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Quant Flashcards

1
Q

large SD means numbers in set are

A

Far apart

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2
Q

If you add numbers farther away from the mean, SD will

A

increase

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3
Q

Does SD ever stay the same if you add numbers to a set?

A

no

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4
Q

If you multiply a set by 0.8, SD changes by

if you add 10 to each number in a set, the SD changes by

A

.8SD

SD stays the same

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5
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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6
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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7
Q

Equations 2 variables in 1 equation

A

Can’t solve if you have 2 variables

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8
Q

Equations If you have multiple 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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9
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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10
Q

(2^3) / (5^3) - same exponent, diff base

A

(2/5)^3

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11
Q

(2^7) / (2^5) - diff exponent, same base

–> if it’s something weird like (1/2)^2 * (1/2)^4

A

2^2 - subtract exponents

–> (1/2)^6 - don’t multiply (1/2) together, you’re double counting

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12
Q

Exponent to the exponent (2^3)^4

A

2^12 - multiple exponents

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13
Q

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

A

Factor out, can’t multiple or add these

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14
Q

Fraction in exponent (8^(2/3)

A

Simplify base first: 2^3

2^(3*2/3) so 2^2

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15
Q

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

Vs multiply by 3

A
  1. Find how many numbers btwn 6 and 100 (not counting 6, so 94)
  2. 94 * 3

3^94 if interval is multiply by 3

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16
Q

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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17
Q

2 fractions divided by each other (A/B) / (C/D)

0.5/4 or (1/2 ) / 4

3 / (3/2)

A

AD/BC bc flip C/D so it’s A/B * D/C

1/2 divide by 4 means it’s 1/2 * 1/4 = 1/8

3 divide by 3/2 means it’s 3 * 2/3

When you have to divide, just rmbr to flip the bottom

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18
Q

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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19
Q

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

A
  1. Split into 2 ineq

2. Or, do the same for each of the 3 (-1 for all 3, multiple -1 for all 3)

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20
Q

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

A

You can add them if in same direction. But can’t subtract / divide.

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21
Q

Retailer has less than twice as many dogs as cats

A

D<2C

or test cases

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22
Q

If asked for what the max product of 2 variables, and you’re given 2 inequalities. What’s strategy?

A

Test extremes like -1000, 1000

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23
Q

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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24
Q

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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25
Q

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

A

D>5, not D=5+C

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26
Q

Direct / inverse ratios

Ex: If you’re given X is dir prop to A and indir prop to B

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

X=kA/B (you can combine)

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27
Q

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

A

Look out for even choices

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28
Q

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

A

divide out by that number

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29
Q

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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30
Q

Memorize x^2-y^2

A

(x-y)(x+y)

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31
Q

Memorize x^2 - 2xy + y^2

A

(x-y)^2

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32
Q

If you see 2xy

A

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

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33
Q

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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34
Q

To figure out how many solutions are in a quadratic,

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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35
Q

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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36
Q

(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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37
Q

Memorize sq rt 2

A

1.4

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38
Q

Memorize sq rt 3

A

1.7

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39
Q

Memorize sq rt 5

A

2.25

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40
Q

14^2

A

196

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41
Q

15^2

A

225

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42
Q

16^2

A

256

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43
Q

25^2

A

625

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44
Q

13^2

A

169

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45
Q

10^3

A

1000

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46
Q

0.001

A

10^-3

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47
Q

Any time you simplify a sq rt, you must

A

+/- the simplified answer, 2 solutions

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48
Q

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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49
Q

Testing numbers

A 
0* 1*
Negatives
Odd/even
Fractions
Extremes
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50
Q

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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51
Q

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

A

Eliminate all answers where y isn’t <1

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52
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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53
Q

If question asks for max, when you backsolve, start with

A

largest number

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54
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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55
Q

