Quant Flashcards
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How do you determine the number of solutions (quadratic)
Look at the value of b^2-4ac:
Positive: 2
0:1
Negative:0
In quadratic equation, what is the sum of 2 solutions
-b/a
In quadratic equation, what is the product of the two solutions
c/a
Divisibility rule of 2
If the units digit is even
Divisibility rule of 3
The sum of all the digits is divisible by 3
Divisibility rule of 4
If the last 2 digits of a number are divisible by 4
Divisibility rule of 5
The last digit is 0 or 5
Divisibility rule of 6
If the number in question is an even number whose digits sum to a multiple of 3
Divisibility rule of 8
If the number is even, divide the three last digits by 8
Divisibility rule of 9
The sum of all the digits is divisible by 9
Divisibility rule of 11
If the sum of odd-numbered place digits minus the sum of the even placed-digits is divisible by 11
Divisibility rule of 12
If a number is divisible by 3 and 4
How do you determine the number of trailing zeros
The number of 5x2 pairs
Find the value of n when 21!/3^n
Divide 21/3 = x
Divide 21/3^2 = y
Until we cannot divide 3^n by something, you then do the sum of x,y …
How do you use the shortcut to determine the number of n in x! when it is even
You just need to break the non-prime number into prime factors and just use
When determining the units digits for numbers, what is the maximum number of combinations
4
Approximate square roots:
2,3,5,6,7,8
14.
1.7
2.2
2.4
2.6
2.8
Approximate cube roots
2,3,4,5,6,7,9
1.3
1.4
1.6
1.7
1.8
1.9
2.1
Approximate fourth roots
2,3,4,5,6,7,8,9
1.2
1.3
1.4
1.5
1.6
1.6
1.7
1.7
Special trick when adding like bases with equal exponents
4 * 4^n = 4^(n+1)
The product of any n consecutive integers is always divisible by
n!
The product of consecutive even integers is divisible by
2^n *n!
How do you know the value of p*q
Multiply the LCD and GCF
In a problem of constant growh, make sure to look at whether it is increasing by a constant amount or constant growth factor.
If it is a constant amount: x + #y
If it is a constant factor: xy^#
What is the difference between simple and compound interest
The simple is : principalratetime
The compound is : P(1+r/n)^(nt)
There is also one very important thing about the interest
It is always on 100.
Exponential growth problems
Initial value * growth^n
Digits problems
The value of any 2 digit number will follow the equation:
10a+b = x
What is the reverse number
10b+a = ba
What are the attributes of a dry mixture problem
Component, units and quantity
What are the attributes of a wet mixture
Components, concentration and quantityO
Object in line
If you are the m^th person counted from the begining of the line and the n^th from the end, the number of people in line is m+n-1.
What is the rate-distance formula
Distance = rate*time
Time = Distance/rate
Rate = Distance/time
What are the 2 important things in rate problems regarding time
Use the travel time, not time of day
The units must be compatible
What is the formula if rate-distance questions ask about average
Average rate = total distance/total time
What is the distance if the object travels from one point to another and then back.
D1=D2 => Total distance = 2D
In converging and diverging rate questions, what is unique
The total distance traveled is equal to the sum of the individual distances each object travels
D1+D2 = total distance
In addition, if they have traveled the same amount of time they both have t.
If two objects leave at different times
Their travel times must reflect the difference between their departure time. The object that leaves early is t+x and the 2nd is t.
If one object travels faster than the other.
The faster is r+x.
Sometimes this is expressed as a percentage.
In catch-up rate
They both travel the same distance but the one that started later is t+x.
What is the shortcut in catch-up problems
Time = delta distance/delta rate
What is the formula of rate-time-work
Work = rate*time
Rate=work/time
If you have the question z is what percent of y
z = x/100 * y
What do you do in overlapping sets
Always do a matrix
What is different in 3 overlapping sets
Use the venn diagram
What is important about the venn diagram
Remember that if you need to calculate, always start from the center and remove numbers to arrive at the larger brackets
When counting inclusive sets, what is the formula
Highest-lowest + 1
If we count excluding the first and last, what is the formula
Last-first-1
What is the formula to determine the median placement for odd and even numbers
odd: (n+1)/2
What is the placement for even numbers
Between n/2 and (n+2)/2
What is the combination formula
n! /
(n-k)!*k!
What do you do in handshake questions
total number * number of people you can meet /2
What is the equivalent property of combinations
nCk = nCn-k
What is the formula for permutations
n! /
(n-k)!
What is the permutation formula for indistinguishable items
n!/(r1!)*(r2)!
Counting 2 dimensional pathways
Identify every checkpoints and determine the number of ways to travel between each pair of successive points, and multiply them.
When it is a grid (no beg and end checkpoints) what do you do
Use the permutation formula for indistinguishable items because you will have many of the same movements (2 down, 3 right).
In addition, if there are 2 sections because each path leads to the following, there is not a choice between the 2, multiply them.
Circular arrangements
number of ways = (k-1)!
For triangle problems of non-collinear problems, what is the formula
Combination formula
For collinear problems
Determine the total number of ways to select 3 points - the number of ways to select 3 collinear points
For geometry, what planes go where (I, II, III, IV)
Starting from top right, it goes counter-clockwise
What is the slope of a line
delta y / delta x
What is the difference between a zero slope and undefined
Zero is horizontal, undefined is vertical. The reason why they are undefined is because of the slope formula cannot divide by 0 (the delta x is zero).
What do the different types of reflections look like:
Origin, y=x, y=-x, y=b, x=a
The first is over the origin point, the image is in the opposite quadrant.
y=x is the line that passes exactly at the origin through the quadrant I and III. The y=-x the same but is negative and passes through quadrant II and IV.
The image of y=b is (x, 2b-y)
The image of x=a is (2a-x, y)
What is the distance between 2 points
((delta x)^2 + (delta y)^2)^0.5
What is the midpoint formula
((x1+x2)/2, (y1+y2)/2))
What is the equation for a circle
(x-a)^2 + (y-b)^2 = r^2
Where (a,b) is the center of the circle. If the origin is the center, the formula is just:
x^2 + y^2 = r^2
What is the difference between the domain and range
The domain is the set of all the numbers a function can use as inputs.
The range is the set of numbers that the function can output.
How do you solve compound fractions
You need to work from the inside out
Maximum and minimum values of quadratic functions
If a>0: minimum occurs when
x = -b/2a
If a<0, the maximum occurs when x=-b/2a
How do you determine whether a graph is the graph of a function
The vertical line test states that any vertical line can only intersect the graph at exactly one point.
What is the formula of an arithmetic sequence
an = a1 + (n-1)*d
Where d is the common difference
What is the sum of the terms of an arithmetic sequence
Sn = n/2 * (a1+an)
What is a geometric sequence
The difference between every pair of 2 consecutive terms is the same
an = a1*r^(n-1)
How do you find the number of factors
find the number of prime factors and do every exponent +1 and then multiply them all
When finding the number of permutations of a triangle within non-collinear points, what formula do you use
combination:
nC3
When finding the number of permutations of a triangle withing collinear points, what formula do you use
Find the total number of ways using the combination formula and deduct from it the number of ways it could be collinear (using the combination formula)
