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GRR > Quant > Flashcards

Quant Flashcards

1
Q

Special triangle 1

A

3, 4, 5 or 6, 8, 10 or 1.5, 2, 2.5 or any multiple of that

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2
Q

Special triangle 2

A

5, 12, 13 or 10, 24, 26

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3
Q

Isosceles triangle

A

x, x, xrt2

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4
Q

30, 60 90 degree

A

x, xrt3, 2

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5
Q

Other odd spec triangles`

A

8, 15, 17 or 7, 24, 25 or 9, 40, 41

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6
Q

Similar triangles, given 2 parallel sides

A

If share angle, then they are similar

*corresponding angles and prop sides; area is sq of proportion of sides

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7
Q

Similar triangles, given 2 parallel lines with vertical angle

A

Vertical angles are the same, corresponding angles are the same
*corresponding angles and prop sides; area is sq of proportion of sides

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8
Q

Similar triangles, both have right angles

A

If share angle, then the last angle must have same measurement
*corresponding angles and prop sides; area is sq of proportion of sides

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9
Q

Consec int: avg # odd consec int

A

always integer

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10
Q

Consec int: avg even # consec int

A

not an integer

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11
Q

If # of int is odd, sum is

A

divisible by n

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12
Q

If # of int is even, sum is

A

not divisible by n

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13
Q

Product of K consec int is divisible by

Product of K evenly spaced int is divisible by

A

K!
(because if you divide the evenly spaced by K!, you’ll get the set of consec int - figure out # of terms in set and if # is a multiple of K!)

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14
Q

3 consec int

A

if middle is odd, then 2 evens on the side (one divis by 2, other divis by 4), always divis by 3

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15
Q

2 consec int

A

must be even int, so product ALWAYS even

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16
Q

E +/- E

A

E

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17
Q

O +/- O

A

E

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18
Q

E */ E

A

E

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19
Q

O */ O

A

O

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20
Q

Sum of 2 primes = E or O?

A

E, unless one’s a 2 and thus it’ll be O

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21
Q

OEOEO (5)

A

O bc 1 pair of O makes E and single O make O

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22
Q

EOEOEO (6)

A

O bc 1 pair of O makes E and single O makes O

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23
Q

If unit digit is 0, 1, 4, 5, 6, 9

A

it’s a perfect square

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24
Q

if unit digit is 1, 5, 6**

A

Any power of that number has same unit digit

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25
Q

Sum of DISTINCT prime is odd

A

then it’s a perfect square (49–> 7 which is odd)

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26
Q

Perfect square (# total factors?)

A

Odd # of total factors (1, number, number)

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27
Q

10!+7 is a multiple of

A

7 because 7 is in both 10! and 7

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28
Q

Evenly spaced set, mean

A

= median (doesn’t matter if it’s odd number or even number of set)

= (1st + last) / 2

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29
Q

a^x*b^x

A

(ab)^x

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30
Q

x^2=-9

A

no real solutions!

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31
Q

x^2-x

A

0

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32
Q

1/x > 1/y

A

when +x< +y

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33
Q

1/x > 1/y

A

when x<y and both are negative

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34
Q

Area of equilateral triangle

A

rt3/4 *s^2

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35
Q

Area of rhombus

A

D1D2 / 2 (D is diagonal) or bh

*Must know D, can’t assume rhombus has 90 deg

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36
Q

Diagonal of a square

A

x rt2

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37
Q

Diagonal of a cube

A

x rt 3

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38
Q

Square maximizes ?? (V or perimeter)

A

Volume

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39
Q

Rectangle maximizes ?? (V or perimeter)

A

Perimeter

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40
Q

Total average speed

A

2 S1 S2 / (S1 + S2)

*distance must be the same or same time with diff speeds

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41
Q

1/A + 1/B = 1/T

A

To complete 1 task, 1/T to finish task in 1 hour

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42
Q

Plug in: if square roots

A

Plug in 1 or -1

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43
Q

Represent 10s digit

A

10x+y

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44
Q

If there’s no shared primes, then GCF is ? LCM is ?

