Quant Flashcards
Even +/- Event = ?
Even
Odd +/- Odd = ?
Even
Even +/- Odd = ?
Odd
3! = ?
6
4! = ?
24
5! = ?
120
6! = ?
720
2^6 = ?
64
2^7 = ?
128
2^8 = ?
256
2^9 = ?
512
2^10 = ?
1024
14^2 = ?
196
15^2 = ?
225
4^4 = ?
256
4^5 = ?
1024
sqrt(2) = ?
1.4 Valentines 2/14
sqrt(3) = ?
1.7 St. Patrick 3/17
is 1 a prime number?
no
if x+y is even, then what do we know about x and y?
They’re both odd or both even
if x+y is odd, then what do we know about x and y?
One odd, one even
if x*y = even, then what do we know about x and y?
one or both of them is even
if x*y = odd, then what do we know about x and y?
both odd
Any n consecutive number includes at least one _______ of n
multiple
[DS question] is positive integer n-1 a multiple of 3? 1. n^3 - n is a multiple of 3 2. n^3 + 2n^2 + n is a multiple of 3
B.
Quadratic Formula
if ax2 + bx + c = 0
then
What does the mnemonic “Fewer Fators, More Multiples” mean?
Factors are the smaller side
Multiples are the larger (infinite) side
If N is a divisor of x & of y,
then is N a divisor of x + y?
Yes!
35 + 21 = 56
5*7 + 3*7 = 8*7
List the first 10 prime numbers
2, 3, 5, 7, 11, 13, 17, 19, 23, 29
What is the factor foundation rule?
if a is a factor of b, and b is a factor of c,
then a is a factor of c
The Prime Box
Given that int. n is divisible by 8 & 15, is n divisible by 12?
n
______|
2, 2, 2 | Yes
3, 5 | 12 = 2*2*3
…? |
_______
Unless 2 is involved, the sum of any two prime numbers is always even/odd?
Even
Principle of Combinatronics
OR means?
Add.
Principle of Combinatronics
AND means?
Multiply.
When to choose Smart Number?
When a problem contains only unspecified values.
Works for % problem too.
Average = ?
Sum / # of Terms
S/N
Formula for Counting Multiples
(Last - First)/Increment + 1
Define the properties of EVENLY spaced sets
- arithmetic mean = median
- mean = median = (first + last)/2
Formula for SUM of consecutive integers
sum = average * # of terms
Average of odd number of conservutive integers will always be __________?
an integer
Average of even number of conservutive integers will __________
Never be an integer
is it possible to determine the MEDIAN of a set containing unknown values?
Depends!
Yes | x, 2, 5, 11, 11, 12, 21
No | x, 2, 5, 11, 12, 12, 33
When to work backwards?
2 conditions
- When answer choices are “nice” numbers
- When question ask for a nice discree number
Rate x Time = what?
Distance
Work
What are the 3 possible scenarios of relative rate?
- bodies move towards each other
- bodies move away from each other
- bodies move in the same direciton on the same path
If an obj moves the same dist. twice, but at diff rate, then the average rate…
will NEVER by the “avg” of the two rates
actual average will lean closer to the slwoer rate as object spends more time on the slower rate.
Average Speed = ?
Total Distance/Total Time
Working together –> ____ the rate
Against each other –> ____ the rate
add
subtract
Figures on PS are drawn to scale. T/F?
True
Any time when two triangles each have a right angle and also share an additional right angle are similar. T/F?
TRUE
Rhombus. Define.
Parallelogram
+
Opposite equal acute angles
+
Opposite equal obtuse angles
Sum of interior angles of a polygon with n sides
(n-2)*180
What’s the trap in this question?
How man books, each with a volume of 100 cubic in, can be packed into a crate witha volume of 5000 cubic in?
it is tempting to do 5000/100 books
WRONG
because you don’t know the dimension of each book.
What are the two basic properties of a triangle?
- sum of angle = 180
- size of angle correspond to size of opposite side. If two angles are equale, then their opposite sides are also equal.
Triangle Inequality Law. Define.
Given two lengths of a triangle.
Length of a third side must lie between the difference & the sum of the two given sides.
Common right triangle dimension triplets & their multiples
3 - 4 -5 | 6 - 8 - 10
| 12 - 16 - 20
5 - 12 - 13 | 10 - 24- 26
8 - 15 - 17 | NONE
9 - 12- 15
The ratio of the sides in an isoscleles right triangle?
short: short:long = x : x : x*sqrt(2)
long: short:short = x : x/sqrt(2) : x/sqrt(2)
What is the rartion of the sides in a 30-60-90 triangle?
Define its relation with an equilateral triangle.
short : mid : long = x : 2x : x*sqrt(3)
you can cut an equilateral triangle in half and employ the property above to label the triangle.
What are the 3 ways to identify similar triangle?
AA / AAA
SSS
SAS
What is the relationship between inscribed angle & central angle of a circle if they both intercept the same arc?
angle(inscribed) = 0.5*angle(central)
Sum of an evenly spaced set = ?
Average * # terms
