Flashcards in Quant Strategies Deck (259):

1

##
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"

2

## Backsolving

### Follow the flow of the problem, plug in the choices

3

## Careless Typo - don't write J as 1

### Slow down

4

## Careless 9 and a in a problem

### Squigly a and straight 9, be careful

5

## Careless 19+7

### 26

6

## Combo If you see the question asking for 2 variables, ie x/y =?

###
- Simplify question if you can

- Try to manipulate answer choices to solve the combo, not indiv var"

7

## Combo If DS option is combo, ie x/y and the question asks what xy=?

### TEST CASES: Instead of plugging it in, you can just say x could be 4, y could be 2

8

## Combo You don't need to solve if in DS, you have combo in stem

### - if you can manipulate the choices to the same as the problem, or the 2 choices are actually the same - not C

9

## DS Data Sufficiency

### AD/BCE, BD/ACE

10

## DS When you have a gnarly fraction, look at answer choices to try to manipulate it there, ie (2t+t-x) / (t-x)

###
"- Signal: 2t+t must be like that for a reason, don't just go 3x

- 2t / (t-x) + 1 bc that's in answers"

11

## 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"

12

## DS When you have equation in question

### Don't assume that it's given, write out equation with "?" for each stem

13

## Equations System of equations

###
"- Figure out what to solve for, x

- Isolate other variables, y (put y on 1 side, and rest on other side), plug into 2nd equation

- Practice both subsitution ^ or add/subtract equations (if it's already laid out)"

14

## Equations 2 variables in 1 equation

### Can't solve if you have 2 variables

15

## Equations If the question has x and y, asks what y could be and gives you multiple choice, solve for...

### Solve for y --> x = y something, that way, you can plug y into the equation

16

## Equations If you have 2 equations, you can; ie xy=2, yz=3, xz=4

### Multiple, add, subtract together; ie x^2y^2z^2=24

17

## Equations If you have 3 equations where all variables don't have coefficient,

### Add the 3 together, then you can sub 1 equation with 2 variables at a time

18

## 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"

19

## Exponents Same exponent but different base in a fraction (no addition / subtraction in between)

###
"Consolidate the fraction and put it all over exponent

- if unsure, check if it works the other way"

20

## Exponents Same base with exponent, if division, you can

### If division, you can subtract exponents. If multiplication, you can add

21

## Exponents Exponent to the exponent (2^3)^4

### Multiple the exponents: 2^12

22

## Exponents See exponential terms being added (11^3 + 11^2)

### Can't multiple exponents, try factoring out

23

## .Exponents Fraction in exponent (8^(2/3)

###
"Can't split fraction by multiplying it out with the same base; not 8^2*8^(1/3)

- Instead, simplify base and see if you can x or / exponents"

24

## Exponents Memorize 4^n, ending unit pattern is

### 4, 6 | 4, 6

25

## Exponents Memorize 9^n, ending unit pattern is

### 9, 1 | 9, 1

26

## Exponents Memorize 5^n, ending unit pattern is

### Always 5

27

## Exponents Memorize 6^n, ending unit pattern is

### Always 6

28

## Exponents Memorize 7^n, ending unit pattern is

### 7, 9, 3, 1 | 7, 9, 3, 1

29

## Exponents Memorize 3^n, ending unit pattern is

### 3, 9,7, 1 | 3, 9, 7, 1

30

## Exponents Memorize 8^n, ending unit pattern is

### 8, 4, 2, 6 | 8, 4, 2, 6

31

## Exponents Memorize 2^n, ending unit pattern is

### 2, 4, 8, 6 | 2, 4, 8, 6

32

## Exponents Memorize that n^n ends in n, single digit options are

### 1, 5, or 6

33

## Exponents Memorize that n^n ends in only 2 digits

### 4 or 9

34

## Exponents -10 * 10^2

### -(10)^3, not -10^1

35

## Formulas Sequence of numbers, given value of a6, need to find a100, if pattern is +3

### Find gap, 100-6 = 94 * 3 (because it's just +3)

36

## Formulas 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"

37

## Fractions Ugly fraction in equation

###
"- Get rid of denominator first

- Cross multiply"

