UPSC Prelims 2023 · CSAT
Question 6: Basic Numeracy
There are four letters and four envelopes and exactly one letter is to be put in exactly one envelope with the correct address. If the letters are randomly inserted into the envelopes, then consider the following statements :
- 1.It is possible that exactly one letter goes into an incorrect envelope.
- 2.There are only six ways in which only two letters can go into the correct envelopes.
Which of the statements given above is/are correct ?
AnswerUPSC’s answer is (b).
Four letters, four envelopes. If three letters are in their correct envelopes, the fourth must also be correct, so exactly one wrong envelope is impossible (statement 1 is false). For exactly two correct, choose which two are right: 4C2 = 6 ways; the other two must then be swapped, which is only 1 way. So there are 6 ways, and statement 2 is true. Answer: 2 only.
- 1. If three letters are correct the last is forced to be correct, so exactly one wrong is impossible.
- 2. Choose the correct pair in 4C2 = 6 ways; the other two must swap.
How you could have got this
- If you were sure statement 1 is not correct, (a) and (c) go: each of them includes 1.
What you needed to know: If three letters are correct the last is forced to be correct, so exactly one wrong is impossible.
- Then, if you were sure statement 2 is correct, (d) goes: it leaves 2 out.
What you needed to know: Choose the correct pair in 4C2 = 6 ways; the other two must swap.
Only (b) 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) Wrong: statement 1 is impossible.
- (b) Right: only statement 2 holds.
- (c) Wrong: statement 1 is false.
- (d) Wrong: statement 2 is true, with exactly 6 ways.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2023, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.