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Is the positive integer p even?
(1) p^2 + p is even.
(2) 4p + 2 is even.
a)Exactly one of the statements can answer the question
b)Both statements are required to answer the question
c)Each statement can answer the question individually
d)More information is required as the information provided is insufficient to answer the question
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
Is the positive integer p even?(1) p^2 + p is even.... more(2) 4p + 2 ...
**Statement 1:** p^2 is even
**Statement 2:** 4p is even
To determine if the positive integer p is even, we need to consider both statements together.
**Analysis:**
1. **Statement 1:** p^2 is even
- If p^2 is even, it implies that p is even because the square of an odd number is odd, and the square of an even number is even.
- Therefore, statement 1 alone is sufficient to conclude that p is even.
2. **Statement 2:** 4p is even
- The product of any integer and an even number is always even.
- Therefore, statement 2 alone is sufficient to conclude that p is even.
Since each statement individually is enough to determine that p is even, the correct answer is **option C** - Each statement can answer the question individually.
**Explanation:**
Both statements provide sufficient information to determine that p is even.
- From statement 1, if p^2 is even, it means p must be even, as the square of an odd number is odd and the square of an even number is even. Therefore, statement 1 alone is enough to conclude that p is even.
- Similarly, from statement 2, if 4p is even, it means that p must be even because the product of any integer and an even number is always even.
Since each statement individually provides enough information to determine that p is even, additional information is not required. Therefore, option D is incorrect.
Hence, the correct answer is **option C** - Each statement can answer the question individually.
**Statement 2:** 4p is even
To determine if the positive integer p is even, we need to consider both statements together.
**Analysis:**
1. **Statement 1:** p^2 is even
- If p^2 is even, it implies that p is even because the square of an odd number is odd, and the square of an even number is even.
- Therefore, statement 1 alone is sufficient to conclude that p is even.
2. **Statement 2:** 4p is even
- The product of any integer and an even number is always even.
- Therefore, statement 2 alone is sufficient to conclude that p is even.
Since each statement individually is enough to determine that p is even, the correct answer is **option C** - Each statement can answer the question individually.
**Explanation:**
Both statements provide sufficient information to determine that p is even.
- From statement 1, if p^2 is even, it means p must be even, as the square of an odd number is odd and the square of an even number is even. Therefore, statement 1 alone is enough to conclude that p is even.
- Similarly, from statement 2, if 4p is even, it means that p must be even because the product of any integer and an even number is always even.
Since each statement individually provides enough information to determine that p is even, additional information is not required. Therefore, option D is incorrect.
Hence, the correct answer is **option C** - Each statement can answer the question individually.
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Is the positive integer p even?(1) p^2 + p is even.... more(2) 4p + 2 ...
If you try to put different integer positive in this case both statements would give one answer as even, put 1,2,3,4.... so each statement alone is sufficient to answer the question
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Is the positive integer p even?(1) p^2 + p is even.... more(2) 4p + 2 is even.a)Exactly one of the statements can answer the questionb)Both statements are required to answer the questionc)Each statement can answer the question individuallyd)More information is required as the information provided is insufficient to answer the questionCorrect answer is option 'D'. Can you explain this answer?
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Is the positive integer p even?(1) p^2 + p is even.... more(2) 4p + 2 is even.a)Exactly one of the statements can answer the questionb)Both statements are required to answer the questionc)Each statement can answer the question individuallyd)More information is required as the information provided is insufficient to answer the questionCorrect answer is option 'D'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Is the positive integer p even?(1) p^2 + p is even.... more(2) 4p + 2 is even.a)Exactly one of the statements can answer the questionb)Both statements are required to answer the questionc)Each statement can answer the question individuallyd)More information is required as the information provided is insufficient to answer the questionCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Is the positive integer p even?(1) p^2 + p is even.... more(2) 4p + 2 is even.a)Exactly one of the statements can answer the questionb)Both statements are required to answer the questionc)Each statement can answer the question individuallyd)More information is required as the information provided is insufficient to answer the questionCorrect answer is option 'D'. Can you explain this answer?.
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