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Old GMAT > Quant Strategies > Flashcards

Quant Strategies Flashcards

1
Q

Absolute value

Complex abs val where there’s multiple, like |4x-7| = |x-8|, what’s x?

A

”- 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”

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2
Q

Backsolving

A

Follow the flow of the problem, plug in the choices

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3
Q

Careless Typo - don’t write J as 1

A

Slow down

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4
Q

Careless 9 and a in a problem

A

Squigly a and straight 9, be careful

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5
Q

Careless 19+7

A

26

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6
Q

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

A
  • Simplify question if you can

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

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7
Q

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

A

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

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8
Q

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

A
  • if you can manipulate the choices to the same as the problem, or the 2 choices are actually the same - not C
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9
Q

DS Data Sufficiency

A

AD/BCE, BD/ACE

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10
Q

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

A

”- Signal: 2t+t must be like that for a reason, don’t just go 3x
- 2t / (t-x) + 1 bc that’s in answers”

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11
Q

DS Don’t forget to test which number?

A

“1; practice starting with 1 unless it’s not allowed

- Helps you get faster with testing cases”

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12
Q

DS When you have equation in question

A

Don’t assume that it’s given, write out equation with “?” for each stem

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13
Q

Equations System of equations

A

”- 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)”
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14
Q

Equations 2 variables in 1 equation

A

Can’t solve if you have 2 variables

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15
Q

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

A

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

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16
Q

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

A

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

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17
Q

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

A

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

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18
Q

Equations If problem asks for what the smallest possible value is, |37-5y|

A

”- Signal: 5y is a divisor, so you can think of 0, 5

- Other strategy is to test number”

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19
Q

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

A

“Consolidate the fraction and put it all over exponent

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

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20
Q

Exponents Same base with exponent, if division, you can

A

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

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21
Q

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

A

Multiple the exponents: 2^12

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22
Q

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

A

Can’t multiple exponents, try factoring out

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23
Q

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

A

“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”

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24
Q

Exponents Memorize 4^n, ending unit pattern is

A

4, 6 | 4, 6

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25
Q

Exponents Memorize 9^n, ending unit pattern is

A

9, 1 | 9, 1

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26
Q

Exponents Memorize 5^n, ending unit pattern is

A

Always 5

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27
Q

Exponents Memorize 6^n, ending unit pattern is

A

Always 6

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28
Q

Exponents Memorize 7^n, ending unit pattern is

A

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

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29
Q

Exponents Memorize 3^n, ending unit pattern is

A

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

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30
Q

Exponents Memorize 8^n, ending unit pattern is

A

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

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31
Q

Exponents Memorize 2^n, ending unit pattern is

A

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

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32
Q

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

A

1, 5, or 6

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33
Q

Exponents Memorize that n^n ends in only 2 digits

A

4 or 9

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34
Q

Exponents -10 * 10^2

A

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

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35
Q

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

A

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

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36
Q

Formulas when you see complicated formula, and variable is also complicated f(2rt3)=2x^4-x^2

A

”- 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”

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37
Q

Fractions Ugly fraction in equation

A

”- Get rid of denominator first

- Cross multiply”

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38
Q

Fractions 2 fractions divided by each other

A

Multiple top 1 and bottomest one / middle 2

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39
Q

Fractions If see many terms in a fraction, if see same terms in num and den

A

Split the numerator to turn 1 of the frxns into 1

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40
Q

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

A

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

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41
Q

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

A

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

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42
Q

Inequalities Retailer has less than twice as many dogs as cats

A

“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”
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43
Q

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

A

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

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44
Q

Inequalities If you know that x is negative and you have to square x<3

A

“Flip ineq: x^2>9

- Doesn’t work if x can be positive”

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45
Q

Inequalities If you know that x is pos, can you square x>3 (both left and right sides are pos)

A

Yes, “Don’t flip ineq: x^2>9

- Doesn’t work if x can be negative”

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46
Q

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

A

D>5, not D=5+C

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47
Q

Negative - Adding negatives

A

Pay attention, double check, slow down

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48
Q

Negative - Subtracting 3-4

A

Pay attention, double check, slow down

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49
Q

Negative - Equations with negatives

A

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

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50
Q

Negative - Negative in answer

A

Don’t forget to choose the answer with negative!