A

GCF = 1, LCM= product

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45
Q

1 even integer in a set, product is divis by?

2 even integers in set, product is divis by?

A

2

4

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46
Q

Never forget __ as a factor

A

1

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47
Q

If asks for ratio and doesn’t specific integer,

A

it could be anything

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48
Q

5! (what’s a multiple)

A

10

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49
Q

2^4

A

16 (think 4^2)

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50
Q

2^5

A

32

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51
Q

2^6

A

64 (think 4^3)

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52
Q

2^7

A

128

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53
Q

2^8

A

256 (think 4^4)

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54
Q

2^9

A

512

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55
Q

2^10

A

1024 (good to know as proxy to 1000)

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56
Q

3^3

A

27

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57
Q

3^4

A

81

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58
Q

3^5

A

243

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59
Q

5^3

A

125

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60
Q

5^4

A

625 (think 25*25)

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61
Q

1/6 ~

A

16.7%

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62
Q

1/7 ~
2/7
3/7

A

14%
28%
42%

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63
Q

1/9 ~
2/9
3/9

A

11%
22%
33%

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64
Q

3!

A

6

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65
Q

4!

A

24

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66
Q

5!

A

120

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67
Q

6!

A

720

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68
Q

7!

A

5040

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69
Q

What’s LCM for 6 and 4

A

Write out primes: 2, 3 and 2, 2 so together it’s 2, 3, 2 that will work for both

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70
Q

What’s GCF for 6 and 4

A

2

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71
Q

Only ___ inequalities

A

ADD! no -, *, /

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72
Q

Sum of consecutive integers cubed

A

Is always a perfect square (hint if ask for sum, make chart with numbers and sum so 1+8+27 so sum is 1, 9, 36

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73
Q

Square root of cumulative sum (of consecutive integers cubed)

A

Is always the sum of consecutive integers

1,9,27 so 1,1+2+3 etc

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74
Q

D, E more likely in

C more likely in

A

middle

end

75
Q

interior angles sum

A

(n-2)*180

76
Q

Diagonal of a rectangular solid

A

SQ RT OF (x^2+y^2+z^2)

77
Q

sphere volume

A

(4/3) pi r^2

78
Q

Sphere area

A

4 pi r^2

79
Q

Surface area of cylinder

A

2 pi r^2 (wrap around) + 2 pi rh (2 circles on top and bottom)

80
Q

x=-b+/- sq rt (b^2-4ac) / 2a
if b^2-4ac is >0
if b^2-4ac is =0
if b^2-4ac is <0

A

2 x-int
1 x-int
0 x-int

81
Q

Parabola f(x)= ax^2+bx+c
If a is large
If a is small

A

graph is narrow

graph is wide

82
Q

1/11

A

.09999

83
Q

2/11

A

.18

84
Q

basically something /11 is

A

multiple of .09

85
Q

18^2

A

324

86
Q

19^2

A

361

87
Q

17^2

A

289

88
Q

16^2

A

256

89
Q

3^9)^(3^9)

A

3^(93^9) bc multiply exponents but can multiple 93*9

3^(3^23^9)=3^ (3^11), don’t just say 3^(93)^9 bc you’re exponentially counting

90
Q

of 2’s or 3’s in set

A

Start w bigger factor and write out numbers - then can simplify so write 3^3, 325 etc

2 is evens but also need to check division by 4, 8 etc bc there’s so many 2s

91
Q

If stuck

A

Plug in numbers!!

