this is y 1 this is X 2 this is y 2 ok and now I can easily plug it to my formula what`s Y 2 y 2 is negative 4 negative 4 minus y 1 is 2 all over what`s X 2 X – 2 – 4 negative 4 minus 2 is negative 6 2 minus 4 is negative 2 and I get that negative 6 divided by negative 2 is reduced to 3 now what`s greater 3 or 3/4 well I think that`s pretty obvious 3 is definitely greater than 3/4 and therefore column B is greater the answer choice is B let`s go and take a look at question number 7 we`re given a blue glass marbles and six red glass marbles and we`re going to go ahead and pick was it`s two marbles out of the bag and in column a your situation your scenario given is what`s the probability of choosing to read glass marbles right so you`re picking one first and then without replacing the marble you`re picking another Marvel what`s the chance of you getting to read glass marbles first is your probability of choosing a blue glass marble plus then a red glass marble so how do you go ahead and do this right this is probability.

Some students don`t actually like this topic okay these since your since we`re not since we`re taking a marble out and not putting it back in right these are two separate they`re these are independent moves right so we have to multiply basically and first what do we do we want to go ahead and find out our denominator right our problem what are we working with here so we have 8 plus 6 all together in a back so we have what is it 14 marbles 8 or blue 6 or red and the probability of us are drawing our first red glass marble is going to be a 6 and 14 chances right because there are six red marbles but now if I take one red marble right I reduce one from the back so now there`s 13 marbles left and well now instead of six red marbles there`s only five red marbles left and there you go you have to go ahead and do this 6 times 5 is 30 14 times 13 will give you 182 and now you have to compare it versus the probability of drawing a blue and then red so once again similarly I have 14 marbles again and my chance of drawing my first blue marble be eight out of 14 chances times a red remember we still have six red glass marbles in this situation so it would be six over thirteen because now we`ve lost a blue marble over here right so 8 times 6 is 48 14 times 13 is 182 and if you go ahead and reduce the fractions using your calculator you will find out that column B is indeed greater than column a therefore your answer is answer choice B question 4 9 y is not equal to 0 what is pod right what which one of these extra system must be positive please keep in mind write this answer choice may have either one and one correct answer choice or most many right in the textbook we`ve labeled it as circle and then square just so just to you know make sure that you guys know that there can be potentially more than one possible answer that`s correct well actually there has to be two or more if y is not equal to 0 what is positive answer choice a is absolute value of y any time you see something with an absolute value the resulting express the resulting answer will always be positive so therefore a must be correct how about Y to the negative 2nd power right you have to recall the laws of exponents right y to the negative 2 you can go ahead and write this as 1 Y to 1 over Y squared right remember anytime of a negative exponent it becomes positive in the denominator and 1 over Y squared so if it`s negative Y it`ll still be positive if it`s if it`s Y is positive it`ll still be positive and 1 over any positive number it will still be a positive number right it might be a small number but nonetheless it will be a positive number therefore answer choice B is correct answer choice C y squared times y to the negative fourth common bases so now we just have to use the laws of exponents so I`m going to add the exponents since I have common bases so 2 plus minus 4 gives us Y to the negative 2 and once again it`s same exact thing right Y to the negative 2 is 1 over Y squared once again I know that it will always result in a positive number why to the zero anything raised to the zero power is always equal to 1 remember that is 1 a positive number of course it is check answer choice e 1 to the Y`s the negative 5th power right remember uh here`s this is a tricky situation over here.

I`ll tell you why this is a negative x this it`s not a problem that this is a negative exponent the problem here is that this 5 is an odd number the exponent is odd what does that mean remember this right so I can go ahead and actually convert this to Y to the 5th right 1 over Y to the negative the same as just watch the 5th this numbers easier to work with I mean this this looks much nicer so let`s go ahead and work with that if Y is 1 well then 1 to the 5th power is a positive number which is good but what if Y is negative 1 right negative 1 raised to the 5th power is negative 1 remember any time you have a odd exponent and a negative base that means that your result will be actually a negative number so in this case we`re not sure if it`s positive or negative because it could be either so answer choice is not a correct answer and then lastly answer choice F Y for the two parenthesis to the 3rd power once again a lot of the vector this question really tests whether you know all the rules of exponents and then in this situation whenever you have this the rule is you must multiply right because it`s being Y to the 2 raised to the power of 3 and the rule is you just multiply simply the exponents which becomes Y to the sixth and of course that results in a positive number because we have an even exponent and the answer choice is going to be f to the end the correct answer is ABCDE and F ok let`s take a look at questions number 10 you`re going 60 miles an hour between 10:30 well not 60 miles an hour sorry you`re actually just going 60 miles you just traveled 60 miles between 10:30 a.m. and 1:45 p.m. what is or how many miles are you going per hour so basically this is a distance over time problem so you can go ahead and get the miles per hour so I know I went sixty miles and now I simply have to find the time this is a simple problem right so what`s the time between 10:30 and 1:45 well pretty simple right 10:30 11:30 12:30 1:30 so it`s three hours and then I have 15 minutes remaining right to three hours and 15 minutes but hopefully you know that you have to convert this 15 minutes by the hours and hopefully you know that each 15 minutes is equal to point 25 right 1/4 of an hour so this is actually just 3.25 over 60 which results in 14 points something 14 point 7 or 8 or something like that and the answer choice should be C 18.5 right you`ll get something that is rounded to eighteen point five.

