Select the option that represents the letters that when sequentially placed from left to right in the blanks below will complete the letter series. _ C _ W _ _ _ C _ W _ _
- (a)CCWWCCWW
- (b)WCCWWWCC
- (c)WWCWWWCW
- (d)CWCWWCCW
Answer
Why
Correct — C. Rule: W C W repeats, three letters at a time, across all twelve slots.
Number the twelve slots. The letters already printed are C at 2, W at 4, C at 8 and W at 10.
Split the row into blocks of three — slots 1 to 3, 4 to 6, 7 to 9, 10 to 12 — and read each block as W, C, W.
Test that against what is printed: slot 2 is the middle of block one, so C. Slot 4 opens block two, so W. Slot 8 is the middle of block three, so C. Slot 10 opens block four, so W. All four match.
Filling the eight blanks in order gives W, W, C, W, W, W, C, W → WWCWWWCW, option (c).
Why the others are wrong
- (a)CCWWCCWW — This fills the row to CCCWWWCCCWWW, a repeat on a six-letter block. A series is read on the shortest unit that fits every printed letter, and the three-letter block WCW already fits.
- (b)WCCWWWCC — The first three fills are W, C, C, which puts C at slot 3 next to the C already at slot 2. No three-letter block starting from slot 1 places two Cs together.
- (d)CWCWWCCW — This opens with C at slot 1, giving C, C across the first two slots. Slot 2 is fixed as C, so slot 1 has to be W for any three-letter block to hold.
Concept
A blank letter series is a periodic pattern with holes. Number the slots, write the printed letters against their numbers, and look for a block length that puts the same letter in the same place inside every block.
Test block lengths from the shortest upward and keep the first that survives, slot by slot.
Length 1 fails because two different letters appear. Length 2 fails because slots 2 and 4 are both even yet hold C and W. Length 3 works: it puts C at slots 2, 5, 8, 11 and W at the other eight, matching every printed letter.
The 6-slot gap between the two Cs, and again between the two Ws, is consistent with a block of 3, but it does not on its own rule other lengths out. Only the slot-by-slot test does.
Two of the options fill the row to a genuinely repeating string. Option (c) gives the three-letter block WCW four times over; the other repeats on a six-letter block. A series is settled on the shortest block that fits every printed letter, which is the reading the key follows.
Key facts
- C is printed at slots 2 and 8 and W at slots 4 and 10, so both gaps are 6.
- A repeating block of length 3, W C W, places C at slots 2, 5, 8 and 11 and matches every printed letter.
- Filling the eight blanks under that block gives WWCWWWCW.
Study next
Common traps
- Filling the blanks left to right without first numbering all twelve slots
- Choosing a longer repeating block when a shorter one already fits every printed letter
- Reading the option as the completed row of twelve rather than the eight letters that fill the blanks
SSC prints the row with underscores and asks for the letters that fill them left to right, so the option is the fill string and not the finished series. The 11 Sep 2024, 16:00 paper uses the same format at Reasoning Q.3 with a five-letter fill.
Related PYQs
No directly related past PYQ was found.