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Students in a college are discussing two proposals --
$A$: a proposal by the authorities to introduce dress code on campus, and
$B$: a proposal by the students to allow multinational food franchises to set up outlets on college campus.
A student does not necessarily support either of the two proposals.
In an upcoming election for student union president, there are two candidates in fray: Sunita and Ragini. Every student prefers one of the two candidates.
A survey was conducted among the students by picking a sample of $500$ students.

The following information was noted from this survey.
1. $250$ students supported proposal $A$ and $250$ students supported proposal $B$.
2. Among the $200$ students who preferred Sunita as student union president, $80\%$ supported proposal $A$.
3. Among those who preferred Ragini, $30\%$ supported proposal $A$.
4.$20\%$ of those who supported proposal $B$ preferred Sunita.
5. $40\%$ of those who did not support proposal $B$ preferred Ragini.
6. Every student who preferred Sunita and supported proposal $B$ also supported proposal $A$.
7. Among those who preferred Ragini, $20\%$ did not support any of the proposals.

How many of the students surveyed supported proposal $B$, did not support proposal $A$ and preferred Ragini as student union president?

  1. $200$
  2. $150$
  3. $210$
  4. $40$
in Logical Reasoning by (11.4k points) 174 680 1522
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