92
Q

Manipulate numbers so if ask for 47*49 try

A

(48-1)(48+1)

93
Q

If multiply by consec integ, product always

A

Product always a factor of ea consec integ

94
Q

Manipulation of exponents often clue -

A

Need to factor out if its 1 difference so 9^a = 10*9 - 9^2 bc you factor out 9 and get (10-1)

95
Q

Gcf

Lcm

A

Product of Every factor in middle - even if There are repeats

Product of all factors (don’t double count ones already in middle); can also calc by taking the product of the numbers / GCF

96
Q

Sum of consec int

A

Median *n and you can test if median is int when n is odd, median isn’t int when n is even

first term: A, last term: A+(n-1)d; so sum is [A+A+(n-1)/d]n/2 —-> so n/2[2A+(n-1)d]

N(n+1)/2 only when starts with 1

If you’re given 2+4+6, factor into 2(1+2+3)

Patterns # of pairs*avg where avg=(1st +last) / 2 and n is ((last-first)+1)/2

97
Q

Divis by 4

A

Last 2 digits divis by 4

98
Q

Divis by 6

A

If even and divis by 3

99
Q

(X-1)(x-4) which #s are positive

A

Negative - btwn 1 and 4

Pos - all else

100
Q

Perpendicular slopes

A

Negate reciprocal

3, -1/3

101
Q

Sum of consec integers - how to get a variation without trying crazy numbers

A

If you’re set is 1 2 345 then try -1,0,1,2,3,4,5,6

Helps prove insuff if number in set is important

102
Q

If you want to find min,

Ex: x _ 55 _ 2x+20

A

max the rest to get min x

x 55, 55, 2x+20, 2x+20

103
Q

Probability - desire outcome for AB

A

AB and BA possibilities so rmbr to multiply by 2

  1. calc probability of AB
  2. calc total sequences (AB, BA so 2)
  3. multiple 2* probability of AB
104
Q

Probability - select 2G and 2B out of 3B and 3G

A

Can use perm/comb:
Numerator use 3C2 * 3C2 because want G AND B, and think like a team
Denom use total ways so 6 total C 4, also think like team bc don’t matter AB or BA

105
Q

Probability if want to choose 2 girls out of 5, 10 ppl total

A

5/104/9 or think of it like perm bc not “team” so 5!/3! so 54 in numerator

106
Q

Probability tips

A
  1. identify max / min to check and elim answer
  2. committees / teams - think combination bc don’t want to dbl count
  3. arrange books / ppl in line - think permutation bc order matters need to count all
  4. # of ways / total <- perm/comb may help find
107
Q

Group grid

A

Use Venn if there’s no outside area (not A or B or AB)
Use group grid if there’s 4 possib
Identify max / min to eliminate / check answer

108
Q

Triangle

A

length of largest side is < sum of 2 sides

109
Q

3 circles in venn diagram

A
  1. sum all 3 =total and create a bunch of equations with each circle then add /subtract equations
  2. a+b+c-(all groups of 2) - 2*(group of 3)+ group of none
    * ** don’t forget *2
    - make sure the groups of 2 are also “clean numbers” and you don’t double count with group of 3
110
Q

Rhombus vs square

A

Rhombus: 4 equal sides, opposite sides and angles parallel, diagonals bisect; DOESN’T HAVE TO HAVE 90 DEG
- is a parallelogram, not a square
Square: 4 equal sides, opp sides parallel, all 90 deg angles, diagonals bisect
- is a parallelogram and rhombus

111
Q

Trick: Estimate

A

Replace decimal / roots w fractions and vice versa or estimate

  • if frxn, can elim by looking at >1 or <1
  • if geom, set limits to how big / small something can be
  • if overestimate, answer is less
112
Q

Trick: pick values

A

pick 0 or 1

if see “except ?s” find how other answers are the opposite

113
Q

Trick: plugging

A

don’t plug if it doesn’t fit in obv place, elim choices first

114
Q

2 eq, 2 var

A

if you see 3 var need 3 eq (even if 2 of the eq only has 2 variables bc you can solve for the 2 var first and get last)

115
Q

Ineq th

A

A>b and b>c then a>c

116
Q

x^a + x^b

A

BEWARE it’s not x^(a+b)

117
Q

x^a* y^b

A

BEWARE it’s not x*y^(a+b)

118
Q

3^a*2^a

A

(3*2)^a

119
Q

Wtd avg

A

Find distance between end points and average, use that proportion and flip it to get the proportion of the weights for each end bucket

