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Flashcards in Quant Strategies Deck (195):
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=?

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 the case where x=?

"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 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 numbesr"

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 a6, need to find a100, if it's just +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

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

"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 If x

Can't square

47

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

D>5, not D=5+C

48

Negative Adding negatives

Pay attention, double check, slow down

49

Negative Subtracting 3-4

Pay attention, double check, slow down

50

Negative Equations with negatives

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

51

Negative Negative in answer

Don't forget to choose the answer with negative!

52

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

the negative does not distribute with an exponent
-16, not 16

53

Number Properties 0 is an integer?

0 is an integer

54

Proportionality If you see 2 sets of 2 variables in ratio form

"- Direct: y=kx, so you can do y1/x1 = y2 / x2
- Inverse: y=k/x so y1x1 = y2x2"

55

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)"

56

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

Look out for even choices

57

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

58

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

divide out by that number

59

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

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

60

Quadratics Memorize x^2-y^2

(x-y)(x+y)

61

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

(x-y)^2

62

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

(x+y)^2

63

Quadratics If you see 2xy

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

64

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

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

65

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"

66

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)

67

Roots sq rt of 4 ^ 5

"- Don't get confused with sq rt, first simplify to 2^5
- Or, it's 4 ^(5/2)"

68

Roots Memorize sq rt 2

1.4

69

Roots Memorize sq rt 3

1.7

70

Roots Memorize sq rt 5

2.25

71

Roots Memorize sq rt 169

13

72

Roots Memorize sq rt 196

14

73

Roots Memorize sq rt 225

15

74

Roots Memorize sq rt 256

16

75

Roots Memorize sq rt 625

25

76

Roots 10^3

1000

77

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

+/- the simplified answer, 2 solutions

78

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."

79

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"

80

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"

81

Mental math Divide by 5

Divide other number by 2, multiply by 10

82

Subtraction When there's a carryover

Write out the carryover instead of doing it in your head

83

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)

84

Variables Combination of variables (x+y = ?)

"- Almost always don't need to solve for x, y separately
- Figure out x+y together"

85

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"

86

Word problem If the questions asks for a ratio

Don't multiply out everything, try crossing out things

87

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

Eliminate all answers where y isn't <1

88

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

89

Word problem - ask yourself

Can I backsolve, instead of algebra

90

Inequalities: If more than twice as many dogs as cats

D>2C

91

When equation is y=x+1, that means y is what compared to x

y will always be 1 greater than x

92

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

93

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

94

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

95

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

96

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

cross out all choices with that choice

97

If you square something with rt (x-y) = A

can square it and (x-y) is positive

98

If you have decimals,

convert to fraction (often can cross out denom)

99

When you square a pos fraction, it gets

smaller than the original (closer to 0)

100

When you square a neg fraction, it gets

bigger than the original (closer to 0)

101

0.9999999 translates to

1 - 10^-8

102

0.1 translates to ...
0.1^n means

10^-1
10^-n

103

Step 1 - read the problem AND....

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

104

.375

3/8

105

.167

1/6

106

.625

5/8

107

.8333

5/6

108

0 is positive or negative?

0 is neither

109

Timing

# T All else 2/ min
6 52 1.4/min
13 42
20 32
25 22 3/min
28 12
31 3

110

GCF

Largest divisor

111

Distinct factors

Don't forget 1, and any repeats
x^2 = 1, x, x (3 factors)

