The English alphabet is reordered in the following manner : The first 6 letters are written in opposite order, the next 6 letters are written in opposite order and so on. At the end, ‘Y’ is interchanged with ‘Z’. Which one of the following is the fourth letter to the right of the 13^th letter ?
- (a)N
- (b)O
- (c)M
- (d)I
Answer
Why
Correct — A, (a) N. Cut the alphabet into blocks of six and turn each block round where it stands. A B C D E F becomes F E D C B A; G H I J K L becomes L K J I H G; M N O P Q R becomes R Q P O N M; S T U V W X becomes X W V U T S. That uses twenty-four letters and leaves Y and Z over, and the stem's closing instruction interchanges those two, so the tail reads Z Y. The rearranged line in full is F E D C B A L K J I H G R Q P O N M X W V U T S Z Y. Number it and the thirteenth position is R — F, E, D, C, B, A take positions 1 to 6, L, K, J, I, H, G take 7 to 12, and R opens the third block at 13. Note what the thirteenth letter is not: it is not M. M is the thirteenth letter of the ordinary alphabet, and this stem asks about the reordered one. Now move four places to the right of R, counting the moves rather than the letters: position 14 is Q, 15 is P, 16 is O, 17 is N. The fourth letter to the right of the thirteenth is N. Two details of the printed stem are worth naming. The ordinal is set as a true superscript, '13' with a raised 'th', which the transcription writes with a caret. And the Y-for-Z interchange, though it must be obeyed, cannot affect this answer at all — those two letters occupy positions 25 and 26, well beyond anything the question reaches.
Why the others are wrong
- (b)O — O stands at position 16 of the rearranged line, three places to the right of R rather than four. It is where you land by counting the anchor itself as the first step — R one, Q two, P three, O four — and it is the single commonest way an alphabet-position item is lost. Fix the convention once and it never costs a mark again: 'the fourth letter to the right of X' means four moves from X, so the counting starts at the letter after X and the anchor is not counted. That is different from 'the fourth letter from the left', where the letter you count to is the one you name. Whenever a stem uses 'to the right of' or 'to the left of', a reference point has been given and it sits outside the count.
- (c)M — M is the thirteenth letter of the untouched English alphabet, so this option rewards a candidate who did the reordering, found nothing changed in their head, and answered the sub-question instead of the question. It has a second route as well: in the rearranged line M occupies position 18, which is five places right of R rather than four, so a loose count from the correct anchor also arrives here. Both routes have the same cure. Write the rearranged line out on the page and number it before reading the question again. Twenty-six letters is exactly the length at which mental tracking starts to fail, and the writing costs less time than a recount.
- (d)I — I sits at position 10, on the wrong side of the anchor altogether. It is what you get by making both of the other two mistakes at once — moving left instead of right, and counting the anchor as the first step: R one, G two, H three, I four. The direction deserves a deliberate thought on this item because the letters inside each block now run backwards, and it is easy to let that infect the counting. It should not: the reversal applies to the contents of the blocks, not to the line itself. 'Right' still means further along the written arrangement, in the direction you would read it, and positions are still numbered from the left.
Concept
Alphabet-position questions rest on two separate skills, and this one tests both. The first is executing a described rearrangement exactly — here, reversing successive blocks of six and then swapping the last two letters. Because 26 is not a multiple of 6, the rule produces four full blocks and a remainder of two, and the stem's closing sentence exists precisely to say what happens to that remainder. The second skill is counting positions under a stated convention. 'The nth letter from the left' includes the letter you name; 'the nth letter to the right of X' does not include X. If you want to short-circuit the writing out, there is an exact formula for a block reversal: in a block occupying positions 6k+1 to 6k+6, the letter now at position p is the one that originally stood at position 12k + 7 − p. For p = 13, which lies in the block with k = 2, that gives 24 + 7 − 13 = 18, and the eighteenth letter of the alphabet is R. Position 17 similarly gives 24 + 7 − 17 = 14, which is N.
The reasoning half of the EPFO EO/AO quantitative block reliably carries one alphabet item, and it is one of the few questions on the paper where the answer can be established with complete certainty inside a minute — provided the arrangement is written down. The habit it rewards is mechanical: build the whole line, number it, then read the question again. Candidates lose it by trying to hold the rearrangement in memory and by treating the counting convention as a matter of feel. Neither the vocabulary nor any outside knowledge is involved, so a card that teaches the method teaches the entire question.
Key facts
- The rearranged line is F E D C B A L K J I H G R Q P O N M X W V U T S Z Y.
