Which of the following terms will replace the question mark (?) in the given series? QGMW, VCPU, AYSS, ? , KQYO
- (a)FUVQ
- (b)FTUO
- (c)FVQO
- (d)FUXO
Answer
Why
Correct — A. Split the clusters into four letter columns and read each column on its own.
Column 1: Q, V, A, ?, K — +5 a step. V + 5 wraps past Z to A, and A + 5 = F, F + 5 = K.
Column 2: G, C, Y, ?, Q — −4 a step. C − 4 wraps below A to Y, and Y − 4 = U, U − 4 = Q.
Column 3: M, P, S, ?, Y — +3 a step, so the missing letter is V.
Column 4: W, U, S, ?, O — −2 a step, so the missing letter is Q.
Reading the four columns down the missing term gives FUVQ → option (a).
Why the others are wrong
- (b)FTUO — F is right, but T falls short of the U that Y − 4 gives, and the final O is the fifth term's last letter copied across rather than the Q the −2 column needs.
- (c)FVQO — Only the leading F survives. Column 2 needs U and this offers V, column 3 needs V and this offers Q, and the O again belongs to the fifth term.
- (d)FUXO — F and U are both right, but column 3 runs M, P, S, V at +3, and X overshoots V by two letters. The trailing O repeats the fifth term as well.
Concept
A four-letter cluster series is four independent one-letter series stacked in a column. Write the terms one under another and the four patterns appear side by side.
Positions are easier to handle than letters. Q = 17 and V = 22, and when a step runs past Z you keep counting: 22 + 5 = 27, which is A at position 1.
The same holds downwards. C = 3, and 3 − 4 = −1, which is Y at position 25. Wrapping in either direction is arithmetic modulo 26, nothing more.
The fifth term KQYO is printed, so every column can be checked in both directions. Working backwards from KQYO is often quicker than working forwards from AYSS.
Key facts
- Alphabet positions: Q=17, V=22, A=1, F=6, K=11 — a +5 step that wraps past Z.
- Alphabet positions: G=7, C=3, Y=25, U=21, Q=17 — a −4 step that wraps below A.
- Column 3 runs M, P, S, V, Y at a constant +3.
- Column 4 runs W, U, S, Q, O at a constant −2.
Study next
Common traps
- Restarting the count at A after Z, which breaks the +5 column
- Copying the final term's last letter, which is how three of the four options end in O
- Solving the first column, seeing every option begin with F, and stopping there
Letter series come in both shapes on 26 Sep 2024, 12:30: Reasoning Q.1 sets a single running series with blanks, and Q.21 sets clusters that carry a number alongside the letters.
Related PYQs
No directly related past PYQ was found.