Q.Two Statements S1 and S2 are given below followed by a Question:
S1: n is a prime number.
S2: n leaves a remainder of 1 when divided by 4.
Question: If n is a unique natural number between 10 and 20, then what is n?
Which one of the following is correct in respect of the above the Statements and Question?
(a) S1 alone is sufficient to answer the Question.
(b) S2 alone is sufficient to answer the Question.
(c) S1 and S2 together are sufficient to answer the Question, but neither S1 alone nor S2 alone is sufficient to answer the Question.
(d) S1 and S2 together are not sufficient to answer the Question.
Correct Answer: (d) S1 and S2 together are not sufficient to answer the Question.
Question from UPSC Prelims 2020 CSAT Paper
Explanation :
Analysis of Statement S2:
– When a number n is divided by 4, remainder is 1
– Such numbers can be written as: n = 4k + 1 (where k is an integer)
– Numbers between 10 and 20 that fit this pattern are: 11, 13, 15, 17, 19
Analysis of Statement S1:
– Number n must be prime
– From the above list, only 11 and 17 are prime numbers
– So S1 alone gives us two possibilities: n = 11 or n = 17
Combined Analysis:
– Both statements together still give us two possibilities
– Both 11 and 17:
Are prime numbers (satisfying S1)
Leave remainder 1 when divided by 4 (satisfying S2)
Conclusion:
Therefore, answer is (d): S1 and S2 together are not sufficient to determine a unique value of n.
