UPSC Prelims 2023 · CSAT
Question 15: Basic Numeracy
Consider the following in respect of prime number p and composite number c.
- 1.(p + c)/(p – c) can be even.
- 2.2p + c can be odd.
- 3.pc can be odd.
Which of the statements given above are correct ?
AnswerUPSC’s answer is (d).
Test each by example; 'can be' needs only one case. Statement 1: p = 11, c = 9 gives (11 + 9)/(11 - 9) = 10, which is even. Statement 2: p = 3, c = 9 gives 2p + c = 15, odd, since an odd composite added to an even number stays odd. Statement 3: p = 3, c = 9 gives pc = 27, odd. A composite number can be odd and a prime can be odd, so all three are possible.
- 1. p = 11, c = 9 gives 20/2 = 10, an even number.
- 2. p = 3, c = 9 gives 15, which is odd.
- 3. p = 3, c = 9 gives 27, which is odd.
How you could have got this
- If you were sure statement 1 is correct, (b) goes: it leaves 1 out.
What you needed to know: p = 11, c = 9 gives 20/2 = 10, an even number.
- Then, if you were sure statement 2 is correct, (c) goes: it leaves 2 out.
What you needed to know: p = 3, c = 9 gives 15, which is odd.
- Then, if you were sure statement 3 is correct, (a) goes: it leaves 3 out.
What you needed to know: p = 3, c = 9 gives 27, which is odd.
Only (d) 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 3 is also possible (3 x 9 = 27).
- (b) Wrong: statement 1 is also possible (11 and 9 give 10).
- (c) Wrong: statement 2 is also possible (2 x 3 + 9 = 15).
- (d) Right: each can happen with suitable values.
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.