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

A

can square it and (x-y) is positive since it’s inside sq rt

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56
Q

When you square a + or - fraction, they get

A

closer to 0

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57
Q

0.99 translates to

A

1-0.01

or 1 - 10^-2

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58
Q

1/6

A

0.167

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59
Q

1/8

A

0.125

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60
Q

3/8

A

0.375

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61
Q

5/6

A

0.833

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62
Q

5/8

A

0.625

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63
Q

7/8

A

0.875

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64
Q

GCF

A

largest divisor

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65
Q

Distinct factors of 25

A

1, 25
5, 5
* 4 distinct factors

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66
Q

Trapezoid area

A

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

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67
Q

Area of piece of pie in circle if given angle s

A

s/360 * Area of full circle

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68
Q

Angle touching center of circle vs angle touching circumference of circle

A

2x vs x

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69
Q

Right triangle options

A

Angles: 45, 45, 90 or 30, 60, 90
Sides: 1, rt 3, 2 or 1, 1, rt2
Pythags: 3,4,5 or 5, 12, 13 or 6, 8, 10 or 8, 15, 17

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70
Q

Given a set of numbers, find average. Trick for backsolving

1, 4, 4

A
  1. Correct answer choice: 3
    #s below it: 1, so the diff is 2
    #s above it: 4, 4 so the diff is 1 and 1 = 2
    BINGO
  2. Wrong: 2
    #s below it: 1 so diff is 1
    #s above it: 4,4 so the diff is 2 and 2 = 4
    2 is too low, go up
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71
Q

Surface area of a cube

A

6x^2

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72
Q

decreased by a factor of 1/3 means

A

multiply 2/3

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73
Q

in a set of consec int (“evenly spaced set”), what about the avg and median?

A

avg = median

avg and median are both a number in the set

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74
Q

Question - what’s the profit, you’re given items purchased and sold, don’t forget to

A

Order sold (rev) - purchased (cost)
Don’t just blindly follow the order it’s given
- you can find profit / unit too

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75
Q

when you see multiple conversions, mile / gallon, gallon / hr, gallons used, expect to

A

multiply the ratios and convert them to 1 unit

* write out the ratios clearly to avoid careless

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76
Q

Slope

Vertical line slope (x=3)
Horiz line slope (y=2)

A

Rise / run

Vert slope = no slope
Horz slope = 0

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77
Q

Perpendicular slope

A

negative reciprocal

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78
Q

Area of a sector if given angle

A

angle / 360 * area of whole circle

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79
Q

V of Cylinder

A

pi *r^2 *h

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80
Q

Total sum of angles of a polygon

A

(n-2)*180

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81
Q

What makes an impossible triangle

A

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

not inclusive**

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82
Q

Exterior angle (outside the triangle) =

A

sum of the 2 angles not adjacent to it

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83
Q

Similar triangles mean

A

2 angles are the same, so all angles are

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84
Q

Area of rhombus

A

d1* d2 / 2

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85
Q

Largest area if given the perimeter for any quadrilateral

A

square

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86
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)

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87
Q

Area of equilateral triangle

A

s^2 * rt3 / 4

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88
Q

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

A

a^2:b^2

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89
Q

diagonal of a cube

A

s rt3

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90
Q

diagonal of a rectangular solid

A

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

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91
Q

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

A

infinite

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

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92
Q

Max area of triangle

A

right triangle

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93
Q

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

A

Try finding the area, then change where you draw the base and height to calc one of the sides

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94
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)

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95
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 +/- so negative when multiplied

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96
Q

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

A

you can split them into 2

OR -2x in all 3 sections to get rid of 2x on both sides

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97
Q

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

A

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

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98
Q

Parallelogram angles

A

opposite angles are equal

You can also say that adjacent angles = 180 (angles in the same line)

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99
Q

When you have quadratic for geometry problem

A

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

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100
Q

Question asks for size of something without telling you the sides, test

A

extremes

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101
Q

When you lay a cylinder flat, the height is

A

the diameter or 2*radius

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102
Q

Isoc triangle in circle must be in

A

b and h are both the radius, point in center

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103
Q

if you think they’re are similar triangles

A

assume it!

