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CSAT 2023

Q15 2023, Basic Arithmetical Operations

Consider the following in respect of prime number p and composite number c:
1. p + c / p – c can be even.
2. 2p + c can be odd.
3. pc can be odd.
Which of the statements given above are correct?

अभाज्य संख्या p और भाज्य संख्या c के बारे में निम्नलिखित पर विचार कीजिए:
1. p + c / p – c सम हो सकता है।
2. 2p + c विषम हो सकता है।
3. pc विषम हो सकता है।
उपर्युक्त कथनों में से कौन-कौन से सही हैं?

Explanation Please wait..

Let’s place some numbers in place of p and c in the given expressions and check them out.

Statement 1: p + c / p – c can be even.

(p + c) / (p - c) can be even if p and c have opposite parities (one even, one odd).

For example, let p=11 (prime) and c=9 (composite).

(p + c) / (p - c) = (11 + 9) / (11 - 9) = 20 / 2 = 10 (an even number)

So, statement 1 is correct.

Statement 2: 2p + c can be odd.

2𝑝+𝑐 can be odd if 𝑝 is odd and 𝑐 is even.

For example, let 𝑝=3 (prime) and 𝑐=4 (composite). => 2(3)+4=6+4=10 (even)

Another example, let 𝑝=3 (prime) and 𝑐=9 (composite). => 2(3)+9=6+9=15 (odd)

Statement 2 is correct.

Statement 3: pc can be odd.

𝑝c can be odd if 𝑝 is odd and 𝑐 is even.

For example, let 𝑝=3 (prime) and 𝑐=4 (composite). => pc = 3×4=12 (even)

Another example, let 𝑝=5 (prime) and 𝑐=9 (composite). => pc = 5×9=45 (odd)

So, statement 3 is correct.

4. Therefore, option (d) is the correct choice.

Let’s place some numbers in place of p and c in the given
expressions and check them out.

Statement 1: p
+ c / p – c can be even.

<ul><li> 
(p
+ c) / (p - c) can be even if p and c have opposite parities (one even, one
odd).</li></ul>

<ul><li> 
For
example, let p=11 (prime) and c=9 (composite).</li></ul>

<ul><li> 
(p
+ c) / (p - c) = (11 + 9) / (11 - 9) = 20 / 2 = 10 (an even number)</li></ul>

<ul><li> 
So,
statement 1 is correct.</li></ul>

Statement 2: 2p
+ c can be odd.

<ul><li> 
For example, let 𝑝=3 (prime) and 𝑐=4 (composite). =>
2(3)+4=6+4=10 (even)</li></ul>

<ul><li> 
Another example, let 𝑝=3 (prime) and 𝑐=9 (composite). =>
2(3)+9=6+9=15 (odd)</li></ul>

<ul><li> 
Statement 2 is correct.</li></ul>

Statement 3: pc
can be odd.

<ul><li> 
For example, let 𝑝=3 (prime) and 𝑐=4 (composite). => pc =
3×4=12 (even)</li></ul>

<ul><li> 
Another example, let 𝑝=5 (prime) and 𝑐=9 (composite). => pc =
5×9=45 (odd)</li></ul>

<ul><li> 
So, statement 3 is correct.</li></ul>

<ul><li> 
4.
Therefore, option (d) is the correct choice.</li></ul>

CSAT Year Wise (Temporary Link, This will be removed and no PDFs shall be downloaded here. Please download CSAT subject wise files) / सी सैट

Q15 2023, Basic Arithmetical Operations

Consider the following in respect of prime number p and composite number c:
1. p + c / p – c can be even.
2. 2p + c can be odd.
3. pc can be odd.
Which of the statements given above are correct?

Explanation Please wait..

व्याख्या Please wait..

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John Doe

CSAT Year Wise (Temporary Link, This will be removed and no PDFs shall be downloaded here. Please download CSAT subject wise files) / सी सैट

Q15 2023, Basic Arithmetical Operations

Consider the following in respect of prime number p and composite number c: 1. p + c / p – c can be even. 2. 2p + c can be odd. 3. pc can be odd. Which of the statements given above are correct?

Explanation Please wait..

व्याख्या Please wait..

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John Doe

Consider the following in respect of prime number p and composite number c:
1. p + c / p – c can be even.
2. 2p + c can be odd.
3. pc can be odd.
Which of the statements given above are correct?