120
Q

prime v factor

A 
factor = 1,2,3 --> don't forget 1 as a factor
prime = only 2, 3
121
Q

1/8

A

.125

122
Q

3/8

A

.375

123
Q

5/8

A

.625

124
Q

7/8

A

.875

125
Q

D=RT

A

Work together, Opposite direction - add rates
Same direction - subtract rates
Work separately - add distance and time, not rates
Tip: find the gap

126
Q

Random pick

A

Ineq - guess C or E
Middle choose ?
End choose C

127
Q

Median and mean if they equal, formula is

A

(A+b+c+d)/4 =(b+c)/2
Once you solve you get a+d=b+c
So much easier to prove than w numbers

128
Q

When you think about remainders,

A 
the divisor (bottom number) must be at least 1+remainder in order to get that remainder 
- remainder can never be > divisor
129
Q

See set of numbers

A

Think even odd, 2x+1

130
Q

Rt 3 estimate

A

1.7

131
Q

3^k+3^k

A

2*3^k not 3^2k

132
Q

A^6-b^6 can also be thought of as

A

|a|=|b| so once you know one is pos/ neg, can tell you a lot

133
Q

Divis by 6

A

Needs to be even and a factor of 3 ( bc divis by 2 and 3)

134
Q

If a number has a factor

A

Always divis by factor! No need to waste time thinking of others

135
Q

When triangles are similar, all sides have the same

A

Ratio! So easy to solve if you know one ratio

136
Q

Tangent on circle

A

2 tangents lines form an angle, minor arc = central angle, outside angle is 180-x bc below

That angle is supplementary to the angle formed inside the circle (kite like shape)

2 chords inside circle form angle x and minor arc=2x

137
Q

When comparing inequalities for fractions

A

Must make sure the base is 10 not 1/10 bc that changed the direction of inequality

138
Q

Increase by 1/3

A

Means multiply existing by 1/3

139
Q

10x the previous number

A

Think 10^n because its likely to be 1010…

140
Q

When you pull out 5^(k-1)-5^k

A

Can do 5^k(5^-1 -1) so its 1/5-1 inside

141
Q

Rt3

A

1.7

142
Q

Rt 5

A

2.25

143
Q

Smaller? -2.3 or -3

A

-3, think to the left in number line

144
Q

Has less than twice as many x as y

A

X<2y

145
Q

4^y+4^y

A

2*4^y
WRONG
4^2y (exponents make it too big, there’s just 2 that you’re adding, only if it’s a multiplication)

146
Q

x^2 - x<0

A

0<1

147
Q

absolute value equations, to check, you MUST

A

plug soln back into ORIGINAL eq

148
Q

reciprocal of inequalities:

if you know the sign of variables, can you flip the inequality x<y

A

the reciprocal is 1/x ___ 1/y
if both positive or negative flip
if opposite signs, don’t flip

149
Q

squaring inequalities:

do you flip the sign of inequality

A

if both are positive - don’t flip
if both are negative, flip when you square
if opp signs, or unclear - CAN’T FLIP, don’t know

150
Q

direct vs inverse

A

easier to just combine equations so
Direct: y1/x1 = y2/x2
Indirect: y1x1=y2x2

151
Q

Calc # of terms

A

Last number - make sure it’s one that is included
First number - is not included in set
last - first + 1 = # of terms

152
Q

sum between 2 numbers

A

avg (of the 1st and last) * # of terms (be careful how you calc # of terms - pay attn to even/odd, incl last but not first)

153
Q

max / min of parabola

A

o Y=a(x-h)^2+k then max is (h,k)

o Or, solve for –b/2a to get x, then plug in x to get y

154
Q

4/x < -1/3

A

if x is neg

12>-x (switch sign, but don’t add a negative)

155
Q

|z| <1

A

-1re faster

156
Q

when you see a number ^2 is < itself

x^2<x

A

then x must be pos fraction

0<1

157
Q

max / min length for triangle / polygon

A

triangle: a-b < ? < a+b
polygon: max is ? < sum of all known sides
min is largest given side - sum of rest (but no min if largest given side is not bigger than the sum of rest)

158
Q

12*18

A

216

159
Q

18*30

A

540

160
Q

if A>B, then if A increases by x% and y decreases by x% is net increase/ decr?