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51
Q

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

A

the negative does not distribute with an exponent

-16, not 16

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52
Q

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

A

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

- Inverse: y=k/x so y1x1 = y2x2”

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53
Q

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

A

”- 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)”

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54
Q

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

A

Look out for even choices

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55
Q

Quadratic If you see variable in denom and different powers,

A

Don’t move constant to other side

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

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56
Q

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

A

divide out by that number

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57
Q

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

A

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

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58
Q

Quadratics Memorize x^2-y^2

A

(x-y)(x+y)

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59
Q

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

A

(x-y)^2

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60
Q

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

A

(x+y)^2

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61
Q

Quadratics If you see 2xy

A

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

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62
Q

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

A

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

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63
Q

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

A

“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”
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64
Q

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

A

Can break it into 2 roots

Can’t for +/- i.e. sq rt (16+25)

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65
Q

Roots (sq rt of 4) ^ 5

A

”- Don’t get confused with sq rt, first simplify to 2^5

- Or, it’s 4 ^(5/2)”

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66
Q

Roots Memorize sq rt 2

A

1.4

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67
Q

Roots Memorize sq rt 3

A

1.7

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68
Q

Roots Memorize sq rt 5

A

2.25

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69
Q

Roots Memorize sq rt 169

A

13

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70
Q

Roots Memorize sq rt 196

A

14

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71
Q

Roots Memorize sq rt 225

A

15

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72
Q

Roots Memorize sq rt 256

A

16

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73
Q

Roots Memorize sq rt 625

A

25

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74
Q

Roots 10^3

A

1000

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75
Q

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

A

+/- the simplified answer, 2 solutions

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76
Q

Roots When you have gnarly roots, try

A

“Squaring it instead of calc the root

- See if it’s close to a square, like 49, 64, 81, etc.”

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77
Q

Smart numbers How to pick smart numbers?

A

”- Don’t pick 0, 1

  • Pick odd and even numbers
  • Don’t pick #s already in the problem”
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78
Q

Smart numbers When to pick smart numbers?

A

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

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79
Q

Mental math Divide by 5

A

Divide other number by 2, multiply by 10

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80
Q

Subtraction When there’s a carryover

A

Write out the carryover instead of doing it in your head

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81
Q

Test cases Often with DS in inequalities

A

“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)

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82
Q

Variables Combination of variables (x+y = ?)

A

”- Almost always don’t need to solve for x, y separately

- Figure out x+y together”

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83
Q

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

A

”- Use smart numbers

- Be careful- plug in the correct smart number”

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84
Q

Word problem If the questions asks for a ratio

A

Don’t multiply out everything, try crossing out things

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85
Q

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

A

Eliminate all answers where y isn’t <1

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86
Q

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)

A

Can leave mph without converting to sec

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87
Q

Word problem - ask yourself

A

Can I backsolve, instead of algebra

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88
Q

Inequalities: If more than twice as many dogs as cats

A

D>2C

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89
Q

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

A

y will always be 1 greater than x

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90
Q

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

A

Test cases

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

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91
Q

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

A
  • 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
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92
Q

Guessing randomly strategies

A
  • 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
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93
Q

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

A

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

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94
Q

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

A

cross out all choices with that choice

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95
Q

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

A

can square it and (x-y) is positive

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96
Q

If you have decimals,

A

convert to fraction (often can cross out denom)

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97
Q

When you square a pos fraction, it gets

A

smaller than the original (closer to 0)

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98
Q

When you square a neg fraction, it gets

A

bigger than the original (closer to 0)

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99
Q

0.9999999 translates to

A

1 - 0.00000001 which becomes 1 - 10^-8

Think 0.1 = 10^-1

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100
Q
  1. 1 translates to …

0. 1^n translates to

A

10^-1

10^-n

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101
Q

Step 1 - read the problem AND….

