Quant Flashcards
What is the formula for sum of consecutive integers
Sum=average*number of terms
Average=(first+last)/2
Number of terms=last-first+1
How would you solve how many integers are there from 14 to 765, inclusive?
(Last-first+1)
765-14+1
How would you solve all the even integers between 12 and 24, inclusive?
((Last-first)/increment)+1
((24-12)/2)+1
How would you solve how many multiples of 7 are there between 10 and 40?
Could find least multiple of 7 and highest multiple of 7 then solve.
((35-14)/7)+1
An integer is divisible by 2 if…
The integer is even
An integer is divisible by 3 if…
The sum of the integer’s digits is divisible by 3
An integer is divisible by 4 if
The integer is divisible by 2 twice or if the last two digits are divisible by 4
An integer is divisible by 5 if
The integer ends in 0 or 5
An integer is divisible by 6 if
The integer is divisible by 2 and 3
An integer is divisible by 8 if
The integer is divisible by 2 three times or if the last three digits are divisible by 8
An integer is divisible by 9 if
The sum of the integer’s digits is divisible by 9
The first 17 prime numbers are…
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59
The product of k consecutive integers is always divisible by…
k factorial (k!)
Example a product of set of 4 consecutive numbers will be divisible by 4!—4x3x2x1=24
Odd+odd=
Even
Even+even=
Even
Even+odd=
Odd
Odd-odd=
Even
Even-even=
Even
Even x even=
Even
Even x odd=
Even
Odd x even=
Even
Odd x odd=
Odd
Even/odd=
Even
Odd/odd=
Odd
Even/even=
Even or odd
Patterns of units digits for powers of 0 is…
end in 0
Patterns of units digits for powers of 2 is…
Follow the four number pattern 2-4-8-6
Patterns of units digits for powers of 3
Follows the four number pattern 3-9-7-1
Patterns of units digits for powers of 4
Two number patter 4-6. All positive odd powers of 4 end in 4. All positive even powers of 4 end in 6.
Patterns of units digits for powers of 5
End in 5
Patterns of units digits for powers of 6
End in 6
Patterns of units digits for powers of 7
Follow the four-number pattern 7-9–3-1
Patterns of units digits for powers of 8
Follow the four number pattern 8-4-2-6
Any factorial >=5! will always have its unit digit
As zero
m=2k+1 where k is an integer. Is this odd or even?
Always odd
If the sum of two prime will always be… and except for…
Even…unless one of those primes is 2
2^1
2
2^2
4
2^3
8
2^4
16
2^5
32
2^6
64
2^7
128
2^8
256
2^9
512
3^4
81
4^3
64
4^4
256
5^3
125
5^4
625
6^3
216
7^3
343
8^3
512
9^3
729
Right triangle triplets are
3, 4, 5
6, 8, 10
5, 12, 13
7, 24, 25
(a+b)^2
a^2 + 2ab + b^2
(a-b)^2
a^2 - 2ab + b^2
a^2 - b^2
(a+b)(a-b)
