A Memorizable List of GMAT Quant Content (Quantent)
Even though there’s no “new math” on GMAT Quant, there is still a ton of content to keep on our radar. And just like the tragic studying for a vocab test, we’ll have to learn 200 different things, even though the test is going to only ask us 31 of those things (because we don’t know which 31 things we’ll get asked on our test day).
How are we going to keep all that stuff in our brain at once? It takes most students at least a couple weeks to cycle through 200 different GMAT Quant problems, so by the time you’re doing the 200th problem, it’s usually been a few weeks since you’ve seen the content on the first 10 problems.
In order to take quicker laps around the GMAT Quant universe, you want to make some of your practice feel like you’re studying for a vocab test. We can take a lap through 200 vocab flashcards much more quickly than we can through 200 GMAT Quant problems.
Instead of having vocab flashcards with Word on one side and Definition on the other, we’ll have GMAT Quant flashcards that have Topic/Stimulus on one side, and First Move/First Thought on the other.
If Pavlov can get dogs to salivate in response to a bell, we can get ourselves to break a number down to primes in response to ‘divisibility language.’ But we’ll have to outdo Pavlov, or at least outdo his dogs, by learning way more than just one stimulus/response pairing. Are you all ready to outdo Pavlov’s certain-to-be-dead-by-now dogs?!
(Moment of silence: I hope in doggy heaven, every time the bell rings, you really do get a treat.)
In the rest of Part 1 (of this 2-part post), I’ll get you started with a baker’s dozen topics. Next month, we’ll finish off the list.
Your job: if you see anything you don’t already know with the ease/certainty of a famous actor’s name/face, then commit that fact to flashcard. Quiz yourself on those flashcards at least three times a week. Add your own flashcards as you review problems you’ve tried and see moves you wish you had made, or number properties you wish you would have inferred.
Let us know if you have any questions.
DIVISIBILITY on GMAT Quant
#1 Move: If we see x is divisible by y, x is a multiple of y, y is a factor of x, x/y is an integer, then we break these numbers down to primes.
Divisibility means “the numerator has at least the primes in the denominator.”
“x is divisible by 45” = x has at least 3 * 3 * 5 in it.
“x is not a multiple of 12” = x either has fewer than two 2’s or doesn’t have a 3, or both.
“36 is a factor of 8x” = 2*2*2*x2*2*3*3 = 2*2*2*x2*2*3*3 = 2x3*3 = x has at least 3*3 in it.
#2 Move: If we see a multiplication cluster + integer, then we think about the logic of multiples and ask, “What are both quantities divisible by?”
If we see 14x + 35, we think “both 14x and 35 are divisible by 7,” so 14x +35 is divisible by 7.
a multiple of 7 + a multiple of 7 = a multiple of 7
If we see 7! + 15, we think “both 7! and 15 are divisible by 5,” so 7! + 15 is divisible by 5.
STATISTICS on GMAT Quant
If we’re talking median,
- arrange everything in ascending order
- odd number of data points → median is the middle data point
- even number of data points → median is the average of the two middle data points
If we’re talking average,
- calculate sum (remember… Sum = Avg * # of things)
If we’re talking standard deviation,
- we need to know how far each data point is from the average and how many data points there are
- adding outlier data points (towards or beyond the current extremes) will increase SD
- adding center data points (on or near the average) will decrease SD
ODDS/EVENS on GMAT Quant
#1 Thought: even * anything = even
#2 Thought: Remember or derive the E/O rules for addition/subtraction/multiplication
E +/- E = E E * E = E
E +/- O = O E * O = E
O +/- O = E O * O = O
Usual #1 Move: Take anything with an even coefficient and translate that quantity into E.
3x + 4y is odd → 3x + E = O → 3x = O – E → 3x = O → x = O
Dealing with division facts: If we see “x/y is even,” we write, xy = Even, and then multiply y to the other side to get x = Even (y). This tells us that x is even (we know nothing about y).
Useful Shortcut: If something has an even coefficient, we won’t learn whether that variable is even or odd. The even coefficient will “hide” which type it is.
