CSAT Solved Papers/ 2021/Q35

2021 CSAT — Q35

Quant Arithmetic & numeracy 2.5 marks Medium

In a group of 120120 persons, 8080 are Indians and rest are foreigners. Further, 7070 persons in the group can speak English. The number of Indians who can speak English is

  1. A 20
  2. B 30
  3. C 30 or less
  4. D 30 or more Answer

Worked rationale

Indians =80=80, foreigners =120−80=40=120-80=40, English speakers =70=70.

The English speakers who are not Indian are at most the number of foreigners, 4040. So the Indians among the 7070 English speakers number at least

70−40=30.70 - 40 = 30.

It could be more — up to 7070 if every English speaker were Indian (possible, since 70≤8070\le 80). So the count is 3030 or more.

Answer: (d) 30 or more.

Why the other options miss

  • A
    wrong subtraction: e.g. computes 80+70−120=3080+70-120 = 30 then drops 1010, or reports the foreigner count as the answer.
  • B
    a floor read as an exact value: finds the minimum 3030 but asserts it as the precise answer, ignoring that more is possible.
  • C
    the bound pointing the wrong way: gets the magnitude right but the direction wrong — 3030 is a floor, not a ceiling.

Specialist insight

This is a minimum-overlap (pigeonhole) question, not an exact-count one. The most English speakers that can avoid being Indian is the foreigner total 4040, forcing at least 70−40=3070-40 = 30 Indian English speakers. The answer is a one-sided bound ("≥30\ge 30"), and the entire trap is reading a minimum as an exact value — the data fix only the floor, never the precise number.

The trap, in one line

At most 4040 English speakers are foreign, so ≥70−40=30\ge 70-40 = 30 are Indian ⇒\Rightarrow "3030 or more" ⇒\Rightarrow (d).

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