Quant Flashcards
large SD means numbers in set are
Far apart
If you add numbers farther away from the mean, SD will
increase
Does SD ever stay the same if you add numbers to a set?
no
If you multiply a set by 0.8, SD changes by
if you add 10 to each number in a set, the SD changes by
.8SD
SD stays the same
Absolute value
Complex abs val where there’s multiple, like |4x-7| = |x-8|, what’s x?
”- Only need to solve for 2 scenarios, both are positive, any one is - /+; like x-2 = 2x-3, and x-2 = - (2x-3)
- DON’T FORGET TO PLUG BACK IN TO CHECK”
DS Don’t forget to test which number?
“1; practice starting with 1 unless it’s not allowed
- Helps you get faster with testing cases”
Equations 2 variables in 1 equation
Can’t solve if you have 2 variables
Equations If you have multiple equations, you can; ie xy=2, yz=3, xz=4
Multiple, add, subtract together; ie x^2y^2z^2=24
Equations If problem asks for what the smallest possible value is, |37-5y|
”- Signal: 5y is a divisor, so you can think of 0, 5
- Other strategy is to test number”
(2^3) / (5^3) - same exponent, diff base
(2/5)^3
(2^7) / (2^5) - diff exponent, same base
–> if it’s something weird like (1/2)^2 * (1/2)^4
2^2 - subtract exponents
–> (1/2)^6 - don’t multiply (1/2) together, you’re double counting
Exponent to the exponent (2^3)^4
2^12 - multiple exponents
See exponential terms being added (11^3 + 11^2)
Factor out, can’t multiple or add these
Fraction in exponent (8^(2/3)
Simplify base first: 2^3
2^(3*2/3) so 2^2
Sequence of numbers, given value of a6, need to find a100, if pattern is +3
Vs multiply by 3
- Find how many numbers btwn 6 and 100 (not counting 6, so 94)
- 94 * 3
3^94 if interval is multiply by 3
when you see complicated formula, and variable is also complicated f(2rt3)=2x^4-x^2
”- Simplify formula without complicated variable first, x^2(2x^2-1)
- Then plug in
‘- Don’t try to simplify with all the complicated variables, easy to mess up”
2 fractions divided by each other (A/B) / (C/D)
0.5/4 or (1/2 ) / 4
3 / (3/2)
AD/BC bc flip C/D so it’s A/B * D/C
1/2 divide by 4 means it’s 1/2 * 1/4 = 1/8
3 divide by 3/2 means it’s 3 * 2/3
When you have to divide, just rmbr to flip the bottom
If see many terms in a fraction, if see same terms in num and den
Split the numerator to turn 1 of the frxns into 1
if you see 2 inequalities, 1>1-ab>0, what to do if you want to -1?
- Split into 2 ineq
2. Or, do the same for each of the 3 (-1 for all 3, multiple -1 for all 3)
If you have 2 separate inequalities, x+a<2, y+a<3
You can add them if in same direction. But can’t subtract / divide.
Retailer has less than twice as many dogs as cats
D<2C
or test cases
If asked for what the max product of 2 variables, and you’re given 2 inequalities. What’s strategy?
Test extremes like -1000, 1000
If you know that x is negative and you have to square x<3
Flip ineq: x^2>9
- Doesn’t work if x CAN be positive
If you know that x is pos, can you square x>3 (both left and right sides are pos)
Yes, “Don’t flip ineq: x^2>9
- Doesn’t work if x CAN be negative”
There are dogs and cats, there are more than 5 dogs
D>5, not D=5+C
Direct / inverse ratios
Ex: If you’re given X is dir prop to A and indir prop to B
- Direct: y=kx, so you can do y1/x1 = y2 / x2
- Inverse: y=k/x so y1x1 = y2x2
X=kA/B (you can combine)
If get fraction, but need whole numbers in answer choice when backsolving
Look out for even choices
If you see all answer choices with rt 5, you know you can
divide out by that number
Typically if you see an equation with ^2 or greater
Watch out for 2 solutions, often x=0 is 1 of them
Memorize x^2-y^2
(x-y)(x+y)
Memorize x^2 - 2xy + y^2
(x-y)^2
If you see 2xy
Simplify by moving it to the side with x^2 and y^2
If question asks for x^2+x2y+y^2
Simplify it to (x+y)^2, always simplify to the possibilities
To figure out how many solutions are in a quadratic,
“Discriminant (b^2 - 4ac) from ax^2 + bx + c = 0, so if it’s +4ac then c is negative
- if +, 2 solutions
- if = 0, 1 solution
- if -, 0 solution”
If there’s a x or / inside the root,
Can break it into 2 roots
Can’t for +/- i.e. sq rt (16+25)
(sq rt of 4) ^ 5
”- Don’t get confused with sq rt, first simplify to 2^5
- Or, it’s 4 ^(5/2)”
Memorize sq rt 2
1.4
Memorize sq rt 3
1.7
Memorize sq rt 5
2.25
14^2
196
15^2
225
16^2
256
25^2
625
13^2
169
10^3
1000
0.001
10^-3
Any time you simplify a sq rt, you must
+/- the simplified answer, 2 solutions
When you have gnarly roots, try
“Squaring it instead of calc the root
- See if it’s close to a square, like 49, 64, 81, etc.”