A

increase bc A>B initially

161
Q

Repeating decimals

A

if denominator is 9, 99, 999 look at numerator for repeating digits
Ex: 23/99=.2323
Ex: 1/9=.11111

162
Q

Tens digit

A

use 10x+y - helps you figure out factoring or other tricks

163
Q

Ratios if you have 10% and final amount is 70%

A

don’t find 100% then 70%, go straight to 70%

x/y=.1/.7

164
Q

Number of terms in a set (evenly spaced)

A

(last-first)/increment + 1

** add 1 after you divide out increment

165
Q

4b=5a, b must be a mult of ___ and a must be a mult of ____

A

b must be a multf 5 and a must be a mult of 4

166
Q

rt6

A

2.5

167
Q

rt 2.5

A

1.6

168
Q

of distinct factors

A

count every number even repeats

Ex: 49= 1, 7, 7 so 3 total

169
Q

Angle in circle - central angle is ___ when it’s corresponding arc is x

what’s inscribed angle

A

x (where angle touches center)

if inscribed angle (angle doesn’t touch center but rather is on the circle), then x/2

170
Q

rt 6=
rt 5=
rt 2.5=
rt 1.6 =

A
  1. 5
  2. 25
  3. 6
  4. 2 (just gets closer to 1)

Benchmark: rt1 =1 rt2= 1.4

171
Q

alternate strategies

A
  1. plug in answers - back solve
  2. smart numbers
  3. estimate / benchmark
172
Q

2 similar triangles, ratio is a:b what’s Area ratio

A

a^2: b^2 for triangles

If it’s a circle, and radius is a:b then Area is a^2:b^2 too
Area - 1:4 then radius is 1:2

173
Q

13n / m

which cannot be a divisor of 35x and 20y

A

m must be 13 or 13 * a part of n or just n
– think how can I cancel out denominator using factors in numerator

same concept, you should try dividing 35x / choice 20x and 20y / choice 20x. 35x/20y=7/4

174
Q

Add / subtract multiples of 3
Add / subtract non multiples of 3
Add / subtract multiple and non multiple

A

will still be divis by 3
may be divis by 3 (19+13=22 NO; 19+14=33 YES)
will NOT be divis by 3

175
Q

If x/N and y/N are integers

A

x+/-y is also divis by N

176
Q

If m contains 2, 3 as factors
n contains 2,5 as factors
m*n contains —-

A

223*5 as factors

177
Q

of factors for complex numbers like 9450

A

2 * 3 * 5^2 * 7

  1. add 1 to ea exponent: 1+1, 1+1, 2+1, 1+1
  2. Multiple together: 48 factors
178
Q

Perf squares have ___ # of total / distinct factors
Perf squares can be expressed as ____ number of prime factors
The p could have ___ number of factors
Sum of perf square factors is ___

A

odd
even
odd or even
odd

179
Q

Divisors means

A

factors

180
Q

Prime factors vs factors

A

Prime factors/ factorization: break out 12= 2^2*3

Factors: 1, 2, 3, 4, 6, 12 (think pairs)

181
Q

DRT- if you travel twice as fast and the difference in time is 15 min, then what’s original time? D is same

A

Think ratios: R: 1:2 T: 2:1 so T is 30:15 –> diff is 15
- 2T (where this is the orig since it takes longer)+T=15 so 2T=30

Or solve D/2x=T-15 and D/x=T get T=30

182
Q

When you see question that asks what the percent change or percent incr/decr

A

Make sure you find the actually change so new -old / old not just the difference!!

183
Q

Percent question, be careful

A

Make sure you write exactly what question asks, if its “of all bulbs turned on what’s the percent…” Make sure you circle xx/ bulbs turned on. Don’t solve for xx/all bulbs

184
Q

Percent terms

- when to use 100-x%

A

reduce by x%

% fewer than x

GRR (5 decks)

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