Question

Find the missing letters.
\[YXZ,{\text{ }}XWY,{\text{ }}...{\text{ }},{\text{ }}VUW,{\text{ }}UTV,{\text{ }}TSU\]
A) VWT
B) WXV
C) TVX
D) WVX

Answer 1

Hint: Consider the given sequence. Note that the sequence follows a specific pattern which is \[{Y_2}{X_3}{Z_1},{\text{ }}{X_3}{W_4}{Y_2},{\text{ }}{W_4}{V_5}{X_3}...\]and so on. So we carefully observe the arrangement of letters and then find the missing letters.

Complete step-by-step answer:
Given sequence is \[YXZ,{\text{ }}XWY,{\text{ }}...{\text{ }},{\text{ }}VUW,{\text{ }}UTV,{\text{ }}TSU\]
First let us number Z as 1, Y as 2, X as 3, W as 4, V as 5, U as 6, T as 7 and so on.
So, basically we are numbering the last letter of Alphabet as 1 and we go on until the first letter which is A and number it as 26.
Now in the given sequence we just add suffix of the respective letters, i.e. \[{Y_2}{X_3}{Z_1},{\text{ }}{X_3}{W_4}{Y_2},{\text{ }}...,{\text{ }}{V_5}{U_6}{W_4},{\text{ }}{U_6}{T_7}{V_5},{\text{ }}{T_7}{S_8}{U_6},.......\]
So now we can observe the numbering of each term, first term has numbering 2, 3, 1 then the second term has the numbering 3, 4, 2, So, basically the numbering follows a pattern which is for nth term we will have numbering as \[(n + 1),(n + 2),n\].
So as we need to find the third term our n will be 3
So, the numbering will be \[(3 + 1),(3 + 2),3\] i.e. 4,5,3
Now we write the corresponding letter of the number i.e. for 4 we have W, for 5 we have V and for 3 we have X, so the missing term will be WVX.
Therefore the missing letters are WVX.
Hence option (D) is correct.

Note: You should have good observation skills, also you can eliminate some options as we can see that the third place of terms is Z, Y,_,W,V,U,… So, we can easily say that X is missing so our third place will be occupied by X.
So, we rule out option (A) and (B).
Now we look at the first letter of each term, they are Y,X,_,V,U,T,…. So, clearly we can see that the missing term will be W.
Hence option (C) is also ruled out, Hence the correct answer will be option (D).