Testing numbers
0* 1* Negatives Odd/even Fractions Extremes
Combination of variables (x+y = ?)
”- Almost always don’t need to solve for x, y separately
- Figure out x+y together”
If you see constraints in the problem, like y<1
Eliminate all answers where y isn’t <1
When equation is y=x+1, that means y will always be xxx than x
y will always be 1 greater than x
If question asks for max, when you backsolve, start with
largest number
If you see roman numeral problem, and you find 1 of them is wrong,
cross out all choices with that choice
Can you square rt (x-y) = A?
can square it and (x-y) is positive since it’s inside sq rt
When you square a + or - fraction, they get
closer to 0
0.99 translates to
1-0.01
or 1 - 10^-2
1/6
0.167
1/8
0.125
3/8
0.375
5/6
0.833
5/8
0.625
7/8
0.875
GCF
largest divisor
Distinct factors of 25
1, 25
5, 5
* 4 distinct factors
Trapezoid area
A = 1/2 (b1+b2) * h
Area of piece of pie in circle if given angle s
s/360 * Area of full circle
Angle touching center of circle vs angle touching circumference of circle
2x vs x
Right triangle options
Angles: 45, 45, 90 or 30, 60, 90
Sides: 1, rt 3, 2 or 1, 1, rt2
Pythags: 3,4,5 or 5, 12, 13 or 6, 8, 10 or 8, 15, 17
Given a set of numbers, find average. Trick for backsolving
1, 4, 4
- Correct answer choice: 3
#s below it: 1, so the diff is 2
#s above it: 4, 4 so the diff is 1 and 1 = 2
BINGO - Wrong: 2
#s below it: 1 so diff is 1
#s above it: 4,4 so the diff is 2 and 2 = 4
2 is too low, go up
Surface area of a cube
6x^2
decreased by a factor of 1/3 means
multiply 2/3
in a set of consec int (“evenly spaced set”), what about the avg and median?
avg = median
avg and median are both a number in the set
Question - what’s the profit, you’re given items purchased and sold, don’t forget to
Order sold (rev) - purchased (cost)
Don’t just blindly follow the order it’s given
- you can find profit / unit too
when you see multiple conversions, mile / gallon, gallon / hr, gallons used, expect to
multiply the ratios and convert them to 1 unit
* write out the ratios clearly to avoid careless
Slope
Vertical line slope (x=3)
Horiz line slope (y=2)
Rise / run
Vert slope = no slope
Horz slope = 0
Perpendicular slope
negative reciprocal
Area of a sector if given angle
angle / 360 * area of whole circle
V of Cylinder
pi *r^2 *h
Total sum of angles of a polygon
(n-2)*180
What makes an impossible triangle
diff of 2 other sides < side < sum of 2 other sides
not inclusive**
Exterior angle (outside the triangle) =
sum of the 2 angles not adjacent to it
Similar triangles mean
2 angles are the same, so all angles are
Area of rhombus
d1* d2 / 2
Largest area if given the perimeter for any quadrilateral
square
Smallest perimeter if given the area or a diagonal for a quadrilateral
If given area, square
if given diagonal, really skinny rectangle (diagonal ~ long side)
Area of equilateral triangle
s^2 * rt3 / 4
similar triangles have a:b sides, area ratio will be
a^2:b^2
diagonal of a cube
s rt3
diagonal of a rectangular solid
sq rt of x^2 + y^2 + z^2 –> super pythag th
Max perimeter of a quadrilateral when they give you an area is 48
infinite
(10^-infinity) * 48 x 10^infinity
Max area of triangle
right triangle
If you can’t figure out how to get a length of a triangle
Try finding the area, then change where you draw the base and height to calc one of the sides
If y=x is the perpendicular bisector to a line, to find the other point….
