The position of how many letters will remain unchanged if each of the letter in the word ‘IMPROVE’ is arranged in English alphabetical order?
- (a)One
- (b)Three
- (c)Two
- (d)Zero
Answer
Why
Correct — D. Write the word out, write its sorted letters underneath, and compare slot against slot.
IMPROVE is I M P R O V E.
Sorted alphabetically it is E I M O P R V.
Slot 1 I against E, slot 2 M against I, slot 3 P against M, slot 4 R against O
Slot 5 O against P, slot 6 V against R, slot 7 E against V
No slot holds the same letter before and after the sort, so the count is zero — option (d).
Why the others are wrong
- (a)One — One is the tally a mis-sort produces. Put I first because the word begins with I and slot 1 seems to hold — but E, not I, is the earliest letter in IMPROVE.
- (b)Three — Three overcounts by accepting near misses. Slots 4 and 5 pair R with O and O with P, and a letter must be identical to its sorted counterpart, not merely close to it.
- (c)Two — Two is the tally if you assume both ends stay put. Neither does: slot 1 holds I against E, and slot 7 holds E against V.
Concept
This format asks how many fixed points a word has once its letters are sorted alphabetically. Do it mechanically.
Write the word in one row, its sorted letters directly beneath, and compare column by column. Count exact matches, never near ones.
A letter keeps its slot only when every letter standing before it in the word also stands before it in the alphabet. In IMPROVE that fails at the very first slot, because E — the earliest letter present — is sitting at the end of the word.
Nothing repeats in IMPROVE, so the sort is unambiguous. When a word does repeat a letter, sort the copies together and the same column comparison still works.
Key facts
- IMPROVE sorted alphabetically is E I M O P R V.
- A letter keeps its slot only if every letter before it in the word also precedes it alphabetically.
- The comparison is slot against slot, not letter against anywhere in the sorted string.
Study next
Common traps
- Sorting by eye and mislaying E, the letter furthest from its sorted home.
- Counting a letter as fixed because it appears in the sorted string at all.
- Reading the question as how many letters move, which is the complement of what is asked.
The same format is used with SIGNATURE at 24 Sep 2024, 16:00, Reasoning Q.13, with DOWNSIZE at 25 Sep 2024, 16:00, Reasoning Q.2, and with SPIDER at 26 Sep 2024, 09:00, Reasoning Q.12.
The first two say the letters are re-arranged from left to right; the task is the same either way.
Related PYQs
No directly related past PYQ was found.