Select the option that is related to the fifth letter-cluster in the same way as the second letter-cluster is related to the first letter-cluster and the fourth letter-cluster is related to the third letter-cluster. CRW: TIN :: DOZ: UFQ :: ALW:?
- (a)RCN
- (b)RCM
- (c)JCN
- (d)JCM
Answer
Why
Correct — A. Turn every letter into its position number and one jump covers all three places.
Rule: each letter moves +17, wrapping past Z by subtracting 26.
CRW to TIN: C(3)+17 = T(20), R(18)+17 = 35−26 = I(9), W(23)+17 = 40−26 = N(14)
DOZ to UFQ: D(4)+17 = U(21), O(15)+17 = 32−26 = F(6), Z(26)+17 = 43−26 = Q(17)
Now run ALW through the same jump:
A(1)+17 = R(18), L(12)+17 = 29−26 = C(3), W(23)+17 = 40−26 = N(14)
That spells RCN — option (a).
Why the others are wrong
- (b)RCM — R and C are right in option (b), but M(13) is one short of N. The sum is 23 + 17 = 40, and 40 − 26 lands on 14, not 13 — a wrap counted one place too far.
- (c)JCN — J(10) is A + 9 in option (c). A +17 shift is the same move as a −9 shift, and adding the 9 instead of subtracting it is exactly the slip that produces J where R belongs.
- (d)JCM — Option (d) makes both slips in one term — J from adding 9 to A, and M from mis-wrapping W — so only the middle letter C survives.
Concept
A letter-cluster analogy is arithmetic wearing letters. Write A = 1 through Z = 26, subtract the first cluster's numbers from the second's, and the rule is on the page.
Two things make the arithmetic quick. Any shift larger than 13 is easier as its negative twin: +17 and −9 land in the same place, because 17 + 9 = 26.
And a wrap past Z is nothing more than a subtraction of 26, so 40 becomes 14 and 43 becomes 17.
The item gives you two solved pairs, not one. Confirm the shift on both before carrying it to the options — a single pair can be fitted by more than one rule, and the second pair is there to kill the extras.
Key facts
- +17 and −9 move a letter to the same place, because 17 + 9 = 26.
- C = 3 and T = 20, R = 18 and I = 9, W = 23 and N = 14, so the first solved pair shows +17 in every position.
- A wrap past Z is a subtraction of 26: 23 + 17 = 40, and 40 − 26 = 14, which is N.
Study next
Common traps
- Applying the shift in the wrong direction after converting +17 into −9.
- Subtracting 26 one step too early or too late, which shifts a letter by exactly one place.
SSC gives two solved pairs and asks you to carry the rule to a third. A uniform shift of +12 is set at 10 Sep 2024, 12:30, Reasoning Q.3 (DOY:PAK :: BQM:NCY :: ILU:?), and a complement rule where each letter and its partner add to 27 is set at 09 Sep 2024, 09:00, Reasoning Q.11 (MEK:NVP :: GYT:TBG :: JWH:?).
Related PYQs
No directly related past PYQ was found.