Flip the point given (x,y) –> (y,x), watch out for signs (visualize it)
x^2 + bx+c, if they’re asking if the products of the roots are +/- and the stem says c<0
c = rs so rs<0, you know that roots +/- so negative when multiplied
3 phrases of inequalities 1+2x < x+5 < 2x + 6
you can split them into 2
OR -2x in all 3 sections to get rid of 2x on both sides
2^4 - 5^2, how do you solve?
Simplify; (2^2 - 5)(2^2+5)
Parallelogram angles
opposite angles are equal
You can also say that adjacent angles = 180 (angles in the same line)
When you have quadratic for geometry problem
negative doesn’t matter bc can’t have negative length
Question asks for size of something without telling you the sides, test
extremes
When you lay a cylinder flat, the height is
the diameter or 2*radius
Isoc triangle in circle must be in
b and h are both the radius, point in center
if you think they’re are similar triangles
assume it!
Weighted averages trick
weights = 1
avg between the 2 numbers provided
box was 1/2 taller than it was before –>
1.5x
Steps in PS
- read problem, glance at choices to elim any extremes
- Draw grid, BSEB
- What’s trap?
- Reread question to check
Compounding interest
Trick - new value vs old value
A=P(1+r/n)^nt
– if compounds quarterly and given annual rate, n=4
Trick: new value isn’t too far from original, takes a lot of time
Plug in: $1, go year by year if easier,
Watch out when given a time series - original amount is x, in 5 years
Don’t forget Y0
Gross (-2%)- Deduct (-2%) = profit (changes by what?%)
-2% only bc % changes are the same
For ratios, if you have 3 variables, you just need
2 ratios of the 3 var to solve
Tens and units digit, see if there’s pattern using
10x+y (ex, 10x+y - 10y+x, you know the common factor is 9)
If given A is dir prop to B, B dir prop to C, A is
dir prop to C.
If Q asks for A if given C, you just need A to C ratio or you need both A to B and B to C
What’s the total of these 4 when ratio is 2:3:5:6
Total must be divisible by sum of ratio
Sum= 16 so 196 isn’t the total
Sum of consec integer - the range of the sum is within
smallest number * avg ~ largest number * avg
If you know there’s at least a pair consec numbers in a set and there are no duplicates
Subtract 1 from any number yields same number of distinct values
?
Slope greater than 1
Steeper than y=x line
Prime numbers <30
2,3,5,7
11,13,17,19
23,29
When you see change in %, you can either
Estimate
OR Eliminate - if it’s clearly not 50% or higher
when you have SD (d) and mean (m), the area below m+d
50% + 1/2 of 1 SD (34% typically) – don’t forget 50%, no need to add up that small tail
Hidden FDP problem: grouping number of people
look out for factors, common divisors
When the Q asks for big enough area to cover 2 spots, think
size and distance apart
Word problems - when you see work, wage, earnings think
work produced or earnings or $ PAID OR LABOR COST = wage * # hrs
Rates - when 2 people walk towards each other, you can —- rates
Add
Rates - when 2 people walk in the same direction, you can — rates
Subtract
when you have a slower and faster rate, the average is
NEVER THE simple avg
**ALWAYS closer to the slower rate (smaller #) (estimate if needed) – doesn’t apply to 2 working together
To get average rate of 2 workers
To combine 2 workers and get their rate together
Add distance and time
Add rates
When you see estimate within 0.5, think
+/- 0.5, so test the extremes
Overlapping sets - WATCH OUT FOR some % or number OF…. VERB
where, who, ….can change denominator
Look for OF…..VERB
Overlapping sets - minimum can be
0, not 1
simultaneously and indep working together means you can xx rates?
add
how to check you counted correctly the # of int btwn a range
try with smaller range
Count integers in a set (divis by 7 btwn 100-150)
(Last - first) divide first by incr, then + 1
Find last and first divis by 7: 105 and 147 so
(147-105)/7+1
Sum of consec integers
Avg = sum / # of terms
Trick to finding sum of 1st 3 int in a set of 6 when given last 3 int sum is 624 (trick only works for even numbered set)
Difference in 1st 3 vs last 3 is: n+3+n+4+n+5-(n+n+1+n+2), so 9
624-9 is answer
terms
(High # - Low #) / interval + 1
Interval is 2 for even or odd
** avg is add, # of terms is subtract
Simplified Q if ask to find the sum of consec integers –>
What is the value of any of the numbers?