Question number 11 we`re given an expression over here and you have to simplify this expression XY 2/3 z to the zero power and your denominator reads X to the 3rd Y to the fourth right off the back you want to go ahead and make your life easier I know right off the back anything raised to the zero power is simply 1 ok and anything times 1 is just it`s the number over here we have so I can just cross this off I don`t really care about that this is nothing.

Let`s cross that off okay because we don`t have a Z over here I have X Y to the third so let me use a red color mark over here X Y to the third once again the laws of exponents you must know it.

So this is x times y raised to the third power and if you wanted to if you want to do that you have to understand that X is being raised to the third power and Y is being rich to the third power so it`s actually X to the third times y to the third all over X to the third times y to the fourth and this promised ly works out very nicely X to the third cancels out with X to the third we`re left with just 1 and then watch a third and watch the fourth once again common bases if I`m if I`m dividing fractions I`m going to go ahead and subtract exponents so 3 minus 1 sorry 3 minuses 4 is negative one so it becomes to watch the negative one or it simply becomes so Y to the negative one is also the same thing as one over Y right make sure you know the laws of exponents right go back to the map manual to write the math primer and make sure you know how to do this.

Y to the negative one power is the same as one to the Y to the positive one power so the answer is just one over Y question number twelve Pythagorean theorem.

Once again this is extremely easy question Chancellor, If you won`t be you won`t see a question that is this easy they`ll definitely give you values that you actually have to do the work and if you know right off the back this is a perfect pie diagram triplet so it`s a 3 4 5 triangle but if you don`t know it let`s go ahead and actually use the formula so we have a right triangle over here anytime you see a right triangle and you`re missing a leg go ahead and write down the equation of Pythagorean theorem a squared plus B squared is equal to C squared where C squared is always a hypotenuse right the hypotenuse is opposite to the right angle and it is actually the largest side.

I know that this is five right what`s five is C squared five or C five right this is a this can be either A or B doesn`t really matter but this is C so this is C let`s just say this is a and this is B.

I know that a is three so it`s three squared plus B well we don`t know this is a variable so this is B squared is equal to 5 squared so that`s 3 squared is 9 9 plus B squared is equal to 25 you want to isolate the variable right so I`ll subtract 9 from both sides and I`ll be left with B squared is equal to 16 and then I can square both sides and get B is equal to 4 right B is equal to 4 and that`s my answer let`s go and look at question number 13 question number 13 reads which one the following could be an integer which one the following could be an integer let`s look at answer choice a so anytime you see this run down each answer choice these average of two consecutive integers, first of all, you have to know what and second it means right consecutive goes in order one two five six nine ten let`s see two plus one is three divided by two is right is that an integer no it`s not right the average.

I hope you know the average for me right the sum of numbers over the number of numbers is equal to the average right so you probably know this-this is you know this is pretty easy you can do it in your head once again 10 plus 9 is 19 19 divided by 2 once again does not result in an integer right you get something point five.

Because the number is odd right anything divided by 2 if it`s not even you-you’re not going to go ahead and get an integer so it does not answer choice an answer is B the average of eight consecutive integers well.

Well let`s just go ahead and what I mean what this is this this no this question really relies on you understanding the number three but let`s forget and say you have no idea what the number theory even is so just go ahead and make your life easy and use hypothetical values right one two three four five six seven eight one two three four five six seven eight eight consecutive integers so uh what so you have one through eight and now you can go ahead and add it up so eight plus seven plus six plus five four three two one gives you 36 all over eight and that results in 4.5 and of course 4.5 it`s not an integer right 4.5 and on an integer there for answer choice B is long correct answer choice series the average of 8 and 11 11 plus 8 is 19 19 divided by 2 already I know that 19 is odd number and any odd number divided by 2 will not result in an integer answer choice D reads the average of three consecutive integers right so the average of three consecutive integers let`s go ahead and [Music] one two three three plus two is five 5 plus 1 is 6 6 divided by 3 is 2 Wow that works out right so this works out so you can go ahead and check for various different examples and you`ll see that indeed you always result in in an integer n short II read average of 11 and 22 once again 21 plus 11 is going to be 20 to 30 33 and then 33 once again it`s odd number and the odd number divided by 2 does not result in an integer so the answer choice is going to be d question number 14 for X my parentheses X minus 1 is equal to X plus 8 you have to use the distributive property so 4 times X and then 4 times negative 1/4 times X is 4x minus 4 times 1 is 4 is equal to X plus 8 I want to isolate and solve for the variable so I will move minus X minus X this cancels out I`m left with 3x is equal to so I`ll do plus 4 here and plus 4 here and I get 12 I can go ahead and divide both sides by 3 X is equal to 4 so the answer would be a s choice a ok so let`s take a look at question number 15 right after a 20 percent discount a bookstore a recipe book sells for $10 what was the original price of the book so we have a 20% discount and the sale price is $10 and the question is asking what is the original price right ok so this is what you do ok you have to remember the formula.

