Qant 2.0 Revisit List Flashcards
Break out into S:A and S:W
Double S:A and halve S:W
10^4 ?
10,000
COUNT THE ZEROS!
10^4 ==> 4 Zeros
10^2 = 2 Zeros –> 100
1/15 in decimal?
0.0666667%
is x/s a repeating decimal if s=4?
What is the initial equation to get things rollin’ ?
9/108 = ?
1/12
What’s the equation?
How do you solve:
(12 *3*E9) / (100E6)
?
Problem: (12 *3*E9) / (100E6)
Step 1: (12 *3*E9) / (1E8)
Step 2: (12 *3*E1)
Step 3: (12 *3*10)
Step 4: (120 *30)
Step 5: (3600)
X is m% of Y translates to?
X/Y * 100 = m
simplify: 1/(2^3*5^4)
1/(2^3*5^4) simplifies to 1/(10^3*5)
Simplify:
1/(10^3) * (1/5)^4
= 1/10^3 * (0.2)^4
= 1/10^3 * (10^-1 * 2)^4
= 10^-3 * (10^-4 * 2^4)
= 10^-7 * 16
What’s the equation?
Set up initial equation:
D.
neither.
You score 100% on a final exam, which is worth 60% of your grade. You scored 80% on your midterm, and it is worth 40% of your grade. What is your grade?
= 100*6/10 + 80* 4/10
= 100*3/5 + 80*2/5
=60 + 32
= 92%
BOOM.
12 and 3/8 lbs translates to…
12 + 3/8 lbs.
What is the equation for PERCENT CHANGE (works for both a VALUE and a RATIO)?
(New - Old) / Old
Ex: If I have old=$25 then it becomes new=$75:
(a) what is the percentage increase from old to new?
+200% increase.
A common trap would be to answer the difference ($50)Remeber, this is NOT the difference ($50)
75 is indeed 200% greater than 25.
(b) new is what percent of old?
300%. 75 is 300% of 25!
When we talk about “percent change”, it is a ratio, not just subtraction. (this one is more confusing, because it’s the percent change of a percentage, but it’s the same formula) Suppose your stock is at 100. Then it goes up to 150. To calculate the percent change, we do new- old / old = (150 - 100)/100 = 50/100 = 50%. Similarly, if we had an interest rate of 10% and then it decreased to 5%, we would calculate percent change as (new - old) / old = (5-10) / 10 = -5/10 = -50%.
Percent increase (of a percentage or ratio):
Know when they are asking for a percent increase versus a value change!
8^(1/3) translates to: what cubed = 8 ?
ex: x^3 = 8, or algebraically: x=8^(1/3) => x^3 = 8.
Simplify
(0.2)^2 = ?
0.04
4^3 = ?
4*4*4 = 64
How to find the sqrt(576) ?
Step 1: Prime Factor 576 into 2^6 + 3^2
Step 2: Sqrt is the multiplication of half of powers, therefore sqrt(576) = 2^3 * 3^1 = 8*3 = 24
What is the initial step/setup?
http://www.wolframalpha.com/input/?i=(+sqrt(x%5E2)+%3C+sqrt(100)+%3C+sqrt(+y%5E2))
Assuming x and y are positive
do this in your head:
sqrt(225) = ?
15
15^2 = 225
y=x is the “Perpendicular Bisector” of line sebment AB
this means that y=x forms a 90 degree angle with respect to AB, and y=x splits AB right down the middle.
Remeber: if I know 1 side, and 2 angles, or 2 sides, and 1 angle, I can solve the triangle !
Remember that the four angles in a quadrilateral always add up to 360. Also, when two straight lines intersect, The sum of the two resulting angles on each side summed up = 180
Remember –> TWO solutions ==> INSUFFICIENT when looking for “A VALUE” for n. (1) is insufficient.
B
REMEMBER: THE STEM SAYS BOTH MUST BE POSITIVE! Common mistake!
Think about the first step, then read the solution
Do first step, then read answer
Think about first step, and the process, then flip and read solution
Answer me this: if Newspaper A’s revenue = r% of newspaper revenue, what is Newspaper B’s revenue?
Likewise, what is b’s percentage sold?
For newspaper B:
revenue = (1-r)%
percentage sold = (1-p)%
Note: since these were given as a PERCENT, if we do any equation (see solution) we need to remember to divide by 100. Ex: (1-r)/100 for revenue percentage conversion.
S:A:W
2:50:100
How do we double S:A = 2:50, and Half S:W = 2:100?
How do we double S:A = 2:50:
2*(2/50) = (4/50) = 4:50
, and Half S:W = 2:100:
(2/100) * (1/2) = (1/100) = 1:100
NOTE: behaves just like ratios! Do multiplication in ratios!
