Each of the letters in the word ‘REDUCTION’ are arranged in the English alphabetical order. How many letters are there in the English alphabetical order between the letter which is the third from the left end and the fourth from the left end in the group of letters thus formed?
- (a)One
- (b)Two
- (c)Four
- (d)Three
Answer
Why
Correct — D. Rule: sort the letters of REDUCTION alphabetically, then count the letters lying strictly between the third and the fourth of the sorted string.
REDUCTION uses R, E, D, U, C, T, I, O, N.
Sorted, that is C, D, E, I, N, O, R, T, U.
Third from the left end is E. Fourth from the left end is I.
E is the 5th letter and I is the 9th, so the letters between them are F, G and H.
That is three letters, which is option (d).
Why the others are wrong
- (a)One — One would require the third and fourth sorted letters to be two apart in the alphabet. They are E and I, four apart, so three letters sit between them.
- (b)Two — Two is the count if you stop the gap at F and G. It runs F, G, H, because I is the ninth letter and E the fifth.
- (c)Four — Four comes from counting an endpoint as well. The question asks only for the letters between E and I, and those are F, G and H.
Concept
These items bolt two operations together, and the mistakes come from the join. Re-order the word's letters alphabetically first; only then apply the counting instruction to the new string.
Sorting REDUCTION gives C D E I N O R T U. Nothing of the original order survives, so do not glance back at the printed word when counting positions.
Then read the instruction precisely. Third and fourth from the left end are positions in the sorted string, and how many letters are between two letters excludes both of them.
The two named letters sit next to each other in the sorted string but four apart in the alphabet, which is the whole point of the item.
Key facts
- REDUCTION sorted alphabetically is C, D, E, I, N, O, R, T, U.
- E is the fifth letter of the alphabet and I is the ninth.
- The letters strictly between E and I are F, G and H.
Study next
Common traps
- Counting positions in the original word instead of in the sorted string
- Including one or both endpoints in a between count
- Miscounting because the alphabet is scribbled out by hand under time pressure
SSC keeps the stem and moves the two reference points. A left-end and right-end version appears at 17 Sep 2024, 16:00, Reasoning Q.2 on MUSICAL, and a version counting from the right end at 19 Sep 2024, 09:00, Reasoning Q.10 on KEYBOARD.
Related PYQs
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