38

## Fractions 2 fractions divided by each other

### Multiple top 1 and bottomest one / middle 2

39

## Fractions 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

40

## Inequalities if you see 2 inequalities, 1>1-ab>0, what to do if you want to -1?

### Remember to do the same for each of the 3 (-1 for all 3, multiple -1 for all 3)

41

## Inequalities If you have 2 separate inequalities, x+a<2, y+a<3

### You can add them (make sure same direction of the sign), never subtract or divide; a

42

## Inequalities Retailer has less than twice as many dogs as cats

###
"d<2c

- Use numbers, D=4, C=2, so you know its D=2C

- But less than so D=5 or 3, 3 so it's D<2C"

43

## Inequalities If asked for what the max product of 2 variables, and you're given 2 inequalities. Also, in general, what's the strategy

### Test all 4 extremes (don't forget negatives). Don't forget 1000, -1000

44

## Inequalities 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"

45

## Inequalities 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"

46

## Inequalities There are dogs and cats, there are more than 5 dogs

### D>5, not D=5+C

47

## Negative - Adding negatives

### Pay attention, double check, slow down

48

## Negative - Subtracting 3-4

### Pay attention, double check, slow down

49

## Negative - Equations with negatives

### Do 1 thing per line, don't try to save time

50

## Negative - Negative in answer

### Don't forget to choose the answer with negative!

51

## Negative If there is no parenthesis, ie -2^4

###
the negative does not distribute with an exponent

-16, not 16

52

## Number Properties 0 is an integer? Even or odd? Pos or neg?

###
0 is an integer, even, neither pos or neg

53

## Proportionality If you see 2 sets of 2 variables in ratio form, think --

###
"- Direct: y=kx, so you can do y1/x1 = y2 / x2

- Inverse: y=k/x so y1x1 = y2x2"

54

## PS If you see answer choices, if it'll be hard to determine right equations (ugly quadratics / fractions), or formulas are messy

###
"- Backsolve from answer choices

- Start with B or D (if can't tell to go up or down, do B, then do D and see how much closer you are)"

55

## PS If get fraction, but need whole numbers in answer choice when backsolving

### Look out for even choices

56

## Quadratic If you see variable in denom and different powers,

###
Don't move constant to other side

Keep them on same side, because you're going to quadratic equation; may work for linear equations

57

## Quadratic If you see all answer choices with rt 5, you know you can

### divide out by that number

58

## Quadratics Typically if you see an equation with ^2 or greater

### Watch out for 2 solutions, often x=0 is 1 of them

59

## Quadratics Memorize x^2-y^2

### (x-y)(x+y)

60

## Quadratics Memorize x^2 - 2xy + y^2

### (x-y)^2

61

## Quadratics Memorize x^2 + 2xy + y^2

### (x+y)^2

62

## Quadratics If you see 2xy

### Simplify by moving it to the side with x^2 and y^2

63

## Quadratics If question asks for x^2+x2y+y^2

### Simplify it to (x+y)^2, always simplify to the possibilities

64

## Quadratics To figure out if there is no solution, 1 or 2 solutions, look at

###
"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"

65

## Roots If there's a x or / inside the root,

###
Can break it into 2 roots

Can't for +/- i.e. sq rt (16+25)

66

## Roots (sq rt of 4) ^ 5

###
"- Don't get confused with sq rt, first simplify to 2^5

- Or, it's 4 ^(5/2)"

67

## Roots Memorize sq rt 2

### 1.4

68

## Roots Memorize sq rt 3

### 1.7

69

## Roots Memorize sq rt 5

### 2.25

70

## Roots Memorize sq rt 169

### 13

71

## Roots Memorize sq rt 196

### 14

72

## Roots Memorize sq rt 225

### 15

73

## Roots Memorize sq rt 256

### 16

74

## Roots Memorize sq rt 625

### 25

75

## Roots 10^3

### 1000

76

## Roots Any time you simplify a sq rt, you must remember

### +/- the simplified answer, 2 solutions

77

## Roots 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."

78

## Smart numbers How to pick smart numbers?

###
"- Don't pick 0, 1

- Pick odd and even numbers

- Don't pick #s already in the problem"

