Each of the letters in the word ‘DARKEN’ is arranged in the English alphabetical order. How many letters are there in the English alphabetical series between the letter which is second from the left end and the one which is third from the right end in the new letter-cluster thus formed?
- (a)Five
- (b)Eight
- (c)Six
- (d)Seven
Answer
Why
Correct — C. Sort the word first, then count between the two named letters.
DARKEN in alphabetical order is A D E K N R.
Second from the left end is D.
Third from the right end is K, counting R first, N second, K third.
D is the 4th letter of the alphabet and K the 11th.
Strictly between them lie E F G H I J — six letters, which is option (c).
Why the others are wrong
- (a)Five — Five is the gap from E to K, the count you reach by taking the third letter from the left instead of the second. The stem asks for the second.
- (b)Eight — Eight comes from sorting in reverse. Read R N K E D A and the two letters become N and E, with F to M — eight letters — between them.
- (d)Seven — Seven is simply 11 − 4, the gap with one endpoint still counted in. Between two letters you must subtract one more: 11 − 4 − 1 = 6.
Concept
Two separate skills are stacked here, and the marks are lost on the second.
First, re-order the letters of the word alphabetically — DARKEN becomes ADEKNR. Only the letters present are sorted, not the whole alphabet.
Second, count strictly between two letters, which is the difference of their alphabet positions minus one. K is 11 and D is 4, so the count is 11 − 4 − 1 = 6, not 7.
Reading one position from the left and the other from the right is deliberate, and it is where careless candidates lose the mark.
The new cluster ADEKNR has six letters, so third from the right and fourth from the left name the same letter, K. Checking that agreement is a quick way to be sure you have counted from the correct end.
Key facts
- DARKEN in alphabetical order is A D E K N R.
- The number of letters strictly between two letters equals the higher position minus the lower position minus one.
- D is the 4th letter and K the 11th, so six letters lie between them: E, F, G, H, I and J.
Study next
Common traps
- Counting inclusively and answering seven
- Taking both positions from the left when the stem names one from each end
- Sorting the word's letters but forgetting to re-index positions in the new cluster
The frame recurs — sort the word, then count between two named positions — but the two positions are not fixed, so read them off the stem every time.
Reasoning Q.9 on 13 Sep 2024 (16:00) uses REDUCTION: third from the left and fourth from the left.
Reasoning Q.23 on 17 Sep 2024 (12:30) uses LASTING: second from the left and fourth from the right.
Reasoning Q.2 on 17 Sep 2024 (16:00) uses MUSICAL: third from the left and third from the right.
A close cousin asks instead how many letters keep their position after sorting, as at Reasoning Q.18 on 10 Sep 2024 (09:00) with PRANKED.
Related PYQs
No directly related past PYQ was found.