Quant 3.0 Revisit List Flashcards
You flip a Heads/Tails coin 7 times.
How many different ways can you flip 5 heads?
How many ways can you arrange exactly 5 heads and 2 tails?
7!/((7-2)!2!)
Think about equation after new people move into the town

Don’t forget the muplier!
(13x + 15)/(2x + 120)

The setup gives us the following two equations:
3w + 2p = 35.20
2w + 3p = 30.80
(where w=sand p=soup)
goal: solve for w
What is the first step?

Multiply equations and then Subtract equations to solve for one variable! OFten, may need to multiply by a negative number.
Remember, the goal is to REMOVE a variable, this will help you find what numbers to multiply by! in this case 3, and -2 make w dissappear so you can solve for p, which then lets you solve for w.



How many different equations do . you need to solve this absolute value?

2.
The absolute value will produce the same value in ++ and –; and -+, +- scinarios:
see example here:




My Q:
I think this equation is wrong because if the number of tickets is less than 100, arnaldo gets punished.. how do we write an equation that accounts for this condition? I realize this equation works properly for t > 100, but the question doesn’t guarantee that. I have encountered this dilemma a few times. How should I think about it?
Ben’s Note: The equation only applies for t>100 because there wouldn’t be a bonus otherwise. For t<100 the money earned is just 11t. But the questions on GMAT dont trick you this way – your concern is not a tested trap.
WE CAN SPECIFY t > 100 in the equation’s application.

Solve for r:

remember, when you take the square root of something under the radical, you get the absolute value of something as a result!
When the sqrt(x) operation is being applied to a variable, the sqrt() returns | x | !!!
sqrt of a number is always positive. Ex: sqrt(25) is 5, not |5| !!
sqrt of a squared variable gives absolute value –> because the variable could be negative, and we get 2 answers

Does a tangent line “intersect” a graph that it shares a point with (or is tangent to) ??
YES. at that one point.


What is the first and last numbers in the sequence?

Remember to look for this trap!
1002…1866



even + even =
odd + odd = ?
even + odd + even + odd = ?
EVEN!
unlike multiplication:
odd*odd*odd*odd = odd (all in a sequence must be odd)
even*any_sequence*2*8*3*9*13*17 = even (single even in multiplication sequence makes all even!)
What is the units digit of the answer, even or odd?
Is the answer negative or even?

Answer: -1997
Hope you were thinking “difference of squares” right away.

Factor this bad boy


Rewrite with a base of (3/5)


Anser options:
1,3,5,6,14



E - Neither!
Note: whenever I choose a DS answer, because of “2 equations, 2 variables, therefore must be C”, Check to make sure both equations are UNIQUE equations. Do a verification: see if I can manipulate S2 to look like S1.
In this case, the trap was that both equations were not unique, they were the same equation, therefore, when S1 and S2 are combined, you end up with 1 unique equation and 2 unknowns.
Do we neglect numerators?

No! They make a denominator that appears to be non-terminating, terminating!



Probably need paper, but should be able to derive main takeaway

Given two points, we know the relationship is LINEAR.
This means we can have two equations of y = mx+b, solve for m and b.


remember 3^150 = 3*3^149 = 3*3*3^148! therefore
9*3^148 - 3^148 = 8*3^148
ALSO, just remember simple exponent math. 3^2*3^148 = 3^150… by ADDING exponents













































































































































