79

## Smart numbers When to pick smart numbers?

###
"- When there are no real numbers, just variables/%/frxn; if there is any real #, try plugging in choices

- Variables in answer"

80

## Mental math Divide by 5

### Divide other number by 2, multiply by 10

81

## Subtraction When there's a carryover

### Write out the carryover instead of doing it in your head

82

## Test cases Often with DS in inequalities

###
"Test 0, 1, frxn, odd/even, neg frxn, neg odd/even (unless constraint)

- 0, 1, 1/2, -1/2, 2 or 3, -2 or-3", really big and really small numbers (extremes)

83

## Variables Combination of variables (x+y = ?)

###
"- Almost always don't need to solve for x, y separately

- Figure out x+y together"

84

## Word problem See difficult word problem without any real numbers just variables/%/frxn, and variable in answer

###
"- Use smart numbers

- Be careful- plug in the correct smart number"

85

## Word problem If the questions asks for a ratio

### Don't multiply out everything, try crossing out things

86

## Word problem If you see constraints in the problem, like y<1

### Eliminate all answers where y isn't <1

87

## Word problem Be careful of units, but don't need to change all units if the units cross out; ie mph / sec = mph / sec (direct proportional)

### Can leave mph without converting to sec

88

## Word problem - ask yourself

### Can I backsolve, instead of algebra

89

## Inequalities: If more than twice as many dogs as cats

### D>2C

90

## When equation is y=x+1, that means y will always be xxx than x

### y will always be 1 greater than x

91

## Inequalities: if question asks: is a>b, stems have a+2b = 1

###
Test cases

OR plug in , 1-2b>b, insuff bc is b<1/3? don't know

92

## Testing cases: if you have answer choices and constraints in problem, you can

###
- simplify answer choices, 51 only has 1, 51 or 3, 17 so if you know you can square the numbers < 100, 51 doesn't work.

- start with max answer choice if ask for max

93

## Guessing randomly strategies

###
- choose answer that looks most similar to other answers, least similar than numbers in problem (narrow down most similar 3, than to similar 2, then see if there's another reason

** SIMILAR TO CHOICES, DIFFERENT TO PROBLEM

94

##
To figure out if you should go for it or guess and move on: If you recognize how to solve it / know strategy

If you get to 2 min and still far from finish line

###
Do it- but if you're still far from the finish line, get out

If you're confused - move on, don't even try

If minute away, don't rush or give up at the very end

How confidence you'll get to answer VS how quickly you can do it

95

## If you see roman numeral problem, and you find 1 of them is wrong,

### cross out all choices with that choice

96

## Can you square rt (x-y) = A?

### can square it and (x-y) is positive

97

## If you have decimals,

### convert to fraction (often can cross out denom)

98

## When you square a pos fraction, it gets

### smaller than the original (closer to 0)

99

## When you square a neg fraction, it gets

### bigger than the original (closer to 0)

100

## 0.9999999 translates to

###
1 - 0.00000001 which becomes 1 - 10^-8

Think 0.1 = 10^-1

101

##
0.1 translates to ...

0.1^n translates to

###
10^-1

10^-n

102

## Step 1 - read the problem AND....

### look at answer choices, you can eliminate things as you go through

103

## .375

### 3/8

104

## .167

### 1/6

105

## .625

### 5/8

106

## .8333

### 5/6

107

## 0 is positive or negative?

### 0 is neither

108

## GCF

### Largest divisor

109

## Distinct factors

###
Don't forget 1, and any repeats

x^2 = 1, x, x (3 factors)

