2006 General Studies, all questions

UPSC Prelims 2006 · General Studies

Question 103: Basic Numeracy

In an office, the number of persons who take tea is twice the number of persons who take only coffee. The number of persons who take coffee is twice the number of persons who take only tea. Consider the following statements:

  1. 1.The sum of the number of persons who take either tea or coffee or both is four times the number of persons who take both coffee and tea.
  2. 2.The sum of the number of persons who take only coffee and those who take only tea is twice the number of persons who take both coffee and tea.

Which of the statements given above is/are correct?

a1 only
b2 only
cBoth 1 and 2
dNeither 1 nor 2

AnswerThe answer is (b).

Let x take only tea, y only coffee, and z both. Tea drinkers are x + z = 2y, and coffee drinkers are y + z = 2x. Subtracting gives x - y = 2(y - x), so x = y, and then z = x. So all three groups are equal, say k each. Statement 1: either or both = 3k, but four times those taking both is 4k, so it is false. Statement 2: only coffee plus only tea = 2k = twice the number taking both, so it is true.

  • 1. Tea or coffee or both is 3k, not 4k.
  • 2. Only tea plus only coffee is 2k, twice those who take both.

How you could have got this

  1. If you were sure statement 2 is correct, (a) and (d) go: each of them leaves 2 out.

    What you needed to know: Only tea plus only coffee is 2k, twice those who take both.

    The red flag in statement 2 is “only”. In UPSC’s papers, statements with “only” were true 27% of the time (82 statements). A hint, not a rule.

  2. Then, if you were sure statement 1 is not correct, (c) goes: it includes 1.

    What you needed to know: Tea or coffee or both is 3k, not 4k.

Only (b) is left. This one needs every statement.

This follows an unofficial answer: UPSC has not published its key for this year, and if that answer is wrong, so is this path.

Which options go is worked out from UPSC’s key and the options, not by a model.

Why each option is right or wrong
  • (a) Statement 1 is false: 3k is not 4k.
  • (b) Correct: only statement 2 holds.
  • (c) Statement 1 is false.
  • (d) Statement 2 is true.

Explanation: written by UPSC Grade, not by UPSC.

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Source: UPSC, Civil Services (Preliminary) Examination 2006, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.