For a positive integer x, the function f(x) is defined as f(x)=2x2+3x+4. Is the value of the function f(x) an even number? x is a multiple of 3 x is a prime numbera)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'C'. Can you explain this answer?

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For a positive integer x, the function f(x) is defined as f(x)=2x²+3x+4

. Is the value of the function f(x) an even number?

x is a multiple of 3
x is a prime number

a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Correct answer is option 'C'. Can you explain this answer?

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For a positive integer x, the function f(x) is defined as f(x)=2x2+3x+...

Step 1 & Step 2: Understanding the Question statement and Drawing Inferences

The function f(x) is defined as f(x)=2x²+3x+4, where x ≥ 1

Now in function f(x), we have three terms being added

1^st part: 2x²
- Now any number multiplied by 2 will always result in an even number.
- So 2x² will always be even

2^nd part: 3x
- 3x will be even, when x is even.
- This is so because, 3 is an odd number and if x → even number, it will result in od dnumber * even number=even number
- 3x will be odd, when x is odd.
- This is so because, 3 is an odd number and if x → odd number, it will result in odd number*odd number=odd number
3^rd part: 4
- 4 will always be even
Now, 2x2+4=evennumber+evennumber=evennumber
So, for f(x) to be even → 3x should be even
3x would be even in cases when x is even (Already established above)
So we have to ultimately find the even-odd nature of x to find whether f(x) is even or not.

Step 3: Analyze statement 1 independently

Statement 1:

x is a multiple of 3.
So x can be even (Example: 6) or it can be odd (Example :3)
So, we will not be able to determine the nature of x whether it is even or odd,
Hence won’t be able to tell whether function f(x) will give an even value or not.
Hence statement 1 is not sufficient to answer the question

Step 4: Analyze statement 2 independently

Statement 2:

x is a prime number.
So x can be an even prime number ‘2’ or it can be odd prime number like 3, 5,7.
So, we will not be able to determine the nature of x whether it is even or odd
Hence won’t be able to tell whether function f(x) will give an even value or not.
Hence statement 2 is not sufficient to answer the question.

Step 5: Analyze the two statements together

From statement 1, we have x is a multiple of 3
From statement 2, we have x is a prime number and thus can be {2,3,5,7,….}
Only one number 3’ will satisfy both the statements because the number ‘3’ is a multiple of 3 and is also a prime number. All other numbers except ‘3’ will be multiple of 3 and hence will not be prime.
Now when x=3, f(x) will be odd, hence its value will not be an even number.
So by combining both statements we are able to arrive at a unique answer.
Hence the correct answer is option C- Both statements together are necessary to arrive at a unique answer.

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For a positive integer x, the function f(x) is defined as f(x)=2x2+3x+4. Is the value of the function f(x) an even number? x is a multiple of 3 x is a prime numbera)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'C'. Can you explain this answer?

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For a positive integer x, the function f(x) is defined as f(x)=2x2+3x+4. Is the value of the function f(x) an even number? x is a multiple of 3 x is a prime numbera)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'C'. 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 For a positive integer x, the function f(x) is defined as f(x)=2x2+3x+4. Is the value of the function f(x) an even number? x is a multiple of 3 x is a prime numbera)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For a positive integer x, the function f(x) is defined as f(x)=2x2+3x+4. Is the value of the function f(x) an even number? x is a multiple of 3 x is a prime numbera)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'C'. Can you explain this answer?.

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