110

## Trapezoid area

### A= 1/2 * (b1+b2) *h

111

## Area of piece of pie in circle if given angle s

### A of pie / A of circle = s / 360

112

## Central angle vs Inscribed angle in circle

### 2x vs x

113

## Special rt triangles

###
x, x, xrt2 --> 45, 45, 90

x, xrt3, 2x --> 30, 60, 90

114

## Pythag triplets

###
3,4,5

6,8,10

5,12,13

8,15,17

115

## Ratio of angles in triangle vs ratio of sides

###
a deg > b deg > c deg

opposite a deg > opposite b deg > opposite c deg

116

## Surface area of a cube

### 6x^2

117

## Slopes

###
y coordinates / x coordinates

Vertical has no slope

Horiz has 0 slope

118

## Perpendicular slope

###
negative reciprocal

2--> -1/2

119

## Area of a sector

###
Fraction of the total area of the circle

(Fraction = angle / 360)

120

## V of Cylinder

### pi *r^2 *h

121

## Total sum of angles of a polygon

### (n-2)*180

122

## What makes an impossible triangle

### diff of 2 other sides < side < sum of 2 other sides

123

## Exterior angle (outside the triangle) =

### Sum of 2 interior angles on the opposite side of triangle

124

## Similar triangles mean

### 2 angles are the same

125

## Area of rhombus

### d1*d2 /2

126

## Largest area if given the perimeter for any quadrilateral

### square

127

## 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)

128

## Area of equilateral triangle

### [s^2 rt 3] / 4

129

## similar triangles have a:b sides, area ratio will be

### a^2:b^2

130

## diagonal of a cube

### s rt 3

131

## diagonal of a rectangular solid

### sq rt of x^2 + y^2 + z^2 --> super pythag th

132

## Max perimeter of a quadrilateral when they give you an area is 48

###
infinite

(10^-infinity) * 48 x 10^infinity

133

## Max area of triangle

### Right triangle

134

## If you can't figure out how to get a length of a triangle

### Try finding the A, then changing where you draw the b and h to calc one of the sides

135

## 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)

136

## 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 are - when multipled

137

## 3 phrases of inequalities 1+2x < x+5 < 2x + 6

###
you can split them into 2

OR try to get rid of the outer x's so you're left with 1 in the middle (do the same for each clause)

138

## 2^4 - 5^2, how do you solve?

### Simplify; (2^2 - 5)(2^2+5)

139

## Smallest side of a triangle and largest side

### difference of 2 other sides < SIDE < sum of 2 other sides

140

## When checking choices, look out for

### Integers - if question asks for one, eliminate all without int

141

## Parallelogram has ---- angles

### 2 pairs of equal angles

142

## When you have quadratic for geometry problem

### negative doesn't matter bc can't have negative length

143

## When given a geometry problem of the size of something without telling you the sides

### Think extremes - big volume, but can have the tiniest height, vs skinniest width but highest height

144

## When you lay a cylinder flat, the height is

### the diameter or 2*radius

145

## Isoc triangle in circle must be in

### center of circle (r and r `are its sides)

146

## Assume similar triangles if you suspect it!!

### xx

147

## Is 1 prime

###
No, prime starts at 2

2 is only even prime

148

## Weighted averages trick

###
Identify it is one bc it gives you ratios in a group

ALWAYS BETWEEN the 2 ratios and closer to the heavier one

149

## Check answer by

###
Check constraints, makes logical sense.

For DS, check constraints in question AND STEM

REREAD PROBLEM

play devil's advocate

150

## box was 1/2 taller than it was before -->

### 1.5x

151

## Split the pot and given % and # type question. How to tackle?

###
1. Plug in choices

2. Figure out the remaining % which equals the only actual number given

152

## 1st step in quant - practice

###
Glancing at choices

If far apart can estimate

As you go through, start eliminating - if something is supposed to be small, cross out all big, +/-, fraction vs integer, odd vs even

153

## Estimate or benchmark

### Use round numbers, get in the range

154

## When testing cases

### Identify what they’re testing or trying to trick you, test those

155

##
30 is what % of 50

Shortcut is

### 30/50 = x%

156

## Faster calc with odd percent like 7%

###
Do 10%/2 to get 5%

Then 1%+1%

157

##
Compounding interest

Trick - new value vs old value

Compound quarterly if given annual rate

###
A=P(1+r/n)^nt

-- n is if quarterly, but you can first annualize the rate

Divide annual rate by 4 for quarterly

May be easier to just go year by year if calc is too hard. 100 becomes 102 becomes 104.04