A

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

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102
Q

.375

A

3/8

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103
Q

.167

A

1/6

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104
Q

.625

A

5/8

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105
Q

.8333

A

5/6

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106
Q

GCF

A

Largest divisor

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107
Q

Distinct factors

A

Don’t forget 1, and any repeats

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

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108
Q

Trapezoid area

A

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

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109
Q

Area of piece of pie in circle if given angle s

A

A of pie / A of circle = s / 360

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110
Q

Central angle vs Inscribed angle in circle

A

2x vs x

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111
Q

Special rt triangles

A

x, x, xrt2 –> 45, 45, 90

x, xrt3, 2x –> 30, 60, 90

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112
Q

Pythag triplets

A

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

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113
Q

Ratio of angles in triangle vs ratio of sides

A

a deg > b deg > c deg

opposite a deg > opposite b deg > opposite c deg

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114
Q

Surface area of a cube

A

6x^2

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115
Q

Slopes

A

y coordinates / x coordinates

Vertical has no slope
Horiz has 0 slope

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116
Q

Perpendicular slope

A

negative reciprocal

2–> -1/2

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117
Q

Area of a sector

A

Fraction of the total area of the circle

Fraction = angle / 360

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118
Q

V of Cylinder

A

pi *r^2 *h

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119
Q

Total sum of angles of a polygon

A

(n-2)*180

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120
Q

What makes an impossible triangle

A

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

121
Q

Exterior angle (outside the triangle) =

A

Sum of 2 interior angles on the opposite side of triangle

122
Q

Similar triangles mean

A

2 angles are the same

123
Q

Area of rhombus

A

d1*d2 /2

124
Q

Largest area if given the perimeter for any quadrilateral

A

square

125
Q

Smallest perimeter if given the area or a diagonal for a quadrilateral

A

If given area, square

if given diagonal, really skinny rectangle (diagonal ~ long side)

126
Q

Area of equilateral triangle

A

[s^2 rt 3] / 4

127
Q

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

A

a^2:b^2

128
Q

diagonal of a cube

A

s rt 3

129
Q

diagonal of a rectangular solid

A

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

130
Q

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

A

infinite

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

131
Q

Max area of triangle

A

Right triangle

132
Q

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

A

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

133
Q

If y=x is the perpendicular bisector to a line, to find the other point….

A

Flip the point given (x,y) –> (y,x), watch out for signs (visualize it)

134
Q

x^2 + bx+c, if they’re asking if the products of the roots are +/- and the stem says c<0

A

c = rs so rs<0, you know that roots are - when multipled

135
Q

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

A

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)

136
Q

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

A

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

137
Q

Smallest side of a triangle and largest side

A

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

138
Q

When checking choices, look out for

A

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

139
Q

Parallelogram has —- angles

A

2 pairs of equal angles

140
Q

When you have quadratic for geometry problem

A

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

141
Q

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

A

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

142
Q

When you lay a cylinder flat, the height is

A

the diameter or 2*radius

143
Q

Isoc triangle in circle must be in

A

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

144
Q

Assume similar triangles if you suspect it!!

A

xx

145
Q

Weighted averages trick

A

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

ALWAYS BETWEEN the 2 ratios and closer to the heavier one

146
Q

Check answer by

A

Check constraints, makes logical sense.
For DS, check constraints in question AND STEM
REREAD PROBLEM
play devil’s advocate

147
Q

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

A

1.5x

148
Q

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

A
  1. Plug in choices

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

149
Q

1st step in quant - practice

A

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

150
Q

Estimate or benchmark

A

Use round numbers, get in the range

151
Q

When testing cases

A

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

152
Q

30 is what % of 50

Shortcut is

A

30/50 = x%

153
Q

Faster calc with odd percent like 7%

A

Do 10%/2 to get 5%

Then 1%+1%

154
Q

Compounding interest
Trick - new value vs old value

Compound quarterly if given annual rate

A

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

155
Q

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

A

Original amount is Y0, don’t put Y1, Always write Y0

156
Q

In addition or substraction, if % increase or decrease is the same, then total
Ex: Gross (-2%)- Deduct (-2%) = profit (??%)

A

will also change by same % increase or decr

-2% also

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

157
Q

Smart numbers trick - find lowest, how?

A

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

158
Q

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

A

2 ratios of the 3 var to solve

159
Q

Tens and units digit, see if there’s pattern using

A

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

160
Q

Given fraction, figure out if terminating decimal

A

Don’t forget numerator, may cross out something in denom

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

161
Q

If given A is dir prop to B, B dir prop to C, A is

A

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

162
Q

15*6

A

90

163
Q

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

A

Divisible by total amount

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

164
Q

Sum of consec integer, you can figure out range

A

Take smallest and largest number * #of terms in range

165
Q

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

A

Subtract 1 from any number yields same number of distinct values

166
Q

Slope greater than 1

A

Steeper than y=x line

167
Q

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

A

2* angle

Inscribed angle

168
Q

Prime numbers <30

A

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

169
Q

When you see change in %, you can either

A

Estimate

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

170
Q

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

A

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

171
Q

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

A

look out for factors, common divisors

172
Q

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

A

size and distance apart

173
Q

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

A

1/9 –> try 5/9=.115
1/11 –> try 5/11=/095
1/6 –> try 5/6 = .167*5=.833
1/7 –> try 5/7 = .14 *5=.7