Remember, if A is literally proportional to B and B is linearly proportional to C, then A is linearly proportional to C. Therefore, given values for A and C I can derive a relationship between them.
Might be tough to do in your head:
Remember, there is some hidden knowledge in these A*10 + B Units/Tens digits problems: WE KNOW that:
1 <= A <= 9
1 <= B <= 9
HUGELY IMPORTANT!
First Step: How do you add rates? What is the equation for R(a and b) ?
You add RATES strait up! Time is inverted when you add. Ex:
1/(Time(a and b)) = 1/ta + 1/tb
Rate(a and b) = Ra + Rb
Note the units of rate are Nails/Hr in the problem. Units of time is hrs.
READ THE QUESTION! A is the answer.
26.5
x 52
What is the first step in this multiplication?
1) make 26.5 => 265, (DO NOT MULTIPLY THE DECIMAL!!)
2) then multiply everything out
3) after doing addition then move the decimal over!
If (x/y) = (1/2)
then x is what percent of the total?
x / (x+y) = 1 (2+1) = 1/3 = 33%
A certain bookcase has 2 shelves of books. On the upper shelf, the book with the greatest number of pages has 400 pages. On the lower shelf, the book with the least number of pages has 475 pages. What is the median number of pages for all of the books on the 2 shelves?
(1) There are 25 books on the upper shelf.
(2) There are 24 books on the lower shelf.
List M = 4, 6, 8, 10, 12, 14, 16, 18, 20, 22
Find the KEY assumption: HINT: READ THE PROBLEM!
May need pen and paper…
READ! TRICKY BASTARDS!
B is answer.
for W = nRT problems, given Ra and Rb, how do we combine them?
Translate: “n^2 is divisible by 72”
This means that n^2 is a multiple of 72.
Hint: What do we think of when we have SUBTRACTION of shapes?
SUBTRACTION. this is the clue to see here.
64*sqrt(3) - 32pi
32pi is likely area of circles… 64*sqrt(3) likely area of triangle
Think about it for a few minutes, then read solution!
Think about for a sec.. then flip
I want you to see the algebraic solving going on. Refresh memory of how to solve (2/3)*x = x^2
BE ON WATCH FOR INTEGER CONSTRAINTS when DS problem has indivisible things:
a pattern I’ve noticed:
a) cannot be divided (coins, people, etc.)
b) greater than zero (people, coins, etc)… can’t have negative people!
Do the rephrase only:
rephrase to ad < cb.
Ratios with inequalities are hard to deal with!
Remember to try and come up with BOUNDS for things. I don’t know what the cubed root of (-9) is, however I do know that:
cubed root of -8 = -2 and cubed root of -27 = -3, therefore I know:
-3 < cubed root of -9 < -2
Moral of the story: Try to find bounds for things if you are stuck finding values.
Step 1: find 0’s in the numerator
simplify 4x^2+36x-144
4(x^2 +9x -36)
simplify: 4(x^2 +9x -36)
4(x+12)(x-3)
rephrase for 1?
a and b different signs
note: A and B cannot equal zero!
rephrase for the question?
plug in and simplify!
he - ht = ?
Also, write that this is a combo problem.
quick mental math:
9.3 > sqrt(66) ?
9.3 > sqrt(66) ?
Well,
sqrt(64)
8
therefore, YES,
N! / (r1! * r2!)
Indistinguishable items must be divided away!
There are 5 seats in a theatre : _ _ _ _ _
2 of the people–Marcus and Colin–cannot ever sit next to each other.
How many different seating arrangements can there be?
ways_5_people_sit_with_marcus_colin_sit_adjacent + ways_5_people_sit_with_marcus_colin_not_sit_adjacent = ways_5_people_sit
ways_5_people_sit_with_marcus_colin_not_sit_adjacent = 5! - 4!
note: how is ways_5_people_sit_with_marcus_colin_sit_adjacent 4! ? Because, we can think of MC in: MC _ _ _ as ONE unit.
answer: 5! - 4!.
BOOM.
How many different ways can 6 people be ordered on a 6-person bench?
6! ways.
Permutation: 6 choose 6 = 6!/(6-6)! = 6!/1! = 6!
how to translate S1 ?
(x choose 2) / (15 choose 2),
where x is the number of right handers out of the 15.
remember: P(no left handers) = P(two right handers)
What is “the trick”
hint: it involves the numerator
trick: assume the unique diamond has already been chosen and reduce the number we are choosing from! Since we know
answer= (5 choose 2) / (6 choose 3)
