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