Quant Strategies Flashcards Preview

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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

I have 20% fewer candies than Susan means

I have 80% of Susan