174
Q

Be ok with switching smart numbers

A

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

175
Q

33^43 ends in what digit. TRICK

A

Divide by 4, not 3

176
Q

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

A

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

177
Q

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

A

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

178
Q

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

A

add rates

179
Q

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

A

subtract rates

180
Q

when you have a slower and faster rate, the average is

A

NEVER THE simple avg

**ALWAYS closer to the slower rate (smaller #) (estimate if needed) – doesn’t apply to 2 working together

181
Q

To get average rate of 2 workers

To combine 2 workers and get their rate together

A

Add distance and time –>

Add rates –>

182
Q

Rate problem steps

A

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

183
Q

When you see estimate within 0.5, think

A

+/- 0.5, so test the extremes

184
Q

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

A

where, who, ….can change denominator

Look for OF…..VERB

185
Q

Overlapping sets - minimum can be

A

0, not 1

186
Q

simultaneously and indep working together means you can add rates?

A

add rates

187
Q

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)

A

try with smaller range

188
Q

if have evenly spaced set, mean is what to median

A

mean = median

189
Q

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

A

Last - first / incr + 1

Find last and first divis by 7 - 105, 147
(147-105)/7+1

190
Q

Sum of consec integers

A

Avg * # of terms bc avg = sum/# of terms

191
Q

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

A

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)

192
Q

terms

A

(High # - Low #) / interval + 1
Interval is 2 for even or odd

** avg is add, # of terms is subtract

193
Q

Simplified Q for set of consec integers –>

A

What is the value of any of the numbers?

194
Q

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

A
  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
195
Q

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

A
  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)
196
Q

If weighted avg is closer to 1st number

A

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

197
Q

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

A

just flip the 2 distances

4:2 not 4:6

198
Q

if question asks for what value of 100x+200y, given x+y=1 and choices are 10, 150, 250

A

WEIGHTED AVG PROBLEM IN DISGUISE
x+y=1 is hint!
Can’t be 10 or 250 - has to be btwn 100 - 250

199
Q

When you label average and median, use

A

Me -for mean and Md for median

200
Q

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

A

median

201
Q

variance=

A

SD^2

202
Q

What components needed for SD

A

difference between mean and each int, # of int

or variance

203
Q

Number prop - strategy

A

test cases

204
Q

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

A

the number of items

-divis by 3

205
Q

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

A

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

206
Q

number divis by 8 if

A

last 3 digits are

or if you can divide by 2 3 times

207
Q

number divis by 9 if

A

sum of digits divis by 9, just like 3

208
Q

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

A

12 is divis by 3

209
Q

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

A

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

210
Q

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

A

a is a factor of c

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

211
Q

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

A

2

212
Q

97/7=

A

NOT 13!!! IT’S 13.SOMETHING

213
Q

2! is

3! is

A

2

6

214
Q

4!

A

24

215
Q

5!

A

120

216
Q

6!

A

720

217
Q

When there are repeats in the combinatorics,

for ex 2 bronze and 3 silver

A

divide by repeats

total! /2!3!

218
Q

when there are 2 groups (tricky bc may say choose from 7 colors, pick 2)

A

1st do the 1: T!/(1!6!)
Then 2nd T!/(2!5!)
THEN MULTIPLY THE 2 TO GET TOTAL

219
Q

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

A

multiply

220
Q

when you see OR in comb / prob

A

add

221
Q

when you see at least 1, trick is to

A

1 - P(none)

222
Q

when you see at most 1, trick is to

A

P(none) + P(1)???

223
Q

LCM calc: 100, 140

A

Find all prime factors, for each unique factor, find the largest multiple
100: 2^25^2
140: 2^25*7
LCM: 2^2 * 5^2 * 7

224
Q

perfect squares contains only odd or even power of primes?

A

even (everything is doubled)

144 = 2^4*3^2

225
Q

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

A

even

226
Q

check your work / calc!! when

A
  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
227
Q

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

A

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

228
Q

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

A

much lower % chance it’s E

229
Q

x! is a multiple of

A

any number between 1 through x

230
Q

10! + 7 is a mult of

A

7 bc both have 7

231
Q

when you see rt x + rt y, think of

A

x + 2 rt (xy) + y

232
Q

Avg of a set of numbers is

A

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

** avg is add, # of terms is subtract

233
Q

2^3a * 2^-3b

A

2^ (3a - 3b)

234
Q

Overlapping matrix - how do you combine the 2 columns

A

ADD NOT MULTIPLY

235
Q

Geometry tricks

A
  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
236
Q

When you need to work with right triangles, always think

A

sides (3-4-5, 6-8-10, etc.)
AND
angles (45-45-90, 30-60-90, etc.)