Anytime you write this you`re trying to find the original price so it`s not so simple you know I have a shirt that`s $100 I have a 50% discount so I simply do a hundred times 2.5 and I get that it`s going to be $50 discounted right it`s not as simple as that but it still is simple ok so anytime you get that you want to use equation where you use 100% minus your discount which is going to be 20% 20% discount times the original price well equal to your sale price right think about it for a second.

Think about this for a second right a hundred minus 20 so I know there`s a 20% discount okay and if I do a hundred minus twenty percent of my original price I`ll get the sale price and I know my cell price already which is ten dollars right and in this case my variable will be the original price .

This is my original price times 100% minus twenty percent is eighty percent but please don`t go ahead and write this on your scrap paper eighty percent you have to convert that into decimal right so it`s point eight times X so it`s point eight X its equal to ten dollars and then you will go ahead and solve for x point eight right divided by 0.8 by both sides X is equal to 0.8 is divided by ten use your calculator it`s going to be twelve point five right twelve points five $12.50 that`s that will be your original price this is how you solve the problem let`s go ahead and question look at question number 16 question umber 16 reads the average of a and B is 16.

Average of a plus B is equal to 16 and the average of a plus B plus C is equal to 20 to find the value of C right what is C, I actually love these kinds of problems right this relies you to use the average formula what is the average formula sum of numbers once again where sum of numbers over a number of numbers is equal to the average

If you don`t do this formula you can easily mess up.

Why take a look at this it`s saying a plus B is not equal to 16 think some I`m a equals B the average of a and B is 16 the average of a B and C is 22.

I can go ahead and find out what can I find out all right can you go ahead to this equation I have the average I have the sum of I have the number of numbers basically and this is what I can do so I have a and B and I know that I have to basically and I can go ahead and find out the sum very easily 16 times 2 is 32 so a plus B is 32 so this is my sum the sum of a and B is 32 the average is 16 and then a plus B plus C the if the average is 22 I can use this formula how many numbers do I have on top it`s 3 so 22 I can go and cross multiply 22 times 3 is 66 so a plus B plus C is equal to 66 so this question doesn`t really rely you to find out what a is equal to or what single simply B is equal to so you can find out what C is equal to I know that a plus B is 32 right a plus B is 32 so I can plug it in right a plus B what`s a plus B I know it is 32 32 plus C is equal to 66 right ignore this and it becomes very easy I have just one variable minus 32 minus 32 C is equal to 4 and 3 and 34 c is equal to 34 which is answer choice C so that`s the correct answer let`s say question look at question number 17 do we have space on this board yeah I`ll cram it.

Hopefully it`s not too messy question number 17 reads which of the following is the slope of a line of the perpendicular line 3x plus 5y is equal to 10 two things you have to know first how do you get the perpendicular line and second is what is the formula actually you should know the line formula is y is equal to MX plus B because right now it is not in this form so right now it`s pretty ugly you can`t really do anything with it so right off the back the first step is to make sure you convert it to this so I want to basically isolate for what I want to solve for y so I`m going to move everything to the right side so it`s going to be 5 y is equal to minus 3x plus 10 right all I did was subtract 3x from both sides and now I`m going to divide by 5 because I want Y by itself so Y is equal to negative 3x plus 10 over 5 or right so now because you have to know the freshen rules right let`s make it let`s make it more simple right it could be this is the same thing as negative 3x over 5 plus 10 over 5 right I can go ahead and separate these two because I`m adding so they`re actually two different terms well they`re like terms but I can go ahead and separate them and well ten divided by five is simply two so this becomes negative 3x over five plus two why did this now why is it 2 MX plus B M is the slope what is the slope here slope happens to be negative three over five right so the slope for this problem is negative three over five but the question is asking you what is a slope of the perpendicular line anytime you go ahead and see a question that`s asked me to find the perpendicular line you have to go ahead and take the reciprocal.

Negate okay so what do you do you negate and take the reciprocal so if it`s negative three or five I`m negating a negative term which is a positive and I`m going to flip this so it becomes positive five over three.

The slope of the perpendicular line to this equation over here is going to be 5 over 3 which is answered choice B.