QUANT Flashcards
Product of k Consecutive Intergers is always divisible by _____
k! (k factorial)
According to the Factor Foundation Rule, every number is divisible by all the factors of its factors. If there is
always a multiple of 3 in a set of three consecutive integers, the product of three consecutive integers will
always be divisible by 3. Additionally, there will always be at least one multiple of 2 (an even number) in
any set of three consecutive integers. Therefore, the product of three consecutive integers will also be
divisible by 2. Thus, the product of three consecutive integers will always be divisible by 3!: 3 × 2 × 1 = 6.
Sum of a set of ODD number of consecutive integers is ALWAYS_____
a multiple of the number of items
————————-
Sum = #of items x Avg
This is true because the sum
equals the average multiplied by the number of items. The average of {13, 14, 15, 16, 17} is 15, so
15 × 5 = 13 + 14 + 15 + 16 + 17.
n-2,n-1, n, n+1, n+2
sum of above -> divisible by n!!
Sum of a set of EVEN number of consecutive integers is _____
NEVER divisible by the number of items
————
This is true because the sum equals the average multiplied by the number
of items. For an even number of integers, the average is never an integer, so the sum is never a multiple
of the number of items. The average of {8, 9, 10, 11} is 9.5, so 9.5 × 4 = 8 + 9 + 10 + 11. That is,
8 + 9 + 10 + 11 is NOT a multiple of 4.
———-
n-2, n-1, n, n+1
Sum of above can’t be divided by n
√A = ____
A ^(1/2)
∛A =
A ^ (1/3)