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104
Q

Weighted averages trick

A

weights = 1

avg between the 2 numbers provided

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105
Q

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

A

1.5x

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106
Q

Steps in PS

A
  1. read problem, glance at choices to elim any extremes
  2. Draw grid, BSEB
  3. What’s trap?
  4. Reread question to check
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107
Q

Compounding interest

Trick - new value vs old value

A

A=P(1+r/n)^nt
– if compounds quarterly and given annual rate, n=4

Trick: new value isn’t too far from original, takes a lot of time

Plug in: $1, go year by year if easier,

108
Q

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

A

Don’t forget Y0

109
Q

Gross (-2%)- Deduct (-2%) = profit (changes by what?%)

A

-2% only bc % changes are the same

110
Q

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

A

2 ratios of the 3 var to solve

111
Q

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

A

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

112
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

113
Q

What’s the total of these 4 when ratio is 2:3:5:6

A

Total must be divisible by sum of ratio

Sum= 16 so 196 isn’t the total

114
Q

Sum of consec integer - the range of the sum is within

A

smallest number * avg ~ largest number * avg

115
Q

If you know there’s at least a pair consec numbers in a set and there are no duplicates

A

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

116
Q

Slope greater than 1

A

Steeper than y=x line

117
Q

Prime numbers <30

A

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

118
Q

When you see change in %, you can either

A

Estimate

OR Eliminate - if it’s clearly not 50% or higher

119
Q

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

A

50% + 1/2 of 1 SD (34% typically) – don’t forget 50%, no need to add up that small tail

120
Q

Hidden FDP problem: grouping number of people

A

look out for factors, common divisors

121
Q

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

A

size and distance apart

122
Q

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

A

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

123
Q

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

A

Add

124
Q

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

A

Subtract

125
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

126
Q

To get average rate of 2 workers

To combine 2 workers and get their rate together

A

Add distance and time

Add rates

127
Q

When you see estimate within 0.5, think

A

+/- 0.5, so test the extremes

128
Q

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

A

where, who, ….can change denominator

Look for OF…..VERB

129
Q

Overlapping sets - minimum can be

A

0, not 1

130
Q

simultaneously and indep working together means you can xx rates?

A

add

131
Q

how to check you counted correctly the # of int btwn a range

A

try with smaller range

132
Q

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

A

(Last - first) divide first by incr, then + 1

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

133
Q

Sum of consec integers

A

Avg = sum / # of terms

134
Q

Trick to finding sum of 1st 3 int in a set of 6 when given last 3 int sum is 624 (trick only works for even numbered set)

A

Difference in 1st 3 vs last 3 is: n+3+n+4+n+5-(n+n+1+n+2), so 9

624-9 is answer

135
Q

terms

A

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

** avg is add, # of terms is subtract

136
Q

Simplified Q if ask to find the sum of consec integers –>

A

What is the value of any of the numbers?

137
Q

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

A

80 ———- 100
40% 60%

Weights are 2:3 so flip them 3x + 2x = 20 (diff)
x=4 so avg is 12 away from 80 or 92

138
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

139
Q

variance=

A

SD^2

140
Q

What components needed for SD

A

difference between mean and each int, # of int

or variance

141
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

142
Q

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

A

12 is divis by 3

bc n can be any integer, but as long as 12 is divis by 3, it’s fine

143
Q

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

A

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

144
Q

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

A

a is a factor of c

If 2 is a factor of 6 and 6 is a factor of 72 then 2 is also a factor of 72

145
Q

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

A

2

146
Q

2! is

3! is

A

2

6

147
Q

4!

A

24

148
Q

5!

A

120

149
Q

6!

A

720

150
Q

When there are repeats in the combinatorics,

for ex 2 bronze and 3 silver

A

divide by repeats

total! /2!3!

151
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

152
Q

when you see AND (2 events happening)

A

multiply

153
Q

when you see OR in comb / prob

A

add

154
Q

when you see at least 1, trick is to

A

1 - P(none)

155
Q

when you see at most 1, trick is to

A

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

156
Q

LCM calc: 100, 140

A

Find all prime factors and powers, take the largest power of each factor
100: 2^25^2
140: 2^25*7
LCM: 2^2 * 5^2 * 7

157
Q

perfect squares contains only odd or even power of primes?

A

even (everything is doubled)

158
Q

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

A

even

159
Q

To check your work,

A

reread problem
check constraints in problem
think what’s trap?