POSITIVE/NEGATIVE on GMAT Quant
#1 Thought: Keep track of possible words with “pos, neg” or “+, -”
#1 Move: Use the pos/neg properties of addition, subtraction, multiplication, and division to eliminate possible words.
x+y > 0 (at least one positive … eliminate neg/neg)
x+y < 0 (at least one negative … eliminate pos/pos)
x-y > 0 (x > y … eliminate neg/pos)
x-y < 0 (x < y … eliminate pos/neg)
xy > 0 or x/y > 0 (same sign … must be pos/pos or neg/neg)
xy < 0 or x/y < 0 (opposite signs … must be pos/neg or neg/pos)
Useful Shortcut: If something has an even exponent, we won’t learn whether that variable is positive or negative. The even exponent will “hide” which type it is.
DECIMALS on GMAT Quant
#1 Move: Clean it up by multiplying by a power of 10.
If we see 0.0045, we write 45 * 10-4
#2 Move: Line up the decimals, add zeros where necessary, then remove the decimal.
If we see 1.2/.03, we write 1.20/0.03 = 120/3 = 40.
UNITS DIGITS on GMAT Quant
#1 Move: Write out the pattern for that units digit. Example: What’s the units digit of 6345?
Write out the pattern for powers of 3 (the patterns are either a constant digit, a cycle of 2, or a cycle of 4).
3¹ ends in 3
3² ends in 9
3³ ends in 7
34 ends in 1
—————-
35 ends in 3
36 ends in 9
37 ends in 7
38 ends in 1
Since every power that’s a multiple of 4 will end in 1, 344 = ends in a 1.
So 345 = ends in a 3, so the units digit of 6345 is 3.
EXPONENTS/ROOTS on GMAT Quant
#1 Move: If any of the bases aren’t currently prime, break the bases down to primes.
If we see 14x * 10y * 85 = 2³² * 5z+1 * 74
Then our next move is: 2x 7x * 2y 5y * (2³)5 = 2³² * 5z+1 * 74
#2 Move: If the problem involves addition or subtraction, we need to factor something out.
If we see 2³² – 230
Then our next move is: 230 (2² – 1) = 230 (3).
INEQUALITIES on GMAT Quant
#1 Thought: Watch out for negatives! (When we multiply or divide by a negative, we have to flip the sign. We shouldn’t multiply or divide by variables unless we know their sign.)
#2 Thought: If it deals with exponents and inequalities, try fractions between 0 and 1, and maybe also fractions between -1 and 0 (numbers between 0 and 1 are the only numbers in the universe where x² < x).
#3 Thought: If we have two inequalities, line up the inequality sign and add them to each other.
ALGEBRAIC STORY PROBLEMS on GMAT Quant
#1 Thought: Should I just backsolve, rather than translating the story into variables/equations and trying to solve that way?
#2 Thought: If I’m going to translate, let me do so carefully.
is (or any other verb) → “=”
of → “multiply”
percent → /100
“There are” → the coefficient goes on the 2nd thing
(“There are 2/3 as many boys as girls” → B = 2/3 G)
LINEAR ALGEBRA on GMAT Quant
#1 Thought: Am I solving for one variable or two (a “Combo”)?
We can solve systems of equations by substitution (isolate some variable or expression in one equation and then substitute the other side of the equation into the second equation).
Or we can solve systems of equations by elimination (stack the equations on top of each other, scale one or both of them up so that the coefficient of one of the variables is the same number, then add or subtract the two equations in order to eliminate the same-numbered variable).
Solving for a Combo, like “What is 3x + 2y?” means that instead of trying to get x = ___ , y = ____ and then plugging those values in for x and y, we should be trying to get 3x + 2y = _____.
TRAP AWARENESS on GMAT Quant
When the two DS statements show you a pair of equations with the same two variables, the answer is almost never C (we refer to that as “the C trap”).
Sometimes, it’s NOT solvable (the answer is E) because the two equations are actually the same equation, if we simplified or scaled them up/down.
What’s the value of x?
1) 3x + 2y = 40
2) 9x – 120 = -6y
(Answer: E)
Other times, it’s solvable with only one statement (the answer is A or B) because one of the statements gives us an equation that we could manipulate into showing us the value of the Combo we’re looking for.
What’s the value of 3x + 2y?
1) 9x – 120 = -6y
2) 5x + 4y = 12
(Answer: A)
More to come next month! ?
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Patrick Tyrrell is a Manhattan Prep instructor based in Los Angeles, California. He has a B.A. in philosophy, a 780 on the GMAT, and relentless enthusiasm for his work. In addition to teaching test prep since 2006, he’s also an avid songwriter/musician. Check out Patrick’s upcoming GMAT courses here!