GRE Math things to remember
was the author objective and respectful? or were they biased in favor of the subject?
"the passage teems with positive words...the neutral aspect would be incorrect"
an x intercept is 4. what is the coordinate?
(4, 0) Y is zero for an x-intercept and vice versa
Facile
(adj.) easily done or attained; superficial; ready, fluent; easily shown but not sincerely felt too simplistic or easy
truculent
(adj.) fierce and cruel; aggressive; deadly, destructive; scathingly harsh
scintillating
(adj., part.) sparkling, twinkling, exceptionally brilliant (applied to mental or personal qualities)
what is 0.32*0.2?
0.064! NOT 0.64
how many factors are there for 52?
1 and 52 2 and 26 4 and 13 no others, 6 total. break into primes, make sure you're writing out all possibilities. you can go number by number to check yourself
2 things to be careful of if you are doing revenue/profit questions
1) are you putting in total price, or price per unit into the equation? 2) did they ask for REVENUE or profit?
You are given angle, and arc length. How do you find the area of the "shaded region" (e.g., 135 degrees and 15pi)
1) find what the ratio of the shaded region to the area of the circle is. in this case, it would be 135/360 = 27/72 = 3/8 2) recognize that must be the ratio of the arc length to the circumference (e.g., 15pi/C = 3/8) 3) Use this to find the full circumference. in this case, 120pi/3 = 40pi 4) Use the full circumference to find the diameter. in this case, 40pi = pi*d. So, d = 40. 5) Find the full area of the circle using the diameter. In this case, r = 20 so A = 400pi 6) Take the appropriate ratio of the full area. In this case, 400pi * 3 = 1200pi, then 1200pi/8 = 150pi 150pi is the answer!
"it may be tempting to do 360 - the angle, but notice the unlabeled angle!" What would you have had to do instead?
1. recognize that the unlabeled angle is 35 degrees as well (opposite angles) 2. do 360 - 35 - 35 = 290!
In 2010, the average tuition at Upper Lower State University was $12,000; after that, it was steadily increasing at an annual rate of 3%. If this trend continued, what was the approximate average tuition in 2020?
12,000 X (1.03) (12,000 X (1.03))(1.03) in general: 12,000 X (1.03)^N, where N is the number of years into the future. in this problem, 12,000 X (1.03)^10. You could make the calculator easier on yourself by doing ((1.03)^2)^5), and so on.
Quick! whats 39-25-17?
14 - 17 = -3 you can't just do whatever order you want when it's subtraction!
the function f(x) has the property that f(x)=f(x+1). If f(4) = 17, what is f(8)?
17! f(x) = f(x+1) tells you that "the input doesn't matter" so, f(8) will equal whatever f(4) is. an example of such an equation would be y = 17 (its the same no matter what you put into the x!)
pattern for the units digit of 3 when 3 is only being raised to an exponent
3, 9, 7, 1
Pythagorean triples
3,4,5 5,12,13 8,15,17 7,24,25
Quick! whats 39-(25-17)?
39 - 8 = 31
volume of a sphere
4/3πr³
how many possible products are there if we roll 3 dice?
6 * 6 * 6 = 216!
pattern for the units digit of 7 when 7 is only being raised to an exponent
7, 9, 3, 1
Area of a parallelogram
A=bh but note that h has to be the perpendicular line, not the "slant height"
t or f: if you are dividing a number and you want to get an integer, the number you divide by has to be an integer
FALSE! I could divide anything by .5 and double it
t or f: a multiple of 2 numbers can be less than one of those numbers
FALSE, fool! That could make your life easier on some of these problems
Multiple nCk 's?
Find each separate piece, and multiply them together
How to check if a number is prime
If it's under 100, you are probably safe if you just check whether the number is divisible by 2, 3, 5, 7, 11
what do you need in order to check that something is implied by the passage?
Is there direct proof? Remember that even a passage mentioning a law that was passed does not include in it's scope the motivation behind why lawmakers did that, etc.
formula for arc length
L = (x/360)∙2πr
How many positive integers less than 100 have a remainder of 2 when divided by 13?
List them out just like you did on the test. 15, 28, 41, 54, 67, 80, 93 But there's one more! 2! 2/13 is 0 with a remainder of 2.
can you cross multiply if the relationship between two quantities is uncertain?
NO you can only cross multiply if equal
say you have an inequality and a variable in the denominator. Should you multiply both sides by that denominator to cancel?
NO! B/c we can't be sure if the variable is positive or not (and multiplying could change the sign, etc.)
is 4-pi greater than 1?
NO! because pi is greater than 3!
A number is chosen at random from the first 100 positive multiples of 5. What is the probability that the chosen number is also a multiple of 3?