Also can try $1 if asks you to compare to original

For 2nd year, don't need to add end of 1st yr + end of 2nd yr, 2nd year already accounts for end of 1st yr

New value isn’t too different than original, takes a lot of years to accumulate

158

## Watch out when given a time series - original amount is x, in 5 years

### Original amount is Y0, don't put Y1, Always write Y0

159

##
In addition or substraction, if % increase or decrease is the same, then total

Ex: Gross (-2%)- Deduct (-2%) = profit (??%)

###
will also change by same % increase or decr

-2% also

If % changes differ, can't subtract add %s

160

## Smart numbers trick - find lowest, how?

### Think about how low you need, if there's a fraction, go as low to get integer, but don't go higher. Need to think and pause about which number is lowest

161

## For ratios, if you have 3 variables, you just need

### 2 ratios of the 3 var to solve

162

## Tens and units digit, see if there's pattern using

### 10x+y (ex, 10x+y vs 10y-x, you know the common factor is 9)

163

## Given fraction, figure out if terminating decimal

###
Don't forget numerator, may cross out something in denom

3, 7, 11 etc. prime #s in denom after fraction is reduced

164

## 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

165

## 15*6

### 90

166

## Ratios, sum of the ratios must be what compared to the total

###
Divisible by total amount

2:3:5:6, sum is 16, so the answer cannot be total 192 which isn't divs by 16

167

## Sum of consec integer, you can figure out range

### Take smallest and largest number * #of terms in range

168

## If you know there’s at least a pair consec numbers in a set, you know there’s duplicates and

### Subtract 1 from any number yields same number of distinct values

169

## Slope greater than 1

### Steeper than y=x line

170

## In circle, if point is on the circle and creates an angle to the other side of the circle, the length of arc is

###
2* angle

Inscribed angle

171

## Prime numbers <30

###
2,3,5,7

11,13,17,19

23,29

172

##
# of Factors- don’t forget what?

Trick to find factors for really big number?

###
Don't forget 1

All pairs so 1. 25, 5, 5

Trick: 1440 = 2^5*3^2 * 5

Get all exp - 5, 2, 1

Add 1 to each

Multiply = 6*3*2= 36

173

## When you see change in %, you can either

###
Estimate

OR benchmark - look at choices and start eliminating if it's clearly not 50% or higher

174

## when you have SD (d) and mean (m), the area below m+d

### 50% + 1/2 of 1 SD -- don't forget 50%, no need to add up that small tail

175

## Hidden FDP problems, when they talk about arranging number of people in groups of or tables of x, look out for

### look out for factors, common divisors

176

## When the Q asks for big enough area to cover 2 spots, think

### size and distance apart

177

## which fractions can you take the first 1/# and multiply it for subsequent ones

###
1/9 --> try 5/9=.11*5

1/11 --> try 5/11=/09*5

1/6 --> try 5/6 = .167*5=.833

1/7 --> try 5/7 = .14 *5=.7

178

## Be ok with switching smart numbers

### or even variables to solve for (total instead of the variable they ask)

179

## 33^43 ends in what digit. TRICK

### Divide by 4, not 3

180

## Word problems - when you see work, wage, earnings think

### work produced or earnings or $ PAID OR LABOR COST = wage * # hrs

181

## Rates - when 2 people walk towards each other, you can ---- rates. Typically ask to figure out the delta in difference

### add rates. Use the total distance / sum of rates = time. With time, you can apply indiv rate to get dist of ea

182

## Rates - when 2 people walk away from ea other, you can -- rates

### add rates

183

## Rates - when 2 people walk in the same direction, you can --- rates

### subtract rates

184

## 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

185

##
To get average rate of 2 workers

To combine 2 workers and get their rate together

###
Add distance and time -->

Add rates -->

186

## Rate problem steps

###
Read through problem, get sense for what is being asked (avg rate?)

Think what is needed

Simplify what's given and derive the real Q

187

## When you see estimate within 0.5, think

### +/- 0.5, so test the extremes

188

## when you see 3 groups in overlapping set

###
Add up all 3 overlapping groups

1) x1 + 2x2 + 3x3 to account for duplicates.