Weighted avg - given the 2 scores (80, 100) and weighting (40%, 60%) , find weighted avg score
80 ———- 100
40% 60%
Weights are 2:3 so flip them 3x + 2x = 20 (diff)
x=4 so avg is 12 away from 80 or 92
if question asks for what value of 100x+200y, given x+y=1 and choices are 10, 150, 250
WEIGHTED AVG PROBLEM IN DISGUISE
x+y=1 is hint!
Can’t be 10 or 250 - has to be btwn 100 - 250
variance=
SD^2
What components needed for SD
difference between mean and each int, # of int
or variance
sum of an ODD number of consecutive integers is divisible by (i.e. 2, 3, 4)
the number of items
-divis by 3
12 is equal to 3n where n is an integer (really saying)
12 is divis by 3
bc n can be any integer, but as long as 12 is divis by 3, it’s fine
if N is a divisor of x+y, then N is ALSO a divisor of what?
x-y (adding/ subtr multiples will yield another multiple)
if a is a factor of b and b is a factor of c, then
a is a factor of c
If 2 is a factor of 6 and 6 is a factor of 72 then 2 is also a factor of 72
if product of 2 prime numbers is even, you know 1 of them must be
2
2! is
3! is
2
6
4!
24
5!
120
6!
720
When there are repeats in the combinatorics,
for ex 2 bronze and 3 silver
divide by repeats
total! /2!3!
when there are 2 groups (tricky bc may say choose from 7 colors, pick 2)
1st do the 1: T!/(1!6!)
Then 2nd T!/(2!5!)
THEN MULTIPLY THE 2 TO GET TOTAL
when you see AND (2 events happening)
multiply
when you see OR in comb / prob
add
when you see at least 1, trick is to
1 - P(none)
when you see at most 1, trick is to
P(none) + P(1)???
LCM calc: 100, 140
Find all prime factors and powers, take the largest power of each factor
100: 2^25^2
140: 2^25*7
LCM: 2^2 * 5^2 * 7
perfect squares contains only odd or even power of primes?
even (everything is doubled)
If you see 3x+1 is prime, the +1 signals x should most likely be
even
To check your work,
reread problem
check constraints in problem
think what’s trap?
x! is a multiple of
any number between 1 and x
10! + 7 is a mult of
7 bc you can factor out 7 (all others! + 1)
when you see rt x + rt y, think of
x + 2 rt (xy) + y
when a sphere is inscribed in a cube, think
slicing the sphere so the circle is inscribed inside the square
r = 1/2 s
Gnarly calculations, first try to
factor out and simplify
If you INCR each number in a set by 10%, to calc the difference in the old and new avg trick
old avg * change in % (here it’s 10%)
If you DECR each number in a set by 10%, to calc the difference in the old and new avg trick
old avg * change in % (also decr by 10% or * 90%)
When you estimate 9900 * 100 / 55,
- write out >9000 * 100 / >50
2. since > is in both num and dum, they “cancel out”
2^3a * 2^-3b
2 ^ (3a-3b)
Overlapping matrix - how do you get the total
ADD NOT MULTIPLY
Geometry tricks
- make sure you solve for right thing - area, perim (reread problem)
- Look to Q for clues if stuck - cubic meters –> volume
- test extremes (max area, can triangle be very fat or skinny)
- Use the silent polygon or bigger shape
When you need to work with right triangles, always think
sides (3-4-5, 6-8-10, etc.)
AND
angles (45-45-90, 30-60-90, etc.)
AND 1-1-rt2, 1, rt3, 2
Geometry shapes in PS are drawn to scale
so visualize and estimate!
DS are not
12000/ 25
1000/25 * 12 so 40 *12
Rate word problem tricks
- visualize
- simplify Q, so if given R and ask for T, simplify and say what’s D?