160
Q

x! is a multiple of

A

any number between 1 and x

161
Q

10! + 7 is a mult of

A

7 bc you can factor out 7 (all others! + 1)

162
Q

when you see rt x + rt y, think of

A

x + 2 rt (xy) + y

163
Q

when a sphere is inscribed in a cube, think

A

slicing the sphere so the circle is inscribed inside the square
r = 1/2 s

164
Q

Gnarly calculations, first try to

A

factor out and simplify

165
Q

If you INCR each number in a set by 10%, to calc the difference in the old and new avg trick

A

old avg * change in % (here it’s 10%)

166
Q

If you DECR each number in a set by 10%, to calc the difference in the old and new avg trick

A

old avg * change in % (also decr by 10% or * 90%)

167
Q

When you estimate 9900 * 100 / 55,

A
  1. write out >9000 * 100 / >50

2. since > is in both num and dum, they “cancel out”

168
Q

2^3a * 2^-3b

A

2 ^ (3a-3b)

169
Q

Overlapping matrix - how do you get the total

A

ADD NOT MULTIPLY

170
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
171
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.)
AND 1-1-rt2, 1, rt3, 2

172
Q

Geometry shapes in PS are drawn to scale

A

so visualize and estimate!

DS are not

173
Q

12000/ 25

A

1000/25 * 12 so 40 *12

174
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
175
Q

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

A

divide 24 by those factors to get the other ones

176
Q

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

A

figure out that missing number (avg*n - sum of rest of the numbers)

177
Q

overlapping sets - careless mistakes

A 
descriptive label (instead of L, do LB)
reread each label in Q
178
Q

When you want to minimize 1 variable, you

A

maximize all the others

179
Q

Geometry trick - triangle

A
  1. if your gut says similar tirangles, just assume

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

180
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

181
Q

what percent of x is y

A

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

182
Q

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

A

figure out how much distance A covered first

183
Q

I have 20% fewer candies than Susan means

A

.8S

184
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
185
Q

Ron’s WP steps

A
  1. answer intuitively
  2. Grid - build Excel (no variables)
  3. Relationships - plug in info (no variables), draw allll relationships
  4. BSEB - solve - now use var. Backsolve, pick #s, est, brute
186
Q

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

A

add 2w to the length and width of frame

187
Q

Ron’s DS 2 line device trick

A

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

188
Q

20% more in her purse than in mine

A

Mine *1.2 = her purse

mine is the base since it’s after than

189
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
190
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
191
Q

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

A
  1. You are = 1+200% so 3x, He is x.
  2. OR take the DIFFERENCE, not just 2x
    (him - you / him) = 200%

(multiple is always 1 more than the % -> just rmbr 100% = 2x)

192
Q

when you see a figure where things are rotating, beware

A

counter clockwise or clockwise!!

193
Q

divisor is the

A

smaller number that you can divide by

Ex: 2 is a divisor of 10

194
Q

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

Ex: grow 16% in Y1, 9% in Y2. 2nd year denom increases by 20%. What’s 1st year denom? (% of % )

A

1000, not 100

195
Q

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

A
  • range the answer should be in (elim too high / low)
  • elim constraints
  • 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)
196
Q

compound interest (semiannual) vs simple interest

A

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

197
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 (takes a lot to raise your avg grade, rmbr)

198
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

199
Q

1 increases 200% =

A

1+2=3

200
Q

given: 9.12 and the remainder is 9, what’s the divisor?

what’s remainder?

A

9/divisor = 12/100
FORMULA: .12*Divisor = Remainder –> .12D=R

Since divisor should be an integer, you can say D = R*25/3 so R has to be divis by 3

201
Q

don’t forget that (10^2)^4 is

A

10^8 not 10^6

202
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

203
Q

Word problems - alternate methods:

A

BSEB

  • Backsolve, smart #s, estimate, brute force
  • Don’t forget to draw arrows for relationships
204
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

205
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

206
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

Since 1.5C+C is btwn 21-28, 2.5C turns into 5/2C is 21~28

C then ~ divis by 5, so you know it’s 25

207
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

208
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

209
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

210
Q

Is 1 prime?