2) x1 + x2 + x3 + N (for neither) = total number

Can solve for any of these x's

189

## Overlapping sets - WATCH OUT FOR some % or number OF.... VERB

###
where, who, ....can change denominator

Look for OF.....VERB

190

## Overlapping sets - minimum can be

### 0, not 1

191

## simultaneously and indep working together means you can add rates?

### add rates

192

## count the book ends of a range vs not, how to count how many #s in between (ie. number of int between 1-11 not incl 1 and 10)

### try with smaller range

193

## if have evenly spaced set, mean is what to median

### mean = median

194

## Count integers in a set (divis by 7 btwnn 100-150)

###
Last - first / incr + 1

Find last and first divis by 7 - 105, 147

(147-105)/7+1

195

## Sum of consec integers

### Avg * # of terms

196

## Trick to finding sum of 1st 3 int in a set of 6 when given last 3 int sum is 624

###
n+3+n+4+n+5

-(n+n+1+n+2)

=9 so take 624-9

(only works for even number set, all n's cross out)

197

## # terms

###
(High # - Low #) / interval + 1

Interval is 2 for even or odd

** avg is add, # of terms is subtract

198

## Simplified Q for set of consec integers -->

### What is the value of any of the numbers?

199

## Weighted avg - given the 2 scores (80, 100) and weighting (40%, 60%) , find weighted avg score

###
1. Find diff of scores = 20

2. Multiply by HEAVIER weight = 20*.6 = 12

3. Add to LIGHTER side 80+12

Could flip 2 and 3, just take OPPOSITE ONES

200

## weighted avg - given 2 scores (80,100) and weighted avg of 92. Find weighting of the 100

###
1. Denom is diff of scores so 20

2. Num is diff of the longer dist so 92-80=12

3. 12/20 is heavier weighting (since you took longer)

201

## If weighted avg is closer to 1st number

### 1st number is weighted heavier, 1st number is teetered down

202

## weighted avg - if you get the 2 distances from the weight avg, to get the ratio, ex: 10---12-----16, ratio fo the 10 to 16 is

###
just flip the 2 distances

4:2 not 4:6

203

## 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

204

## When you label average and median, use

### Me -for mean and Md for median

205

## If # of terms * 1 of the numbers = # of terms *avg, then avg =

### median

206

## variance=

### SD^2

207

## What components needed for SD

###
difference between mean and each int, # of int

or variance

208

## Number prop - strategy

###
test cases

209

## sum of an odd number of consecutive integers is divisible by (i.e. 2, 3, 4)

###
the number of items

-divis by 3

210

## sum of an even number of consecutive integers is divisible by ie 2,3,4,5

###
NOT the number of items (avg of even set is not an integer so sum isn't divis)

avg is 3.5 so sum is 13, not divis by 4

211

## number divis by 8 if

###
last 3 digits are

or if you can divide by 2 3 times

212

## number divis by 9 if

### sum of digits divis by 9, just like 3

213

## 12 is equal to 3n where n is an integer (really saying)

### 12 is divis by 3

214

## if N is a divisor of x and y, then N is a divisor of what?

### x+y or x-y (adding/ subtr multiples will yield another multiple)

215

## if a is a factor of b and b is a factor of c, then

###
a is a factor of c

if 72 is divis by 12, then all factors of 12 are divis by 72

216

## if sum or product of 2 prime numbers is even, you know 1 of them must be

### 2

217

## 97/7=

### NOT 13!!! IT'S 13.SOMETHING

218

##
2! is

3! is

###
2

6

219

## 4!

### 24

220

## 5!

### 120

221

## 6!

### 720

222

##
When there are repeats in the combinatorics,

for ex 2 bronze and 3 silver

###
divide by repeats

total! /2!3!

223

## combinatorics - 2 types:

###
1) making decisions

2) arranging groups

224

##
when there are 2 groups - chosen vs not, make sure to

Ex: 8 members, choose 3

###
divide by both

8! / (3!*5!)