Notice that to be a multiple of 5 & 3, it has to be a multiple of 15. Max number is 5 X 100 = 500 how many 15s can we fit into 500? About 33 33/100 = the answer!
probability of A or B but not both
P(A) + P(B) - 2* P(A and B) Think about the venn diagram!
probability of A or B
P(A) + P(B) - P(A and B)
t or f: x% of y = y% of x
TRUE! this becomes clear when we see (x/100)*y = (y/100)*x
Not sure which order to do % change with on a graph?
They went from left to right in terms of the bar graph in a review question
How many positive divisors are there for 9?
Three! 1, 3, 9 You might be tempted to say 4 because of 1, 3, 3, 9 in your list, but I assure you this isn't right!
facile
Too simplistic or easy
T or F: in a circle, an inscribed right angle intercepts the endpoints of a diameter
True!
Clyde drove 30 miles in 20 minutes, and then drove an additional 10 miles in 10 minutes. What was his average speed?
We want to calculate this as (total miles) over (total time). If you do it in pieces and then average, you'll miss the fact that the two parts of the trip are not equal in size. 40mi/30min = 80mi in 1 hour and that's it!
Choice A states that the x-intercept is twice the y-intercept. Can we conclude that both intercepts have the same sign? What does that imply about the slope of the given line?
Yes, we can! The line has a negative slope!
how many ways can you arrange the letters in mississippi?
You can do it your way, or you can do: 11!/ (4!) (4!) (2!) total over repeats! you can apply this to other situations, too. How many ways can I arrange 2 heads in a group of 5 coin flips? same as, "how many ways can I spell TTTHH"? well: 5!/(2!) (3!)
x and y are integers greater than 5. x is y percent of x2 relationship between x and 10?
You got this wrong because you thought of an example with 5 and 20. The thing is, though, that 5 doesn't work for x AND y being greater than 5.
What did you do wrong with the "multiple pumps working to fill a tank" question?
You solved for the time it would take to fill a WHOLE tank. But they wanted just HALF of the tank.
why did you get that circle/line/triangle question wrong?
You thought that the angle between the two line was 90 degrees, but that's not necessarily guaranteed. So, you thought we were in a hypotenuse-of-a-right-triangle situation. In reality, that angle could vary and the line in question could be much smaller or much larger.
rout
an overwhelming defeat
boondoggle
an unnecessary, wasteful project
imperious
arrogantly domineering or overbearing
a skewed distribution has a tail on the right. which is bigger, median or average?
average! "average follows the tail"
solopsistic
believing that oneself is all that exists
you messed up a question on one of the quizzes because you failed to see that a small positive number is greater than a large negative number. take your time!
blerg
trick when thinking about rules for multiples
break into the prime factorization!
interred
buried
how can you tell if something is a multiple of 4?
check out the last 2 digits!
strategy for "at least how many...."
choose numbers and work through examples, but choose small numbers/think about the pattern.
normal distribution, they gave you the 60th and 90th percentile. Is the value for the 75th percentile closest to the value of the 60th percentile, or the 90th percentile?
closer to the value of the 60th! numbers in a normal distribution bunch towards the center
probability of choosing 3 things out of a group, etc
desired out of total * desired out of (total-1) * desired out of (total-2) you only multiply by the exact same probability if you are repeating independent events
If x>0, and two sides of a certain triangle have lengths 2x+1 and 3x+4 respectively, which of the following could be the length of the third side of the triangle?
difference< side < sum x+3 < side < 5x+5 plug in x=1 into this and into the answer choices to have easy bounds to work with! here's what you did wrong--you added/subtracted x+1 instead of 2x+1
strategy for the quantitative comparison
does this hold for negative numbers, positive numbers, and zero?
remember that triangle where you thought you were fancy thinking "oh, "a" is in the 3rd quadrant, so it must be negative?"
don't even trip. just do top - bottom, left - right as you initially thought. The negative numbers will still be able to go in there.
ersatz
fake
erstwhile
former
another way to think about permutations and combinations
how many ways can I order around members of a group? ex: I want to know how many ways I can arrange 2 H and 3 T in a group of 5 That's 5 C 2!
if x is a number such that 0<x<=20, for how many values of x is 20/x an integer?
infinite amount!!!
T or F: if they're asking about a rule and it's a numeric entry question, what should be true?
it should work with any example you plug in (there is only one correct answer!)
fact about stats in equally spaced sets?
mean = median! example: sum of integers 1 - 7 = mean * 7 = 28 example: 7 * median = 7 * 4 = 28 the former is really helpful for adding up numbers (say 1- 100). Just remember that it is only true for evenly spaced sets
a skewed distribution has a tail on the left. which is bigger, median or average?
median! "average follows the tail"
making an odd number
multiply by an odd number, add or subtract 1, add an even number and an odd number
nCk formula
n!/[k!*(n-k)!]
fealty
obligated loyalty or faithfulness
sartorial
of or relating to a tailor or to tailoring
sometimes you tend to think of things in terms of "any number"
pay attention to specific restrictions. maybe they would have restricted to "consecutive odd integers" or something
what does "non-negative" mean?