112

Trapezoid area

A= (b1+b2)/2*h

113

Area of piece of pie in circle if given angle s

A of pie / A of circle = s / 360

114

Central angle vs Inscribed angle in circle

2x vs x

115

Special rt triangles

x, x, xrt2 --> 45, 45, 90
x, xrt3, 2x --> 30, 60, 90

116

Pythag triplets

3,4,5
6,8,10
5,12,13
8,15,17

117

Ratio of angles in triangle vs ratio of sides

a deg > b deg > c deg
opposite a deg > opposite b deg > opposite c deg

118

Surface area of a cube

6x^2

119

Slopes

y coordinates / x coordinates

Vertical has no slope
Horiz has 0 slope

120

Perpendicular slope

negative reciprocal

2--> -1/2

121

Trapezoid area

A= (b1+b2)/2*h

122

Area of piece of pie in circle if given angle s

A of pie / A of circle = s / 360

123

Central angle vs Inscribed angle in circle

2x vs x

124

Special rt triangles

x, x, xrt2 --> 45, 45, 90
x, xrt3, 2x --> 30, 60, 90

125

Pythag triplets

3,4,5
6,8,10
5,12,13
8,15,17

126

Ratio of angles in triangle vs ratio of sides

a deg > b deg > c deg
opposite a deg > opposite b deg > opposite c deg

127

Surface area of a cube

6x^2

128

Slopes

y coordinates / x coordinates

Vertical has no slope
Horiz has 0 slope

129

Perpendicular slope

negative reciprocal

2--> -1/2

130

Area of a sector

Fraction of the total area of the circle
(Fraction = angle / 360)

131

V of Cylinder

pi *r^2 *h

132

Total sum of angles of a polygon

(n-2)*180

133

What makes an impossible triangle

IF the sum of any 2 sides is smaller than the 3rd side, must be greater

1 side must be greater than the difference between 2 sides

134

Exterior angle (outside the triangle) =

Sum of 2 interior angles on the opposite side of triangle

135

Similar triangles mean

2 angles are the same

136

Area of rhombus

d1*d2 /2

137

Largest area if given the perimeter for any quadrilateral

square

138

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)

139

Area of equilateral triangle

s^2 rt 3 / 4

140

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

a^2:b^2

141

diagonal of a cube

s rt 3

142

diagonal of a rectangular solid

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

143

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

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

144

Max area of triangle

Right triangle

145

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

146

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)

147

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

148

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)

149

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

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

150

Smallest side of a triangle and largest side

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

151

When checking choices, look out for

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

152

Parallelogram has ---- angles

2 pairs of equal angles

153

When you have quadratic for geometry problem

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

154

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

155

When you lay a cylinder flat, the height is

the diameter or 2*radius

156

Isoc triangle in circle must be in

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

157

Assume similar triangles if you suspect it!!

xx

158

Is 1 prime

No, prime starts at 2
2 is only even prime

159

Weighted averages trick

Identify it is one bc it gives you ratios in a group
ALWAYS BETWEEN the 2 ratios (10%

160

Check answer by

Check constraints, makes logical sense.
For DS, check constraints in question AND STEM

161

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

1.5x

162

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

163

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

164

Estimate or benchmark

Use round numbers, get in the range

165

When testing cases

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

166

30 is what % of 50

Shortcut is

30/50 = x%

167

Faster calc with odd percent like 7%

Do 10%/2 to get 5%
Then 1%+1%

168

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

169

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

170

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

171

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

172

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

2 ratios of the 3 var to solve

173

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)

174

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

175

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

176

15*6

90

177

Ratios, sum of the raw form of ratios must be

Divisible by total amount

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

178

Sum of consec integer, you can figure out range

Take smallest number * # in range

179

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

Subtract 1 from any number yields same number of distinct values

180

Slope greater than 1

Steeper than y=x line

181

In circle, if point is on the circle and creates an angle, the length of arc is

2* angle

Inscribed angle

182

Prime numbers <30

2,3,5,7
11,13,17,19
23,29

183

# 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

184

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

185

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

186

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

187

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

size and distance apart

188

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

189

Be ok with switching smart numbers

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

190

33^43 ends in what digit. TRICK

Divide by 4, not 3

191

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

work produced or earnings = wage * # hrs

192

Rates - when 2 people walk towards each other, you can ---- rates

add rates

193

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

add rates

194

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

subtract rates

195

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