Chapter 9 The Rest of the Story TYING UP LOOSE ENDS So here it is the last chapter about quantitative topics on the GRE Most of the material we review in this chapter will probably appear less frequently on the GRE and most of it deals with data analysis There are a lot of formulas in this chapter that you d do well to memorize because it will save you a considerable amount of time when you sit down to take the test Let s begin FUNCTIONS Sometimes the GRE will make up a mathematical operator You will see some weird shape which you ve never seen in a math problem and be asked to solve a problem using this weird shape This is simply the GRE trying to confuse you These questions are asking about functions A function is simply a set of directions For instance think of the word chop in a recipe The word chop is actually telling you to do many things take out a cutting board rinse the vegetable or fruit to be chopped take out a knife place the vegetable on the cutting board etc If a recipe says Chop 3 carrots then you must do all those things that chopping entails but using carrots If the recipe says Chop 2 stalks of celery then you must do all of those chopping things but with celery A function is the same way It is a set of rules and the GRE will ask you to perform those rules on a certain number If the GRE invents some function for instance that x 4x 2 and then asks what 5 is then figure out what rules you need to follow The original function was x but notice how 5 replaced the x that was after the with a 5 Well do the same thing with the equation given for x Replace each x with a 5 You get 5 4 5 2 20 2 22 Try a practice problem Look for what numbers you ll need to place in the original function and where each number will go Here s How to Crack It Here you have a completely made up mathematical operator This question says that whenever you see a you must find the sum of all the prime integers between those two numbers Rather than write out all the primes and figure out which numbers you could pick to get 17 try PITA As you plug in each answer choice find the sum of all the prime integers between those two numbers So 1 10 is the sum of all the prime integers between 1 and 10 which is 2 3 5 7 17 so A is an answer Since 4 10 5 7 12 cross off B Since 6 12 7 11 18 cross off C For the last answer the only prime integer between 14 and 18 is 17 and since the sum of 17 and nothing is 17 D is also an answer The answers are therefore A and D You may also see function questions of the form f x x2 5 In that case if they ask for f 3 then wherever there used to be an x in the original function put a 3 f 3 32 5 9 5 14 Whenever you see something unfamiliar on a GRE question look to see if the question itself tells you what to do and follow those directions FACTORIALS The term n is referred to as n factorial and whenever a factorial shows up on the GRE it pertains to the number of ways a number of elements can be chosen or arranged We ll discuss this further when we get to the section on arrangements and combinations a little later But for now The term n read as n factorial represents the product of all integers from n to 1 inclusive For example 5 5 4 3 2 1 or 120 Factorial questions can look like they require more work than they really do This is because you can usually cancel a lot of numbers and make a huge sequence of multiplications into something much more manageable Here s an example Here s How to Crack It When evaluating Quantity A it might look like you re about to spend 10 minutes multiplying all those numbers on your calculator Break the fraction down first though and you ll see that all but one of the numbers cancels out As you can see you can cancel out everything from the 23 on and you re left with 24 Quantity B also equals 24 4 3 2 1 so the answer is C Sometimes however a GRE question will involve adding or subtracting factorials In that case you re going to have to factor Here s How to Crack It 15 is too large to enter into the calculator so factor out what 15 and 14 have in common Since 15 is the same as 15 14 13 12 11 10 and 14 is 14 13 12 11 rewrite 15 as 15 14 Both 15 14 and 14 contain 14 so rewrite the fraction as Note that if you distributed the 14 to each term within the parentheses you d have back the original numerator 15 14 You can simplify the 15 1 inside the parentheses to get Now it s time to cancel out the two factorials as you did with the previous example question 196 Factorials Quick Quiz or 25 Explanations for Factorials Quick Quiz 1 The first term is equivalent to 25 24 and the second term equals Therefore the final term is 2 All of the answer choices are equivalent to 6 or 720 except E because is the same as Because 12 11 10 is already 1 320 it s possible to see that this is far bigger than 720 without even bothering with your calculator The answer is E 3 Since there are no variables in this question eliminate D There are factorials combined with subtraction so you re going to have to factor 17 is the same as 17 16 15 14 You can therefore rewrite Quantity A as 17 16 15 14 14 Since you have 14 in both terms factor out 14 to get 14 17 16 15 1 Now it s time for a bit of calculator work which gives you 14 4 080 1 14 4 079 Both quantities have 14 so focus on the other parts Since 4 079 is larger than 4 078 14 4 079 is larger than 4 078 14 and the answer is A 4 There are variables in the answer choices and question stem so Plug In Pick a number that is easy to work with for n such as n 5 If n 5 then the target answer can be found by reducing the expression in the question stem The question stem now reads which if expanded reduces to 6 5 4 120 which is the target answer Now plug in 5 for all values of n in the answer choices and see which results in a value of 120 Choice A …