- Its thirteenth letter is R; four places to the right of it is N, at position 17.
- M is the thirteenth letter of the ordinary alphabet, which is what makes option (c) tempting.
- 26 letters give four complete blocks of six plus Y and Z left over, which the closing instruction interchanges.
- In a reversed block spanning positions 6k+1 to 6k+6, the letter now at position p originally stood at position 12k + 7 − p.
- 'The fourth letter to the right of X' means four moves from X — the anchor is excluded from the count.
- The nth letter from the left of a 26-letter line is the (27 − n)th from the right.
- The booklet prints the ordinal with a true superscript 'th', which the transcription renders with a caret as 13^th.
- Cut the alphabet into blocks of six and turn each block round where it stands. A B C D E F becomes F E D C B A; G H I J K L becomes L K J I H G; M N O P Q R becomes R Q P O N M; S T U V W X becomes X W V U T S.
- That uses twenty-four letters and leaves Y and Z over, which is exactly why the stem carries a closing instruction: interchange them, so the tail reads Z Y. Those two occupy positions 25 and 26, well beyond anything this question reaches, so the swap cannot affect the answer at all.
- The rearranged line in full: F E D C B A L K J I H G R Q P O N M X W V U T S Z Y.
- Number it. F, E, D, C, B, A take positions 1 to 6; L, K, J, I, H, G take 7 to 12; and R opens the third block at position 13. The thirteenth letter is R — and it is NOT M, which is the thirteenth letter of the ordinary alphabet rather than of the reordered one.
- Now move four places to the right, counting the MOVES and not the letters: position 14 is Q, 15 is P, 16 is O, 17 is N. ‘The fourth letter to the right of X’ means four moves from X, so the anchor is excluded from the count — landing on O means the anchor was counted as the first step, which is the commonest way an item of this shape is lost.
- To skip writing the line out, there is an exact formula for a block reversal: in a block occupying positions 6k+1 to 6k+6, the letter now at position p is the one that originally stood at position 12k + 7 − p. For p = 13, which lies in the block with k = 2, that gives 24 + 7 − 13 = 18, and the eighteenth letter of the alphabet is R. For p = 17 it gives 14, which is N.
Study next
Common traps
- Counting the anchor letter as the first of the four moves, which shortens the answer by one place.
- Taking the thirteenth letter from the ordinary alphabet instead of from the rearranged one.
- Letting the reversed blocks reverse the direction of counting as well. Positions are still numbered from the left.
- Trying to build the arrangement mentally. Twenty-six letters is beyond reliable mental tracking under exam conditions.
- Forgetting that 26 is not a multiple of 6, so the last two letters are not part of any reversed block.
EPFO EO/AO reasoning items on the alphabet almost always state a rearrangement rule in one sentence and then ask for a letter at a stated offset from a stated position. The options are single letters, so nothing about the answer can be estimated, and the whole item turns on executing the rule and honouring the counting convention.
Related PYQs
EPFO_EOAO_2020_Q83Open & attempt →‘M’ is 60 years old. ‘R’ is 5 years junior to ‘M’ and 4 years senior to ‘V’. The youngest brother of ‘V’ is ‘B’ and he is 6 years junior to ‘V’. What is the age difference between ‘M’ and ‘B’ ?
- (a) 18 years
- (b) 15 years
- (c) 13 years
- (d) 11 years
Answer(b) 15 years
The reasoning item immediately before this one. Both hand you a rule in prose and are decided by writing the resulting order out before answering, and on both the printed instruction — a direction word there, a counting convention here — carries the whole difficulty.
EPFO_EOAO_2020_Q21Open & attempt →How many times does the digit 3 appear between 1 and 100 such that the number where 3 appears is not divisible by 3 ?
- (a) 11
- (b) 12
- (c) 13
- (d) 17
Answer(b) 12
The paper's other item that has to be solved by generating a list under a stated condition and then counting within it, rather than by recalling any formula.
Practice
- practice — not a real PYQ
The English alphabet is reordered so that the first 6 letters are written in opposite order, the next 6 letters are written in opposite order and so on, and at the end ‘Y’ is interchanged with ‘Z’. Which one of the following is the seventh letter to the left of the twenty-second letter ?
- (a)N
- (b)O
- (c)P
- (d)Q
Answer(c) P
- practice — not a real PYQ
If the first thirteen letters of the English alphabet are written in reverse order and the remaining letters are left unchanged, which one of the following is the third letter to the right of the seventh letter ?
- (a)D
- (b)E
- (c)F
- (d)C
Answer(a) D