Is 1 a factor?

A

No

Yes

211
Q

0 is …
Is 0 a +/- number?
Is 0 even/odd?
Is 0 an integer?

A

Neither
Even
Yes

212
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

213
Q

when you see 3 groups in overlapping set

A 
x1+x2+x3+none = total number provided
x1+2x2+3x3 = sum of the 3 indiv groups, which incl overlap
x2 = sections with 2 groups that overlap
x3 = the center section with all 3 groups overlapping
214
Q

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

A

estimate, eliminate, guess

215
Q

Probability of A or B occurring is

A

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

P(A, not B) + P(not A, B) in the case when 1 = P(A and B) + P(not A, not B) + P(A, not B) + P(not A, B)

216
Q

How many different options can you get selecting 2 people out of 10? Order matters (AB and BA not the same).
Ex: no. 140

What’s the probability to select 2 women if 50% are women out of 10 ppl?

A

__ __
10*9

Fraction:
(54) / (109)

217
Q

10 total people, need to choose 2. Order doesn’t matter (AB and BA are the same)
Ex: no. 187

A

10!/(2!*8!)

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

218
Q

When you have multiple intervals on a circle, DON’T FORGET TO COUNT

A

all of them until you get back to where you started, don’t just stop at the last tick before the starting point!

219
Q

180 is what % greater than 80? Trick

A

Base is what’s after “than” so 80
80 is close to 90, 180 is 100% greater than 90
so 180 is MORE THAN 100% greater than 80

220
Q

Quant - each problem, strive for

A

PRECISION AND EFFICIENCY (must get all easy Qs right, find tricks / traps in hard ones)

  1. most efficient way (don’t waste energy)
  2. avoid careless
  3. avoid trap
221
Q

30,000 = (100 + w)(200 + w), can you factor out 100?

A

NO!! Can’t do 300=(1+w)(2+w)!

222
Q

Doubling the area of a rectangle, how much do the sides increase (Ex: 100x150=15K)

A

Less than DOUBLE the sides

100x150=15K –> 150x200 = 30K

223
Q

To avoid careless mistake if question asks for x+16,

A

Draw grid, circling the blank spot next to x+16

Practice this grid so you get used to filling it in

224
Q

(rt 82 + rt 82)^2 tricks

A

(2rt82)^2

or 82 + 2(82) + 82 bc the middle is 2 rt82 * rt 82

225
Q

when the population doubles, think

A

exponents (2^x)

NOT multiplying by the number of times it doubles (2x)

226
Q

DS question where it vaguely says isoc triangle

A

draw both a right isoc and a isoc without right angles

227
Q

when given (-5,r) as a point, but you don’t know what r is, you should

A

test cases for r ie: r=1, r=25

228
Q

if constraint is positive, integer, write the 1st possible answer

A

write out “1” - reminds you to start here

229
Q

Solve for 4x^2 from rt(3-2x)=rt(2x) + 1

with pen and paper

A

Answer: 6x-1 = 4x^2

  • *Don’t forget to move all terms with x to 1 side
  • *Don’t forget to multiply 2 in the middle part 2rt(2x(3-2x)
230
Q

hemisphere radius and height

A

equal

Hemisphere is basically half of a sphere

231
Q

President, sec, treasurer. What’s probability of you getting secretary out of 10 ppl?

A

Not getting president: 9/10
Getting sec: 1/9
Not getting treasurer: don’t need to do bc you already got sec
Prob = 9/10 * 1/9

232
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

233
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

234
Q

To speed up testing cases,

A

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

235
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

236
Q

246 = factor out 2

A

2^3 * (123)

237
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

238
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

239
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)

240
Q

When you’re picking smart numbers, don’t forget

A

0 (lots of variables, get rid of 1 of them easily)

1 (lowest number to start plugging in)

241
Q

Testing numbers for % increases, try

A

200% (3x) or 300% (4x)

Just rmbr 100% = 2x

242
Q

10^-8 (how many 0’s before 1)

A

7 0’s

Think 10^-2 = 0.01 so only a 0 before 1

243
Q

Rate - if the question asks whether D>100, does R / T have to be > or < ?

