BPSC 69th CCE Prelims Q149: Find the odd one in the following groups : Q,W,Z,B B,H,K,M

Q: What is the answer to BPSC 69th CCE Prelims Q149?

C. Correct — C, W,C,G,J. Write the alphabet position under each letter and take the gaps, treating the alphabet as a circle so that A follows Z — when the next position is the smaller number, add 26 before subtracting. Group one, Q,W,Z,B: 17, 23, 26, 2, so the gaps are 23 − 17 = 6, 26 − 23 = 3 and (2 + 26) − 26 = 2, giving 6, 3, 2. Group two, B,H,K,M: 2, 8, 11, 13, so the gaps are 6, 3, 2. Group four, M,S,V,X: 13, 19, 22, 24, so the gaps are again 6, 3, 2. Three groups therefore share one signature. Group three, W,C,G,J: 23, 3, 7, 10, so the gaps are (3 + 26) − 23 = 6, then 7 − 3 = 4 and 10 − 7 = 3 — the signature 6, 4, 3. That is the group that breaks the pattern, and it is option (c). Two details are worth fixing in memory. Every one of the four groups opens with a gap of 6, so the first step discriminates nothing and a candidate who checks only the first pair learns nothing; the answer is decided at the second gap, 3 against 4. And had the third group been built to the majority rule it would read W, C, F, H — starting at 23 and stepping 6, 3, 2 gives 3, 6, 8 — which is a useful way to confirm that the break is real and not a counting slip.

BPSC 69th CCE Prelims General Studies · Question 149 of 144

Verified against the official question booklet. Answer as per the official BPSC answer key.

Answers derived, not from the official key. BPSC published an answer key for BPSC 69th CCE at the time, but it is no longer available from the Commission or in any web archive. The answers here are our best-supported answers — solved from the question itself and cross-checked against primary sources — and each card says how certain it is. The question text is verbatim from the official booklet. These are not the Commission's answer key.

Question order, option order and answers follow the official BPSC Booklet Series A (booklet 201-A), paper code 19-C/FI/CC/PT-2023.

Find the odd one in the following groups : Q,W,Z,B B,H,K,M W,C,G,J M,S,V,X

(a)Q,W,Z,B
(b)M,S,V,X
(c)W,C,G,J
(d)B,H,K,M

Answer

Why

Correct — C, W,C,G,J. Write the alphabet position under each letter and take the gaps, treating the alphabet as a circle so that A follows Z — when the next position is the smaller number, add 26 before subtracting. Group one, Q,W,Z,B: 17, 23, 26, 2, so the gaps are 23 − 17 = 6, 26 − 23 = 3 and (2 + 26) − 26 = 2, giving 6, 3, 2. Group two, B,H,K,M: 2, 8, 11, 13, so the gaps are 6, 3, 2. Group four, M,S,V,X: 13, 19, 22, 24, so the gaps are again 6, 3, 2. Three groups therefore share one signature. Group three, W,C,G,J: 23, 3, 7, 10, so the gaps are (3 + 26) − 23 = 6, then 7 − 3 = 4 and 10 − 7 = 3 — the signature 6, 4, 3. That is the group that breaks the pattern, and it is option (c). Two details are worth fixing in memory. Every one of the four groups opens with a gap of 6, so the first step discriminates nothing and a candidate who checks only the first pair learns nothing; the answer is decided at the second gap, 3 against 4. And had the third group been built to the majority rule it would read W, C, F, H — starting at 23 and stepping 6, 3, 2 gives 3, 6, 8 — which is a useful way to confirm that the break is real and not a counting slip.

Why the others are wrong

(a)Q,W,Z,B — Its gaps are 6, 3, 2, exactly the majority signature. It attracts votes because it is the only group containing Z and because it visibly crosses the end of the alphabet, which reads as an irregularity. It is not one: on a circular alphabet, Z to B is a step of 2 like any other, and the wrap is a feature the setter has planted in two of the four groups precisely to be misread as oddness.
(b)M,S,V,X — Gaps 6, 3, 2 again — it obeys the rule. It looks like a candidate because all four of its letters sit in the back half of the alphabet and it never wraps, so it appears the plainest group on the page. Plainness is not the property under test. Note also that it is printed last in the stem but listed second among the options, which is enough to make a hurried candidate mark the wrong letter.
(d)B,H,K,M — Gaps 6, 3, 2, so it too follows the rule. With positions 2, 8, 11, 13 it is the arithmetically easiest group on the page, which makes it the natural template to check the others against rather than the answer. Candidates who reach it last, after the pattern is already established, rarely pick it; those who start with the hardest group sometimes do.

Concept

Letter-group odd-one-out items ask which of four sets of letters fails to share a property that the other three have. The property is drawn from a short list: the gaps between successive alphabet positions, the same gaps read backwards, letters all drawn from one class such as vowels or consonants, letters sharing a visual property such as vertical symmetry, or letters that are mirror images of one another across the middle of the alphabet. The first decision is therefore which property is in play, and the gap signature is by far the most common, so it is the one to test first. The mechanics rest on two things being automatic — the alphabet positions A = 1 to Z = 26, and the convention that the alphabet is circular, so that A follows Z and a step that appears to run backwards is really a forward step of that number plus 26. Without the circular convention two of the four groups here produce negative gaps and the question looks unanswerable.

