Question

Identify the rules which is followed by given series
A. Divide the number by $2$ and square the quotient.
B. Multiply the number by $3$ and divide the product by $2$.
C. Add $16$ to the number and divide the sum by $2$.
D. Divide the numbers by $2$ and add the square of the quotient to the number.
E. Square the number and divide by half of the number.
$8121415$
$8163264$
$8121827$
$816641024$
$8241687224$

Answer 1

In this case, operations as suggested in the rules are not performed on a separate set of numbers, but on the numbers appearing in the given sets only.
Consider rule $A$:
'Divide the number by $2$ and square the quotient'.
Let us start with $8$.
$\frac{8}{2}=4;4^2=16$
$\frac{16}{2}=8;8^2=64$
$\frac{64}{2}=32;{32}^2=1024$
$(8,16,64,1024)$ are the numbers given in set number $4$. So, set $4$ is based on rule $A$.
Cosider rule $B$:
'Multiply the number by $3$ and divide the product by $2$'.
$8\times 3=24;\frac{24}{2}=12$
$12\times 3=36;\frac{36}{2}=18$
$18\times 3=54;\frac{54}{2}=27$
So, the third set i.e., $(8,12,18,27)$ is based on rule $B$.
Consider rule $C$:
'Add $16$ to the number and divide the sum by $2$'.
Start with first number $8$.
$8+16=24;\frac{24}{2}=12$
$12+16=28;\frac{28}{2}=14$
$14+16=30;\frac{30}{2}=15$
So, the first set i.e., $(8,12,14,15)$ is based on rule $C$.
Consider rule $D$.
Divide the number by $2$ and add the square of the quotient to the number.
Start with first number $8$.
$\frac{8}{2}=4;4^2=16,8+16=24$
$\frac{24}{2}=12;{12}^2=144,24+144=168$
$\frac{168}{2}=84;{84}^2=7056,168+7056=7224$
So, the fifth set i.e., $(8,24,168,7224)$ is based on rule $D$.
Consider rule $E$:
'Square the number and divide by half of the number'.
Start with first number $8$.
$8^2=64;\frac{64}{\left(8/2\right)}=\frac{64}{4}=16$
${16}^2=256;\frac{256}{\left(16/2\right)}=\frac{256}{8}=32$
${32}^2=1024;\frac{1024}{\left(32/2\right)}=\frac{1024}{16}=64$
The second set i.e., $(8,16,32,64)$ is based on rule $E$.
$8121415$ - $\text{Rule C}$
$8163264$ - $\text{Rule E}$
$8121827$ - $\text{Rule B}$
$816641024$ - $\text{Rule A}$
$8241687224$ - $\text{Rule D}$