Set Theory: A Three-Amenity Housing Society Survey Quiz — 5 Free Questions

📖 Read the passage, then answer the questions below

A survey was conducted among 500 residents of a large housing society to find out which of three shared amenities they use: the Gym, the Swimming Pool, and the Jogging Track. It was found that 195 residents use the Gym, 170 residents use the Pool, and 150 residents use the Track. Among these, 75 residents use both the Gym and the Pool, 65 residents use both the Gym and the Track, and 60 residents use both the Pool and the Track. It is also known that exactly 35 residents use all three amenities, and 150 residents use none of the three at all.

Question 1

How many residents use only the Gym, and no other amenity?

Question 2

How many residents use the Track but not the Gym?

Question 3

What percentage of the total 500 residents use at least one of the three amenities?

Question 4

What percentage of the total 500 residents use none of the three amenities?

Question 5

How many residents use the Gym or the Pool, or both?

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About Set Theory: A Three-Amenity Housing Society Survey

CLAT's Quantitative Techniques section pairs a short data-rich scenario with several straightforward numeric questions -- here, a three-set Venn diagram worked out from given totals and overlaps, so every answer can be worked out from the figures given, without any outside knowledge.

This quiz is built around one survey: five hundred residents and their use of three shared amenities, with every individual and overlapping total given up front. Every question below is answered using that same set of figures -- nothing new is introduced question to question.

The twenty questions move through the kind of angles CLAT actually tests: exactly-one and exactly-two counts, "only" counts for a single amenity, at-least and at-most counts, percentages of the total, ratios and differences between groups, and a multi-statement combination question.

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