225

## 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

226

## when all items are chosen, just in different order AND NO REPEATS in combinatorics

### can do slot method __*__*__

227

## when you see AND (2 events happening) in comb / prob

### multiply

228

## when you see OR in comb / prob

### add

229

## when you see at least 1, trick is to

### 1 - P(none)

230

## when you see at most 1, trick is to

### 1-P

231

## LCM calc: 100, 140

###
Find all prime factors, for each unique factor, find the largest multiple

100: 2^2*5^2

140: 2^2*5*7

LCM: 2^2 * 5^2 * 7

232

## perfect squares contains only odd or even power of primes?

###
even (everything is doubled)

144 = 2^4*3^2

233

## test trick: If you see A is so obv wrong in DS, guess choice

### C

234

## If you see 3x+1 is prime, the +1 signals x should most likely be

### even

235

## check your work / calc!! when

###
1. if you finish quickly

2. if there's simple calc (longer calc less likely to get choices if you screw up)

3. if you're doing something "new", may have to come up w strategy on the fly so need to play devil's advocate

--> Slow down, don't worry about speed

--> Question every step's logic of problem (think about trap) - NOT REDO ACTUALLY CALC (10 #s divis by 3, then does 6 really have 2 3's)

**THINK ABOUT WHAT'S CAUSING PROBLEM / CARELESSNESS

236

## Use test trick - in PS, if you want to test multiple numbers, know that

### there is only 1 choice, so the cases you test should always yield the same choice (don't need to test multiple cases)

237

## DS - never guess E unless you know it's E, esp harder DS Qs

### much lower % chance it's E

238

## x! is a multiple of

### any number between 1 through x

239

## 10! + 7 is a mult of

### 7 bc both have 7

240

## when you see rt x + rt y, think of

### x + 2 rt (xy) + y

241

## Avg of a set of numbers is

###
Avg of 1st and last terms or (1st + Last) /2

** avg is add, # of terms is subtract

242

## 2^3a * 2^-3b

### 2^ (3a - 3b)

243

## Overlapping matrix - how do you combine the 2 columns

### ADD NOT MULTIPLY

244

## Geometry tricks

###
1. make sure you solve for right thing - area, perim (reread problem)

2. Look to Q for clues if stuck - cubic meters --> volume

3. test extremes (max area, can triangle be very fat or skinny)

4. Use the silent polygon or bigger shape

245

## 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.)

246

## Geometry shapes in PS are drawn to scale

###
so visualize and estimate!

DS are not

247

## 12000/ 25

### easier to say 1000/25 = 40 and 12*40 = 480

248

## Rate word problem tricks

###
1. visualize

2. simplify Q, so if given R and ask for T, simplify and say what's D?

3. like overlapping set, fill in as much of grid as possible, more suff

249

## if given a few factors (1, 2, 3, 4 ) for ex: 24, you can figure out the other factors by

###
multiply the other factors that you know

so 6, 8, 12, 24

250

## if given median = average and all but 1 numbers in a set, you can

### figure out that missing number

251

## overlapping sets - careless mistakes

###
descriptive label (instead of L, do LB)

reread each label in Q

252

## When you want to minimize 1, you

### maximize all the other

253

## Geometry trick - triangle

###
if your gut says similar tirangles, just assume

LOOK FOR RIGHT angle - COULD BE AT THE TOP , RIGHT OR LEFT

254

## Given slope is -3 and line passes through point (-2, r), it hits the origin if r is

### 6 bc slope -3 = r / -2

255

## what percent of x is y

### P/100 * x = y or P is y/x*100

256

## rate problem trick - if given person A starts before person B

### figure out how much perosn A did first

257

## If you see stems that look similar, giving you same info, guess

###
A or B, likely a trick that your'e not seeing

UNLESS it's giving you the same exact info when you simplify - D or E

258

## if question starts using ratios and asks what the total number is, think

###
add the ratios and find common multiple

ie 2:3 so total must be multiple of 5

and always simplify so 4:6 is 2:3

259