- like overlapping set, fill in as much of grid as possible, more suff
if given a few factors (1, 2, 3, 4 ) for ex: 24, you can figure out the other factors by
divide 24 by those factors to get the other ones
if given median = average and all but 1 numbers in a set, you can
figure out that missing number (avg*n - sum of rest of the numbers)
overlapping sets - careless mistakes
descriptive label (instead of L, do LB) reread each label in Q
When you want to minimize 1 variable, you
maximize all the others
Geometry trick - triangle
- if your gut says similar tirangles, just assume
2. LOOK FOR RIGHT angle - COULD BE AT THE TOP , RIGHT OR LEFT
Given slope is -3 and line passes through point (-2, r), it hits the origin if r is
6 bc you can get the slope with the other point (0,0) and (-2, r) so slope -3 = r / -2
what percent of x is y
P/100 * x = y or P is y/x*100
rate problem trick - if given person A starts before person B
figure out how much distance A covered first
I have 20% fewer candies than Susan means
.8S
Ron’s DS yes/no steps
Use 2 line device - be explicit with 2 options Top: question, x>2 Bottom: x <=2 Row: A, B, C
Ron’s WP steps
- answer intuitively
- Grid - build Excel (no variables)
- Relationships - plug in info (no variables), draw allll relationships
- BSEB - solve - now use var. Backsolve, pick #s, est, brute
when you add a width to a frame, don’t forget to
add 2w to the length and width of frame
Ron’s DS 2 line device trick
you can assume that the top row is checked, just need to prove bottom row
20% more in her purse than in mine
Mine *1.2 = her purse
mine is the base since it’s after than
sum of even integers btwn 100 and 200
avg = 300/2 # int is 200-100=100 /2 (bc even) so 50 +1 =150*51
sum of integers btwn 100 and 200
avg = 300/2 # int 200-100=100+1 (no /2 bc it's not even or odd) =150*101
200% more than him - to get to the value of “him”, you need to
- You are = 1+200% so 3x, He is x.
- OR take the DIFFERENCE, not just 2x
(him - you / him) = 200%
(multiple is always 1 more than the % -> just rmbr 100% = 2x)
when you see a figure where things are rotating, beware
counter clockwise or clockwise!!
divisor is the
smaller number that you can divide by
Ex: 2 is a divisor of 10
If you’re picking smart numbers and question asks to find a % of %, use
Ex: grow 16% in Y1, 9% in Y2. 2nd year denom increases by 20%. What’s 1st year denom? (% of % )
1000, not 100
when you’re estimating / checking answers, make sure to look at
- range the answer should be in (elim too high / low)
- elim constraints
- draw comparisons with existing (OG machine vs new)
- round up and down to estimate
- odd vs even hint
- redraw figures to visualize
- if ask for range, take middle value
- if the answer choice is exactly the number in the problem (likely eliminate)
compound interest (semiannual) vs simple interest
compound interest will be a little bit higher than simple (apply interest more times)
weighted avg estimate - if you have a bunch of numbers with a lower score, the only way to increase your average with 1 score is
if that 1 score is really high (takes a lot to raise your avg grade, rmbr)
when you plug in smart numbers, remember to think about
what makes sense - if 2 machines work together, their hours should be LESS than the 1 machine
1 increases 200% =
1+2=3
given: 9.12 and the remainder is 9, what’s the divisor?
what’s remainder?
9/divisor = 12/100
FORMULA: .12*Divisor = Remainder –> .12D=R
Since divisor should be an integer, you can say D = R*25/3 so R has to be divis by 3
don’t forget that (10^2)^4 is
10^8 not 10^6
when you have a crazy root (ie 1+rt2) in an equation like x^2+x+1 , you can always
PLUG IN that crazy root
Word problems - alternate methods:
BSEB
- Backsolve, smart #s, estimate, brute force
- Don’t forget to draw arrows for relationships
Geometry - coordinates - if you redraw, make sure
you draw ACCURATELY as possible, if you mess up, redo. It’s better than carelessly making a mistake
if you see the word “ANY” in a question about list of numbers
Ex: sum of ANY 3 numbers is 12
be wary - ANY means every single possible variation HAS to be equal to 10…that’s very restrictive
hint: likely all the numbers have to be the same
Trick when you’re trying to find the total number of 2 variables and you’re given a ratio (B=1.5C) AND the total is btwn 21-28
Since 1.5C+C is btwn 21-28, 2.5C turns into 5/2C is 21~28
C then ~ divis by 5, so you know it’s 25
“at a particular time” signifies that at this 1 point in time, everything must happen
can they process 500 calls if there are x machines?
this isn’t is 500 divisible by x. It’s is x >=500 because it has to process it ALL AT ONCE
if you’re given an inequality like A+C >10 and you need to find C, you can assume that ….
more than 1 pair will work so it’s not enough info. Even if there’s a complicated 324A+4598C = 230492834
Also way too time consuming to find…and you don’t have time
when you have a border, don’t forget to LABEL all 4 sides
so if the inside is 8x10, then it becomes 8+2w x 10+2x, it’s not just 8+w
Is 1 prime?
