Question

Rules :
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.
$15253555$
$79223439727$
$21354963$
$90240462756$
$184070108$

Answer 1

Analysis:
Consider rule BB, which states 'Add the number to its square'.
So, the numbers are of the form (n2+n)(n2+n).
Try to find out the set of numbers which is based on the above rule (n2+n)(n2+n).
The fourth set of numbers (90,240,462,756)(90,240,462,756) is based on the rule n2+nn2+n.
90=81+9=(92+9)90=81+9=(92+9)
240=225+15=(152+15)240=225+15=(152+15)
462=441+21=(212+21)462=441+21=(212+21)
756=729+27=(272+27)756=729+27=(272+27)
Thus, rule BB applies to the fourth set of numbers.
Here, the basic set of numbers is (9,15,21,27)(9,15,21,27). By performing operations on this set of numbers as suggested in rule BB, we get the numbers in set 44 i.e., (90,240,462,756)(90,240,462,756).
Now, examine as to whether the remaining four sets of numbers can also be derived from the basic set of numbers (9,15,21,27)(9,15,21,27).
Check rule AA which states 'Divide the number by 33 and add the square of the quotient to the number'.
9÷3=332=99+9=189÷3=332=99+9=18
15÷3=552=2525+15=4015÷3=552=2525+15=40
21÷3=772=4949+21=7021÷3=772=4949+21=70
27÷3=992=8181+27=10827÷3=992=8181+27=108
Hence, fifth set of numbers (18,40,70,108)(18,40,70,108) is based on rule AA.
Check rule EE.
'Add one-third of the number to twice the number'.
9÷3=39×2=1818+3=219÷3=39×2=1818+3=21
15÷3=515×2=3030+5=3515÷3=515×2=3030+5=35
21÷3=721×2=4242+7=4921÷3=721×2=4242+7=49
27÷3=927×2=5454+9=6327÷3=927×2=5454+9=63
The third set of numbers (21,35,49,63)(21,35,49,63) is based on rule EE.
Check rule DD.
'Square the number and substract 22'
92−2=81−2=7992−2=81−2=79
152−2=225−2=223152−2=225−2=223
212−2=441−2=439212−2=441−2=439
272−2=729−2=727272−2=729−2=727
The second set of numbers (79,223,439,727)(79,223,439,727) is based on rule DD.
So, the first set of numbers (15,25,35,55)(15,25,35,55) is based on rule CC.
Check whether the first set of numbers can be obtained from the basic set of numbers (9,15,21,27)(9,15,21,27) by applying rule CC. No, its not possible. However, we can get the first set of numbers by applying rule CC, on a different set of numbers (6,10,14,22)(6,10,14,22) as worked out here under
Rules :
'Add half of the number to twice the number'.
(6×2)+(6÷2)=12+3=15(6×2)+(6÷2)=12+3=15
(10×2)+(10÷2)=20+5=25(10×2)+(10÷2)=20+5=25
(14×2)+(14÷2)=28+7=35(14×2)+(14÷2)=28+7=35
(22×2)+(22÷2)=44+11=55(22×2)+(22÷2)=44+11=55
First set of numbers are not derived from the magic numbers i.e.,(9, 15, 21, 27)First set of numbers are not derived from the magic numbers i.e.,(9, 15, 21, 27).
1525355515253555 - Rule CRule C
7922343972779223439727 - Rule DRule D
2135496321354963 - Rule ERule E
9024046275690240462756 - Rule BRule B
184070108184070108 - Rule ARule A