Aptitude and Reasoning Questions

Take a Look at this series :

23 - 22 =  8 - 4 = 4  

33 - 32 = 27 - 9 = 18 

43 - 42 = 64 - 16 = 48  

53 - 52 = 125 - 25 = 100  

63 - 62 = 216 - 36 = 180 

73 - 72 = 343 - 49 = 294 

83 - 82 = 512 - 64 = 448

Specified letters from the left are N and O , and the letter from the right is I.

With these letters , according to the conditions given in the question , one Word ONION can be formed. Clearly , first letter of this word is O. 

The difference of the two consecutive numbers are 1, 4, 9, 16, 25, 35. 

This is clearly , +12, +22, +32, +42, +52,+62 

Here 35 is wrong, So our wrong number is 91

Each number is twice the preceding one with 1 added or subtracted alternatively.

So, the next number is (2 x 261 + 1) = 523.

- There are 8 letters in the word.

- The coded word can be obtained by taking the immediately following letters of word, expect the first and the last letters of the given word but in the reverse order. That means, in the coded form the first and the last letters have been interchanged while the remaining letters are coded by taking their immediate next letters in the reverse order.

Justification:      

We can find the code for 'home' from the second and third statements.

For finding the code for 'they', we need the code for 'go' which cannot be determined from the given data.
Clearly, statement A is not necessary.

Find out the positions of both the letters from the left and divide the sum of the positions of both the letters from the left by 2. Here 13+23=36. Now divide 36 by 2 , i.e 18. Hence R is the required letter.

2nd letter to the left of 17th letter from the right means (2 + 17 = ) 19th letter from the right = (26 - 19 + 1 =) 8th letter from the left end , i.e H.  Thus, 8th letter falls into the second section of the reversed sequence. Now, the sequence FGHIJ is reversed and becomes JIHGF. Clearly, position of H remains unchanged. Hence the required letter is H.