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UPSC Prelims

Mathematics

Theme:

Number System / संख्या पद्धति

Q67 2022, Number System

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. pq 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?

दो धनपूर्ण संख्याओं p और q के बारे में, जो इस प्रकार हैं कि p अभाज्य और q भाज्य संख्या है, निम्नलिखित कथनों पर विचार कीजिए :
1. pq विषम संख्या हो सकती है।
2. q/p अभाज्य संख्या हो सकती है।
3. p + q अभाज्य संख्या हो सकती है।
उपर्युक्त कथनों में से कौन-से सही है?

Explanation Please wait..

Statement is telling a possibility(use of ‘can’ in statement) thus while taking examples if even one case is like the statement then the statement will be true.

p is a prime number and q is a composite number. Lets assume p = 3, q = 9

Statement 1 – p × q = 3 × 9 = 27 is an odd number. So, statement 1 can be true.

Statement 2 - q/p = 9/3 = 3 is a prime number. So, statement 2 can be true.

Statement 3 – This statement is not true for same value of p and q as above however if we change the values for eq; p = 3, q = 4 then p+q = 7 which is a prime number, This statement becomes correct.

Thus answer is d.

व्याख्या Please wait..

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