UPSC Prelims 2023 · CSAT
Question 14: Basic Numeracy
Three of the five positive integers p, q, r, s, t are even and two of them are odd (not necessarily in order). Consider the following :
- 1.p + q + r – s – t is definitely even.
- 2.2p + q + 2r – 2s + t is definitely odd.
Which of the above statements is/are correct ?
AnswerUPSC’s answer is (a).
Only parity matters. Adding or subtracting an integer gives the same parity, and 2 times anything is even. Statement 1: p + q + r - s - t has the parity of the sum of all five numbers. Two odds make that sum even, so it is definitely even. Statement 2: 2p + q + 2r - 2s + t has the parity of q + t, which is even if q and t are both odd or both even, and odd otherwise. So it is not definitely odd.
- 1. Its parity equals that of the sum of all five numbers, which has two odds and so is even.
- 2. Its parity is that of q + t, which can be even or odd.
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: Its parity equals that of the sum of all five numbers, which has two odds and so is even.
- Then, if you were sure statement 2 is not correct, (c) goes: it includes 2.
What you needed to know: Its parity is that of q + t, which can be even or odd.
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: statement 1 is always even; statement 2 can be even or odd.
- (b) Wrong: statement 2 is not definitely odd.
- (c) Wrong: statement 2 fails when q and t have the same parity.
- (d) Wrong: statement 1 is definitely even.
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.