237
Q

Geometry shapes in PS are drawn to scale

A

so visualize and estimate!

DS are not

238
Q

12000/ 25

A

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

239
Q

Rate word problem tricks

A
  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
240
Q

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

A

multiply the other factors that you know

so 6, 8, 12, 24

241
Q

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

A

figure out that missing number

242
Q

overlapping sets - careless mistakes

A 
descriptive label (instead of L, do LB)
reread each label in Q
243
Q

When you want to minimize 1, you

A

maximize all the other

244
Q

Geometry trick - triangle

A

if your gut says similar tirangles, just assume

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

245
Q

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

A

6 bc you can get the slope with the other point (0,0) and (-2, r) so slope -3 = r / -2

246
Q

what percent of x is y

A

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

247
Q

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

A

figure out how much perosn A did first

248
Q

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

A

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

249
Q

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

A

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

250
Q

I have 20% fewer candies than Susan means

A

I have 80% of Susan

251
Q

Ron’s DS yes/no steps

A 
Use 2 line device
- be explicit with 2 options
Top: question, x>2
Bottom: x <=2
Row: A, B, C
252
Q

Ron’s WP steps

A
  1. answer intuitively
  2. build Excel (no variables)
  3. plug in info (no variables), draw allll relationships
  4. solve - now use var. Backsolve, pick #s, est, brute
253
Q

when you add a width to a frame, don’t forget to

A

add 2w to the length and width of frame

254
Q

Ron’s DS 2 line device trick

A

you can assume that the top row is checked, just need to prove bottom row

255
Q

20% more in her purse than in mine

A

Mine *1.2 = her purse

mine is the base since it’s after than

256
Q

sum of even integers btwn 100 and 200

A 
avg = 300/2
# int is 200-100=100 /2 (bc even) so 50 +1
=150*51
257
Q

sum of integers btwn 100 and 200

A 
avg = 300/2
# int 200-100=100+1 (no /2 bc it's not even or odd)
=150*101
258
Q

200% more than him - to get to the value of “him”, you need to

A

take the DIFFERENCE, not just 2x

(him - you / him) = 200%

259
Q

when you see a figure where things are rotated, beware

A

counter clockwise or clockwise!!

260
Q

divisor is the

A

smaller number that you can divide by

Ex: 2 is a divisor of 10

261
Q

If you’re picking numbers and question asks to find a % of %, use

A

1000, not 100

Ex: 16% for 1 yr, 9% for another yr. You need a denominator but you’re given that the 2nd denominator increases by 20% (% of % )

262
Q

when you have multiple calculations ex: 3x2x2, avoid careless

A

do each one separately
3x2 = 6
6x2 = 12

263
Q

when you’re estimating / checking answers, make sure to look at

A
  • range the answer should be in (elim too high / low)
  • draw comparisons with existing (OG machine vs new)
  • round up and down to estimate
  • odd vs even hint
  • redraw figures to visualize
  • if ask for range, take middle value
  • if the answer choice is exactly the number in the problem (likely eliminate)
264
Q

compound interest (semiannual) vs simple interest

A

compound interest will be a little bit higher than regular (apply interest more times)

265
Q

weighted avg estimate - if you have a bunch of numbers with a lower score, the only way to increase your average with 1 score is

A

if that 1 score is really high

266
Q

a sphere inside a cube means the radiuses are

A

radius of sphere = 1/2 side of cube

267
Q

when you plug in smart numbers, remember to think about

A

what makes sense - if 2 machines work together, their hours should be LESS than the 1 machine

268
Q

careless in division - better to write it out

A

78 / 3 (actually cross out so you don’t put 29 instead of 26)

269
Q

200% of 1 is

A

1+2(1)=3

to check: (3-1)/1=200%

270
Q

when you put the remainder over the divisor ex: 9.12 where remainder is 9

A

that means 12/100 = 9 / divisor

271
Q

don’t forget that (10^2)^4 is

A

10^8 not 10^6

272
Q

when you have a crazy root (ie 1+rt2) in an equation like x^2+x+1 , you can always

A

PLUG IN that crazy root

273
Q

Word problems - alternate methods:

A

BSEB

  • Backsolve, smart #s, estimate, brute force
  • Don’t forget to draw arrows for relationships
274
Q

