You are given the following series:32.5, 35, 40.5, Y, 77.5, 113Select the appropriate value of Y from the choices provided.
Answers
Given :- 32.5, 35, 40.5, Y, 77.5, 113 ?
Answer :-
checking the difference we get,
→ 32.5 + 2.5 = 35
→ 35 + 5.5 = 40.5
→ 40.5 + x = y
→ y + z = 77.5
→ 77.5 + 35.5 = 113
x must be in half of an natural number .
also,
→ 2.5 + 3 = 5.5 ,
taking , 5.5 + 3 = 8.5 = x we get,
→ 40.5 + 8.5 = 49 = y
→ z = 77.5 - 49 = 28.5
as we can see that, difference between x and z is (28.5 - 8.5) = 20 ≠ 3 .
so, (+3) series does not satisfy .
taking in increasing order now, (+4), (+5)
→ 5.5 + 4 = 9.5 = x
→ 40.5 + 9.5 = 50 = y
→ z = 77.5 - 50 = 27.5 again does not satisfy any series .
taking, multiple of 3, (+6), (+9), (+12) ____
→ 5.5 + 6 = 11.5 = x
→ 40.5 + 11.5 = 52 = y
→ z = 77.5 - 52 = 25.5 => 11.5 + 9 ≠ 25.5 . does not satisfy .
increasing prime numbers , (3, 5, 7, 11)
→ 5.5 + 5 = 10.5 = x
→ 40.5 + 10.5 = 51 = y
→ z = 77.5 - 51 = 26.5 => 10.5 + 7 ≠ 26.5 .
increasing prime number in by skip 1, (3, 7, 13,)
→ 5.5 + 7 = 12.5 = x
→ 40.5 + 12.5 = 53 = y
→ z = 77.5 - 53 = 24.5 => 12.5 + 13 = 25.5 . which is near .
if z would have been 78.5 , this series satisfy upto here.
Some data is not correct in the series .
Lets try to solve similar type of series :- 8, 10, 14.5, 22.5, 35, 53, 77.5 , ?
Solution :-
checking the difference we get,
→ 10 - 8 = 2
→ 14.5 - 10 = 4.5
→ 22.5 - 14.5 = 8
→ 35 - 22.5 = 12.5
→ 53 - 35 = 18
→ 77.5 - 53 = 24.5
now, difference of difference,
→ 4.5 - 2 = 2.5
→ 8 - 4.5 = 3.5
→ 12.5 - 8 = 4.5
→ 18 - 12.5 = 5.5
→ 24.5 - 18 = 6.5
as we can see that, difference of difference is increasing in (+1) order .
then,
→ next difference will be = 24.5 + 7.5 = 32 .
therefore,
→ Next number = 77.5 + 32 = 109.5 (Ans.)
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