A

if D>100 then R/T also >

244
Q

a club has 20 members, what is the number of 5-member committees that can be formed

A

it’s not 4!!

NUMBER = how many 5 member committees so combinatorics - 20!/15!5!

245
Q

if there’s a number of blocks arranged in a square, what does it mean to remove 1 row and 1 block from each row?

A

Removing a row on the top and left already removes 1 block. You go from 8x8 to 7x7

246
Q

weighted avg, if it’s about $ and number of items and you’re given the wtd avg and total units, what do you need?

A

Need the both $s –> can figure out the # of items for both

Need both numbers –> can figure out $ for both

247
Q

if you’re diligent about using Ron’s 2 line device, if you can’t seem to find a test case for the bottom row,

A

use algebra and use other stem as a hint

248
Q

when given rate, make sure that it’s a

A

ratio of some sort: liters / hr, miles / hr

Ex: rate of k liters for every x hrs –> rate is k/x not just k

249
Q

In DS, if you have 3 equations, make sure you

A

plug in all the numbers you’re given - typically need 2 equations to solve if you plug in everything you’re given

250
Q

5^(x-3)-5^x - how do you simplify?

A
  1. 5^(x-3) [ 1-5^3] –> you always factor out the smallest one
  2. TEST CASES, x=4, answer choices also have x
251
Q

Quant tricks - time efficiency

A
  1. skip - combinatorics, geometry, wordy WP, 3 part (I, II, III)
  2. test cases - 1, but if you’re trying to prove it wrong, try fractions or negatives
  3. fill in as much as you can (ie overlap set, equations)
252
Q

elimination tricks in choices

A
  • decimals vs integer (# of ppl should always be int)
  • even vs odd
  • > 1 for probabilities / wtd avg
  • answer should end in a certain number
253
Q

DS tricks

A
  • look at both stems to get a hint, NOTE DIFFERENCE IN 2, start with easier one
  • 2 line device - test bottom row first
  • test cases
254
Q

PS trick

A
  • figure out what the Q is REALLY asking
  • look at choices to eliminate right away
  • test cases - be diligent about grid
  • BSEB
255
Q

Overall quant tricks

A
  1. read Q, paraphrase - what is Q really asking?
  2. look at choices (proceed with DS/PS tricks)
    - -> when you can’t figure out path forward / can’t find answer in choice, SKIP
  3. reread Q, think what’s trap?
256
Q

when you see “what % did something change”

what % did the ratio of royalties to sales decrease from $20 to $108

A

what % = percent change, don’t just subtract ratios

257
Q

when you see average, and given the min of a set, can you get the max?

A

No

When you see avg - get the sum, you’ll see that there are multiple max’s that still add up to the sum

258
Q

when you have the weighted avg and the 2 #s at each side, do you know which one has more students / “weight”?

A

Yes
80—–84–86 - 86 has more weight
You won’t be able to tell exactly how many students in each end.

259
Q

1 hour is how many seconds

A

3600 or 60*60, not just 60!

260
Q

even for “easy” problems, don’t forget to

A
  1. read the question - write down what the Q is really asking
261
Q

when you see ratio, make sure you don’t

A

forget that there are VARIOUS sets of numbers that work for the ratio, unless you have constraints

262
Q

.18/.3 =

A

NOT 6

.18 / .30 so 3/5

263
Q

when you see time remaining and 10% completed,

A

time remaining = how much time it takes to do 90%

264
Q

4+8+…36
What’s the average?
What’s the # of int?
What’s the sum?

A 
Avg = (36+4) / 2=20
# of int = (36-4) / 4 + 1 = 9
Sum = A*n = 20*9=180
265
Q

when you see l^2+w^2=200^2 and l+w=280, think

A

you can square (l+w)^2 = 280^2, and get l^2+2lw+w^2

l^2+w^2 you already have, so just solve for lw

266
Q

280^2-200^2

A

(280-200)(280+200)

267
Q

when you see machine produces x widgets every 4 min

A

rate is x/4

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