The efficient route is to build a small table rather than to stare at the letters. Write the four groups as rows of numbers — 17 23 26 2, then 2 8 11 13, then 23 3 7 10, then 13 19 22 24 — and take differences across each row, adding 26 wherever the next number is smaller. Four short rows of three gaps each is about twenty seconds of work and it settles the question with no judgement involved. The discriminating fact is narrow and easy to miss: all four groups agree on the opening gap of 6, and three of them agree on 3 and 2 after it, while one runs 4 and 3. A candidate who checks only the first pair of letters in each group, which is the natural time-saving instinct, gets four identical answers and no information. The other thing to guard against is treating the wrap as the anomaly. Two groups cross the end of the alphabet, Q,W,Z,B at Z to B and W,C,G,J at W to C, and only one of them is the answer — so wrapping cannot be the property. That is deliberate: giving the wrap to both a correct group and the odd group is how the setter stops it from being a shortcut.

Key facts

Alphabet positions of the four groups: Q 17, W 23, Z 26, B 2; B 2, H 8, K 11, M 13; W 23, C 3, G 7, J 10; M 13, S 19, V 22, X 24
Gap signatures on a circular alphabet: Q,W,Z,B = 6, 3, 2; B,H,K,M = 6, 3, 2; M,S,V,X = 6, 3, 2; W,C,G,J = 6, 4, 3 — the last is the odd group
Wraparound rule: when the next letter's position is the smaller number, add 26 before subtracting — Z to B is (2 + 26) − 26 = 2, and W to C is (3 + 26) − 23 = 6
All four groups open with a gap of 6, so the first step discriminates nothing; the answer turns entirely on the second gap, 3 against 4
Built to the majority rule, the third group would read W, C, F, H — from 23 stepping 6, 3, 2 gives 3, 6, 8

Alphabet positions and gap signatures for the four groups

Q, W, Z, B → 17, 23, 26, 2→gaps 6, 3, 2 ✓ follows the rule (Z to B wraps: 2 + 26 − 26 = 2)

B, H, K, M → 2, 8, 11, 13→gaps 6, 3, 2 ✓ follows the rule

W, C, G, J → 23, 3, 7, 10→gaps 6, 4, 3 ✗ breaks the rule — this is the odd group

M, S, V, X → 13, 19, 22, 24→gaps 6, 3, 2 ✓ follows the rule

What it should have been→W, C, F, H — from 23, stepping 6, 3, 2 gives 3, 6, 8

Every group opens with a gap of 6, so the first step tells you nothing. The second gap decides it: three groups step 3 then 2, while W, C, G, J steps 4 then 3.

Study next

Letter series with a fixed or a changing shift, and continuing them across the Z-to-A wrapMirror or opposite letters, where a letter pairs with the one 27 minus its position (A with Z, B with Y, M with N)Letter-group items built on a property other than gaps — all vowels, all letters made only of straight lines, all symmetric lettersAlphanumeric series mixing letters, digits and symbols, and counting items on themThe alphabet position table A = 1 to Z = 26 and its reverse, which underlies almost every verbal reasoning item BPSC sets

Common traps

Checking only the first pair of letters in each group — all four open with a gap of 6, so that check returns nothing
Reading a wrap past Z as the anomaly, when two of the four groups wrap and only one of them is the answer
Marking by position rather than by content: the groups appear in the stem in a different order from the option list

BPSC's reasoning block reliably contains one item that reduces to alphabet positions — a group odd-one-out here in 2023, a letter-shift code in the 2025 block — so the position table is the highest-yield thing to have memorised for this part of the paper. UPSC keeps letter series and classification in CSAT Paper II under general mental ability, where they are usually asked as a series to be continued rather than as four groups to be compared.

Related PYQs

No directly related past PYQ was found.

Practice

practice — not a real PYQ
Find the odd one out among the following groups of letters.
- (a)D,J,M,O
- (b)F,L,O,Q
- (c)P,V,Y,A
- (d)T,Z,B,E
Answer(d) T,Z,B,E — the other three step 6, 3, 2 through the alphabet (D 4, J 10, M 13, O 15; F 6, L 12, O 15, Q 17; P 16, V 22, Y 25, A 1 after the wrap), while T 20, Z 26, B 2, E 5 steps 6, 2, 3.
practice — not a real PYQ
In the series below each letter moves forward by the same number of places, the alphabet being treated as a circle in which A follows Z. Which letter completes it? X, C, H, M, ?
- (a)P
- (b)Q
- (c)R
- (d)S
Answer(c) R — the step is 5 places: X 24 → C 3 (24 + 5 = 29, wrapping to 3), C → H, H → M, and M 13 + 5 = 18, which is R.