UPSC Prelims 2022 · CSAT
Question 67: Basic Numeracy
Consider the following statements in respect of two natural numbers p and q such that p is a prime number and q is a composite number :
- 1.p×q can be an odd number.
- 2.q/p can be a prime number.
- 3.p+q can be a prime number.
Which of the above statements are correct?
AnswerUPSC’s answer is (d).
Take p prime and q composite. Statement 1: p = 3, q = 9 gives 27, which is odd, so the product can be odd. Statement 2: p = 2, q = 6 gives 6 ÷ 2 = 3, a prime. Statement 3: p = 2, q = 9 gives 11, a prime. One example shows each can happen, so all three are correct.
- 1. 3 × 9 = 27 is odd.
- 2. With p = 2 and q = 6, q/p = 3, a prime.
- 3. 2 + 9 = 11 is prime.
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: 3 × 9 = 27 is odd.
- Then, if you were sure statement 2 is correct, (c) goes: it leaves 2 out.
What you needed to know: With p = 2 and q = 6, q/p = 3, a prime.
- Then, if you were sure statement 3 is correct, (a) goes: it leaves 3 out.
What you needed to know: 2 + 9 = 11 is prime.
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) Incomplete: statement 3 is also possible (2 + 9 = 11).
- (b) Incomplete: statement 1 is also possible (3 × 9 = 27).
- (c) Incomplete: statement 2 is also possible (6 ÷ 2 = 3).
- (d) Correct: each is shown by an example.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2022, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.