Permutations: Circular Arrangements and Repeated Letters Quiz — 5 Free Questions

📖 Read the passage, then answer the questions below

A jewellery designer is arranging 6 distinct gemstones around a circular pendant frame, and wants to know how many visually distinct arrangements are possible. Arrangements that can be obtained from each other simply by rotating the pendant are considered identical, but arrangements that are mirror images of each other are considered different, because the pendant has a decorative clasp fixed on one specific side that fixes its orientation when worn.

Separately, the designer is also working out how many distinct ways the letters of the word "JEWELLERY" can be rearranged to form new sequences, treating identical repeated letters as indistinguishable from one another, and wants to compare this to the number of distinct rearrangements possible for two other words, "LEVEL" and "COMMITTEE," which also contain repeated letters.

Question 1

How many letters are there in total in the word "COMMITTEE"?

Question 2

If the pendant's arrangements also treated mirror-image reflections as identical, how many distinct arrangements of the original 6 gemstones would there be?

Question 3

How many letters are there in total in the word "JEWELLERY"?

Question 4

How many letters are there in total in the word "LEVEL"?

Question 5

How many times does the letter L appear in "LEVEL"?

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About Permutations: Circular Arrangements and Repeated Letters

CLAT's Quantitative Techniques section pairs a short data-rich scenario with several straightforward numeric questions -- here, circular permutations and word arrangements with repeated letters applied to a single invented jewellery workshop, so every answer can be worked out from the figures given, without any outside knowledge.

This quiz is built around two setups: gemstones arranged around a circular pendant frame, and several words whose letters are rearranged, with repeated letters treated as indistinguishable, fully described up front. Every question below is answered using those same figures -- nothing new is introduced question to question.

The twenty-four questions move through the kind of angles CLAT actually tests: circular arrangements with a fixed orientation, letter and repeat counts, arrangement counts for several words, ratios and differences between them, and a multi-statement combination question.

Only five of the twenty-four questions are shown on any single attempt, so replaying this quiz brings a genuinely different mix of angles on the same gemstones and words rather than the same five memorised by rote.