Is 1 a factor?
No
Yes
0 is …
Is 0 a +/- number?
Is 0 even/odd?
Is 0 an integer?
Neither
Even
Yes
of Factors- don’t forget what?
Trick to find # of factors for really big number?
Don’t forget 1
ALLL pairs so for 25 it’s 1. 25, 5, 5
Trick: 1440 = 2^53^2 * 5
Get all exp - 5, 2, 1
Add 1 to each
Multiply = 63*2= 36
when you see 3 groups in overlapping set
x1+x2+x3+none = total number provided x1+2x2+3x3 = sum of the 3 indiv groups, which incl overlap
x2 = sections with 2 groups that overlap x3 = the center section with all 3 groups overlapping
when you see APPROX in the question, be prepared for ugly math
estimate, eliminate, guess
Probability of A or B occurring is
P(A) + P(B) - P(A and B occurring)
P(A, not B) + P(not A, B) in the case when 1 = P(A and B) + P(not A, not B) + P(A, not B) + P(not A, B)
How many different options can you get selecting 2 people out of 10? Order matters (AB and BA not the same).
Ex: no. 140
What’s the probability to select 2 women if 50% are women out of 10 ppl?
__ __
10*9
Fraction:
(54) / (109)
10 total people, need to choose 2. Order doesn’t matter (AB and BA are the same)
Ex: no. 187
10!/(2!*8!)
Includes people not chosen because not being chosen is also a combination
When you have multiple intervals on a circle, DON’T FORGET TO COUNT
all of them until you get back to where you started, don’t just stop at the last tick before the starting point!
180 is what % greater than 80? Trick
Base is what’s after “than” so 80
80 is close to 90, 180 is 100% greater than 90
so 180 is MORE THAN 100% greater than 80
Quant - each problem, strive for
PRECISION AND EFFICIENCY (must get all easy Qs right, find tricks / traps in hard ones)
- most efficient way (don’t waste energy)
- avoid careless
- avoid trap
30,000 = (100 + w)(200 + w), can you factor out 100?
NO!! Can’t do 300=(1+w)(2+w)!
Doubling the area of a rectangle, how much do the sides increase (Ex: 100x150=15K)
Less than DOUBLE the sides
100x150=15K –> 150x200 = 30K
To avoid careless mistake if question asks for x+16,
Draw grid, circling the blank spot next to x+16
Practice this grid so you get used to filling it in
(rt 82 + rt 82)^2 tricks
(2rt82)^2
or 82 + 2(82) + 82 bc the middle is 2 rt82 * rt 82
when the population doubles, think
exponents (2^x)
NOT multiplying by the number of times it doubles (2x)
DS question where it vaguely says isoc triangle
draw both a right isoc and a isoc without right angles
when given (-5,r) as a point, but you don’t know what r is, you should
test cases for r ie: r=1, r=25
if constraint is positive, integer, write the 1st possible answer
write out “1” - reminds you to start here
Solve for 4x^2 from rt(3-2x)=rt(2x) + 1
with pen and paper
Answer: 6x-1 = 4x^2
- *Don’t forget to move all terms with x to 1 side
- *Don’t forget to multiply 2 in the middle part 2rt(2x(3-2x)
hemisphere radius and height
equal
Hemisphere is basically half of a sphere
President, sec, treasurer. What’s probability of you getting secretary out of 10 ppl?