Geometry - coordinates - if you redraw, make sure

A

you draw ACCURATELY as possible, if you mess up, redo. It’s better than carelessly making a mistake

275
Q

if you see the word “ANY” in a question about list of numbers
Ex: sum of ANY 3 numbers is 12

A

be wary - ANY means every single possible variation HAS to be equal to 10…that’s very restrictive
hint: likely all the numbers have to be the same

276
Q

Trick when you’re trying to find the total number of 2 variables and you’re given a ratio (B=1.5C) AND the total is btwn 21-28

A

Take the TOTAL so 1.5C + C = 2.5C or 5/2C and that must be equal a number in the range.
In this case, that total number must be divis by 5

277
Q

“at a particular time” signifies that at this 1 point in time, everything must happen

can they process 500 calls if there are x machines?

A

this isn’t is 500 divisible by x. It’s is x >=500 because it has to process it ALL AT ONCE

278
Q

if you’re given an inequality like A+C >10 and you need to find C, you can assume that ….

A

more than 1 pair will work so it’s not enough info. Even if there’s a complicated 324A+4598C = 230492834

Also way too time consuming to find…and you don’t have time

279
Q

Trick to DS per Connie

A

figure out what the Q is REALLY asking

- trick: fill in as much as you can

280
Q

when you have a border, don’t forget to LABEL all 4 sides

A

so if the inside is 8x10, then it becomes 8+2w x 10+2x, it’s not just 8+w

281
Q

Is 1 prime?

Is 1 a factor?

A

No, prime starts at 2 (2 is only even prime)

1 is a factor

282
Q

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

A

0 is an integer
Even
Neither pos or neg

283
Q

of Factors- don’t forget what?

Trick to find # of factors for really big number?

A

Don’t forget 1
ALLL pairs so for 25 it’s 1. 25, 5, 5

Trick: 1440 = 2^53^2 * 5
Get all exp - 5, 2, 1
Add 1 to each
Multiply = 63*2= 36

284
Q

when you see 3 groups in overlapping set

A

x1 = only 1, x2= in 2 of the circles, x3 = in all 3
1) x1 + 2x2 + 3x3 = sum of the 3 groups that include overlap
2) x1 + x2 + x3 + N (for neither) = total population excl overlap
Can solve for any of these x’s

285
Q

when you see APPROX in the question, be prepared for ugly math

A

so estimate!

or guess if you don’t have time

286
Q

Probability of A or B occuring is

A

P(A) + P(B) - P(A and B occurring)

287
Q

How many options 2 ppl out of 10?
- no repeating
- order matters (AB and BA are different)
Ex: no. 140

Probability to get women if 50% are women

A 
\_\_ \_\_ (slot machine)
10*9

Prob of women:
Numerator is 54
Denom is now 109

288
Q

You have total number, need to choose 2 of them. Order doesn’t matter (AB and BA are the same)
Ex: no. 187

A

10!/(8!*2!)

Includes people not chosen because not being chosen is also a combination

289
Q

Don’t forget that PS, you should always

A

eliminate when you can

BSEB

290
Q

Don’t forget that DS, you should always

A

test cases

291
Q

how many times a triangle intersects the circle, think of

A

times when the triangle TOUCHES the circle (intersect just means overlap so if they share a point, then it intersects)

292
Q

For geometry, if you have to solve for an angle,

A

write out as many angles as you know like 180-R before solving

293
Q

what’s the prime factor of 2^3 * (123) + 1

A

When you see the +1, it indicates that the prime factor must be greater than 3 since without +1, it would be 3

294
Q

246 = factor out 2

A

2^3 * (123)

295
Q

If the question asks “Did one of the members do something” interpret as

A

Did AT LEAST 1 do something, not EXACTLY 1 does something

296
Q

To speed up testing cases,

A

start with proving the bottom row, flip or do the opposite to prove the top row

297
Q

when you’re given 2 variables and asked what their greatest prime factor is, think

A

Test the variables with crazy prime factors like with 7 or 11 or 13 and a regular like 2

298
Q

10,000 initial amount, 4% annual interest, compound QUARTERLY. What’s amount after 6 mths

A 
Q1 = 10,000(1+.01) = 10.000+100=10,100
Q2 = 10,100(1+.01) = 10,100+101=10,201

Formula = 10,000(1+4%/4) ^ (4*1/2) = 10,000(1+.01)^2

299
Q

Trick: 10% of 10,000

1% of 10,000

A

Remove a 0 so 1,000

Remove 2 0’s so 100

Old GMAT (3 decks)

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