The position of how many letters will remain unchanged if each of the letters in the word ‘DOWNSIZE’ is re-arranged in the English alphabetical order from left to right?

Correct — B. Rule: write the word out, sort its letters, then compare slot by slot.

DOWNSIZE is D O W N S I Z E.
Sorted alphabetically it is D E I N O S W Z.

Line the two up. Slot 1 holds D in both. Slot 4 holds N in both.

Every other slot moves: O gives way to E, W to I, S to O, I to S, Z to W and E to Z. That leaves two letters unmoved — option (b).

Why the others are wrong

• (a)
  One — This counts D at slot 1 and stops. N is unmoved too: it is the fourth letter of DOWNSIZE and the fourth letter of the sorted string D E I N O S W Z.
• (c)
  Three — There is no third fixed letter. S is the nearest miss, standing fifth in the word and sixth after sorting, one slot out.
• (d)
  Four — Four would need half the word to hold still, and only D and N do. W drops from slot 3 to slot 7, and E climbs from slot 8 to slot 2.

This is a sorting question dressed as a coding question. Write the letters in one row, write the alphabetically sorted letters underneath, and read down the columns.

The only skill it asks for is care. A single mis-sorted letter shifts everything after it and changes the count.

Vowels, consonants and the meaning of the word are all irrelevant here.

Key facts

• DOWNSIZE sorted alphabetically is D E I N O S W Z.
• Only the 1st letter D and the 4th letter N occupy the same slot before and after sorting.
• The number of unchanged positions plus the number of changed positions equals the length of the word.

Common traps

• Sorting from memory instead of writing the alphabet out, which usually misplaces the middle letters
• Stopping at the first fixed letter and answering One

No directly related past PYQ was found.