positive OR zero!
strategy for dealing with remainder questions on the GRE:
put in a few real numbers as examples/walk through it!
which is a bigger payout? 10% applied 5 times, or 50% now?
remember that with compounding the base changes. in the former, we get the 10% pieces applied to a bigger and bigger base each time (more of a total payout) in the latter, we get the full 50% times the smallest base in this scenario (the original amount)
which is a bigger discount? 10% applied 5 times, or 50% up front?
remember that with compounding the base changes. so in the former, we get the 10% pieces applied to a smaller and smaller base each time (less of a total discount) in the latter, we get the full 50% times the largest base possible (the original amount)
you had a hard time with the vegetarian meal question. what was the right way to go about it, and why was your initial way wrong?
right way was to do (all possible groups) - (groups that have only meat) AKA 9C3 - 4C3 you forgot that the formula for a combination has the k in the denominator, too. your original strategy for solving this was wrong because you were treating the "vegetarian phase" as unique even though it wasn't!
extirpated
root out and destroy completely
you took a long time on an inequality question --what was ETS' way of working around this?
solve as an equation with a "?" instead of an "=" make a judgement based on the information given then reverse the steps/go back to get to the original comparison
they tell you to solve for something in terms of b and y, but the diagram of those odd triangles was showing you b, y, and x. What did you need to do to solve?
structure equations/substitute so as to get rid of x! also, remember that an exterior angle of a triangle is equal to: sum of the two inside opposite angles, or: 180 - (180 - a -b) [if you look at the algebra above you'll see that this is the same thing]
v + w - 4 = x + y - 5 which is greater, the average of v and w, or the average of x+y?
the average of v and w is (v+w)/2 the average of x and y is (x+y)/2 notice that v+w = x+y-1 the right side tells us that v+w is SMALLER than x+y. So, the average of v and w will be smaller than the average of x and y
you have two distributions. both are symmetric, and have the same values on the x axis. but, one is u shaped and one is bell shaped. which one has the smaller standard deviation?
the bell shaped one! this is the same as asking the question, "which one has more of their numbers closer to the average"?
hoi polloi
the common people; the masses
a triangle is inscribed in a circle with a 90 degree angle. what is the hypotenuse equal to?
the diameter of the circle!
what was the mistake you made with the "how much money molly made this summer?" question?
the question told you that every two weeks she was paid $1 + the previous weeks all combined. You had done $1 + the previous week (singular) over the course of the periods
Concept: if perimeter is held constant, what kind of rectangle maximizes area?
the rectangle that is closest to a square! same for triangles, ovals, etc...
property of sides of a triangle
the remaining 2 sides must be bigger than the 3rd side
The remainder when dividing something by 10 always equals what?
the units digit of whatever that "something" was! 18 / 10 = 1 with a remainder of 8
there are 16 points on a circle. how many triangles can be inscribed with these points?
this is really just 16C3 17!/ (13!) (3!) = (16x15x14) / (3x2x1) = (16x5x7) = 16x35 = 560
feign
to pretend show a fake!
recapitulate
to review a series of facts; to sum up
solving "parts of a whole" questions
total = group A + group B - both + neither
t or f: if x were increased by 20%, decreased by 25%, then increased by 60%, it would be multiplied by 1.2, 0.75, and 1.6 (1.44 when all multiplied together)
true even if you just picked an example and walked through it you would see that this is true
t or f: if n is an integer and you are looking at n^3, then for every prime factor n has, there must be three of them (prime factors coming in triples?)
true!
what will give you the maximum number of combinations? (nCk?)
whatever k is right in the middle! the extremes aren't very big say you had 8 things 8C8= 8!/8! = 1 8C1 = 8!/1!(8-1)! = 8 meanwhile, 8C4 = 8!/4! 4! = 70
when are combinations and permutations helpful?
when figuring out the total number of ways that we could pick something overall. For example, I have 5 numbers. What's the probability that when I choose 3 of those numbers, the product is positive? numerator will be case dependent/you'll just have to walk through it, but the denominator is just 5 C 3! 5! / 3! (2!) = 5*4 / 2 = 10
wag
wit, joker
if a and b are 2 multiples of x, is a+b a multiple of x?
yes! a*6 + b*6 = 6*(a+b)
what's something you could think of doing if substitution or elimination seem to be taking a while?
you could add or subtract the two equations from each other! especially helpful if you have two terms whose coefficients switch, etc. (e.g., 3x+4y and 4x+3y)
what was the mistake you made in the "maximize the last person's contribution" problem?
you forgot to subtract the total you created from the larger relevant total. Your answer for this was not meant to be the total you created (351) but instead the last donation only (450 -351 = 99)
Wording! Be careful if--
you found a % but they really want to know about the number