Not getting president: 9/10
Getting sec: 1/9
Not getting treasurer: don’t need to do bc you already got sec
Prob = 9/10 * 1/9
10,000 initial amount, 4% annual interest, compound QUARTERLY. What’s amount after 6 mths
Q1 = 10,000(1+.01) = 10.000+100=10,100 Q2 = 10,100(1+.01) = 10,100+101=10,201
Formula = 10,000(1+4%/4) ^ (4*1/2) = 10,000(1+.01)^2
when you’re given 2 variables and asked what their greatest prime factor is, think
Test the variables with crazy prime factors like with 7 or 11 or 13 and a regular like 2
To speed up testing cases,
start with proving the bottom row, flip or do the opposite to prove the top row
If the question asks “Did one of the members do something” interpret as
Did AT LEAST 1 do something, not EXACTLY 1 does something
246 = factor out 2
2^3 * (123)
what’s the prime factor of 2^3 * (123) + 1
When you see the +1, it indicates that the prime factor must be greater than 3 since without +1, it would be 3
For geometry, if you have to solve for an angle,
write out as many angles as you know like 180-R before solving
how many times a triangle intersects the circle, think of
times when the triangle TOUCHES the circle (intersect just means overlap so if they share a point, then it intersects)
When you’re picking smart numbers, don’t forget
0 (lots of variables, get rid of 1 of them easily)
1 (lowest number to start plugging in)
Testing numbers for % increases, try
200% (3x) or 300% (4x)
Just rmbr 100% = 2x
10^-8 (how many 0’s before 1)
7 0’s
Think 10^-2 = 0.01 so only a 0 before 1
Rate - if the question asks whether D>100, does R / T have to be > or < ?
if D>100 then R/T also >
a club has 20 members, what is the number of 5-member committees that can be formed
it’s not 4!!
NUMBER = how many 5 member committees so combinatorics - 20!/15!5!
if there’s a number of blocks arranged in a square, what does it mean to remove 1 row and 1 block from each row?
Removing a row on the top and left already removes 1 block. You go from 8x8 to 7x7
weighted avg, if it’s about $ and number of items and you’re given the wtd avg and total units, what do you need?
Need the both $s –> can figure out the # of items for both
Need both numbers –> can figure out $ for both
if you’re diligent about using Ron’s 2 line device, if you can’t seem to find a test case for the bottom row,
use algebra and use other stem as a hint
when given rate, make sure that it’s a
ratio of some sort: liters / hr, miles / hr
Ex: rate of k liters for every x hrs –> rate is k/x not just k
In DS, if you have 3 equations, make sure you
plug in all the numbers you’re given - typically need 2 equations to solve if you plug in everything you’re given
5^(x-3)-5^x - how do you simplify?
- 5^(x-3) [ 1-5^3] –> you always factor out the smallest one
- TEST CASES, x=4, answer choices also have x
Quant tricks - time efficiency
- skip - combinatorics, geometry, wordy WP, 3 part (I, II, III)
- test cases - 1, but if you’re trying to prove it wrong, try fractions or negatives
- fill in as much as you can (ie overlap set, equations)
elimination tricks in choices
- decimals vs integer (# of ppl should always be int)
- even vs odd
- > 1 for probabilities / wtd avg
- answer should end in a certain number
DS tricks
- look at both stems to get a hint, NOTE DIFFERENCE IN 2, start with easier one
- 2 line device - test bottom row first
- test cases
PS trick
- figure out what the Q is REALLY asking
- look at choices to eliminate right away
- test cases - be diligent about grid
- BSEB
Overall quant tricks
- read Q, paraphrase - what is Q really asking?
- look at choices (proceed with DS/PS tricks)
- -> when you can’t figure out path forward / can’t find answer in choice, SKIP - reread Q, think what’s trap?
when you see “what % did something change”
what % did the ratio of royalties to sales decrease from $20 to $108
what % = percent change, don’t just subtract ratios
when you see average, and given the min of a set, can you get the max?
No
When you see avg - get the sum, you’ll see that there are multiple max’s that still add up to the sum
when you have the weighted avg and the 2 #s at each side, do you know which one has more students / “weight”?
Yes
80—–84–86 - 86 has more weight
You won’t be able to tell exactly how many students in each end.
1 hour is how many seconds
3600 or 60*60, not just 60!
even for “easy” problems, don’t forget to
- read the question - write down what the Q is really asking
when you see ratio, make sure you don’t
forget that there are VARIOUS sets of numbers that work for the ratio, unless you have constraints
.18/.3 =
NOT 6
.18 / .30 so 3/5
when you see time remaining and 10% completed,
time remaining = how much time it takes to do 90%
4+8+…36
What’s the average?
What’s the # of int?
What’s the sum?
Avg = (36+4) / 2=20 # of int = (36-4) / 4 + 1 = 9 Sum = A*n = 20*9=180
when you see l^2+w^2=200^2 and l+w=280, think
you can square (l+w)^2 = 280^2, and get l^2+2lw+w^2
l^2+w^2 you already have, so just solve for lw
280^2-200^2
(280-200)(280+200)
when you see machine produces x widgets every 4 min
rate is x/4
