UPSC Prelims 2021 · CSAT
Question 67: Basic Numeracy
Consider the following statements :
- 1.The sum of 5 consecutive integers can be 100.
- 2.The product of three consecutive natural numbers can be equal to their sum.
Which of the above statements is/are correct ?
AnswerUPSC’s answer is (c).
Statement 1: five consecutive integers n to n + 4 sum to 5n + 10. Setting this equal to 100 gives n = 18, so 18 + 19 + 20 + 21 + 22 = 100. True. Statement 2: take 1, 2, 3: the product is 6 and the sum is 6. True. Both statements are correct. Remember: 'can be' statements need just one example, and writing consecutive terms algebraically makes the test quick.
- 1. 5n + 10 = 100 gives n = 18, so 18 to 22 sum to 100.
- 2. 1 × 2 × 3 = 6 = 1 + 2 + 3.
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: 5n + 10 = 100 gives n = 18, so 18 to 22 sum to 100.
- Then, if you were sure statement 2 is correct, (a) goes: it leaves 2 out.
What you needed to know: 1 × 2 × 3 = 6 = 1 + 2 + 3.
Only (c) 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) Statement 1 is true, but 2 is also true: 1 × 2 × 3 = 1 + 2 + 3.
- (b) Statement 2 is true, but 1 is also true: 18 to 22 sum to 100.
- (c) Right: 18 + 19 + 20 + 21 + 22 = 100 and 1 × 2 × 3 = 1 + 2 + 3.
- (d) Both statements have a working example, so this fails.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2021, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.