Question

A number series is given, with one wrong term. Select the wrong term from the given
alternatives :
3, 10, 29, 60, 127, 218, 345
​

Answer 1

AnswEr :

• Given Series :

◐ 3, 10, 29, 60, 127, 218, 345

we just have to find the sequence of this series. Here is One of the Possible Sequence.

◗ T(n) = ( n³ + 2 )

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Let's try this Sequence, whether it's following or not in this Series.

⋆ T(1) = (1³ + 2) = (1 + 2) = 3

⋆ T(2) = (2³ + 2) = (8 + 2) = 10

⋆ T(3) = (3³ + 2) = (27 + 2) = 29

⋆ T(4) = (4³ + 2) = (64 + 2) = 66

⋆ T(5) = (5³ + 2) = (125 + 2) = 127

⋆ T(6) = (6³ + 2) = (216 + 2) = 218

⋆ T(7) = (7³ + 2) = (343 + 2) = 345

As, we can see that this is Matching very much to the Given Series. Therefore Correct Series will Be :

◐ 3, 10, 29, 66, 127, 218, 345

We can see there should be 66 in the series Instead of 60, therefore that's wrong term in series.

∴ 60 is the wrong term in the series.

Answer 2

Question :-- A number series is given, with one wrong term. Select the wrong term from the given

alternatives : 3, 10, 29, 60, 127, 218, 345..

||✪✪ Solution (1) ✪✪||

when we look all number in the given series we can see that, all are nearby values of cubes of Natural numbers.

So, lets check them first .

→ 1³ = 1

we will add 2 , and get = 3 .

we will do same in next now, see if it fits the pattern ..

→ 2³ = 8,

again, will add 2 , and get = 10 .

lets check one more for sure ,

→ 3³ = 27 ,

again, will add 2 , and get = 29 .

with this we can say that, our series is = (n)³ + 2.

So, Now, we can say that,

→ 1³ + 2 = 1 + 2 = 3

→ 2³ + 2 = 8 + 2 = 10

→ 3³ + 2 = 27 + 2 = 29

→ 4³ + 2 = 64 + 2 = 66 . ( That is wrong).

(Lets see next also,)

→ 5³ + 2 = 125 + 2 = 127

→ 6³ + 2 = 216 + 2 = 218

→ 7³ + 2 = 343 + 2 = 345 .

So, 60 is wrong in the series , and in place of 60 it will be 66.

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|| ✰✰ Solution (2) ✰✰ ||

Lets Try to solve it with Difference Tree method Now,

→ when we see difference of given numbers and again we find , their difference of difference, we gets a pattern or new series . Actually This is the basic method and very helpful in Tough series , we are unable to find the hidden Pattern .

Lets see Now,

→ 10 - 3 = 7 difference

→ 29 - 10 = 19 difference => now, 19 - 7 = 12 difference,

→ 60 - 29 = 31 difference , => and, 31 - 19 = 12 difference,

→ 127 - 60 = 67 difference , => and, 67 - 31 = 36 differnce.

( Here, we can see pattern is little bit wrong , as 12, 12, 36 is not a series ).

→ To confirm it , lets move further now,

→ 218 - 127 = 91 difference, => and , 91 - 67 = 24

→ 345 - 218 = 127 difference, => and , 127 - 91 = 36.

when we see First difference, now,

7, 19,. 31 ,. 67, 91 , 127

12. 12. 36 24. 36

if we make second difference, multiple of 6 , we get,

→ 7, 19,. 31 ,. 67, 91 , 127

12. 18. 24 30 . 36

we get,

→ 7+12=19=>19+18= 37=> 37+24 = 61=> 61+30 = 91 =>91+36 = 127

Here , we can see that, our 60 is wrong .

Our Complete right tree will be now,

3 10. 29. 66 127. 218 345

7. 19 37 61 91 127

12 18 24. 30 36

[ Cross - Multiply add Each term from back and you will get all digits now.. ]

❁❁ Proof ❁❁

Start with multiplying from 12 in last,

→ 7 + 12 = 19 , 19 + 18 = 37 , 37 + 24 = 61 , 61 + 30 = 91, 91 + 36 = 127 .

Now, start adding In cross - Multiply again,

→ 3+7 = 10 , 10 + 19 = 29, 29 + 37 = 66 , 66 + 61 = 127 , 127 + 91 = 218 , 218 + 127 = 345..

Hence, we can say that, 60 is wrong in the series , and in place of 60 it will be 66.

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