UPSC Prelims 2019 · CSAT

Question 31: Basic Numeracy

All members of a club went to Mumbai and stayed in a hotel. On the first day, 80% went for shopping and 50% went for sightseeing, whereas 10% took rest in the hotel. Which of the following conclusion(s) can be drawn from the above data ?

1.40% members went for shopping as well as sightseeing.
2.20% members went for only shopping.

Select the correct answer using the code given below :

a1 only

b2 only

cBoth 1 and 2

dNeither 1 nor 2

AnswerUPSC’s answer is (a).

Ten percent rested, so 90% went out, shopping or sightseeing or both. Those who did both are counted twice in 80% + 50% = 130%, so both = 130% - 90% = 40%: statement 1 is true. Only shopping = 80% - 40% = 40%, not 20%, so statement 2 is false. This uses the overlap rule, union = A + B - both, assuming the ones who rested did neither.

1. 80 + 50 - 90 = 40% did both.
2. Only shopping is 80 - 40 = 40%, not 20%.

How you could have got this

If you were sure statement 1 is correct, (b) and (d) go: each of them leaves 1 out.
What you needed to know: 80 + 50 - 90 = 40% did both.
Then, if you were sure statement 2 is not correct, (c) goes: it includes 2.
What you needed to know: Only shopping is 80 - 40 = 40%, not 20%.

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

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) Right: 40% did both, so only statement 1 holds.
(b) Wrong: only-shopping is 40%, not 20%.
(c) Wrong: statement 2 fails.
(d) Wrong: statement 1 holds.

Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.

Practise this paper timedPrevious question Next question

Source: UPSC, Civil Services (Preliminary) Examination 2019, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.