A function f(x) is defined as f(x) = x + x2 for an integer x. If a is an integer, is f(a) a prime number?1. f(a)+f(a+1) is a prime number2. The greatest common divisor of f(3) f(4) is f(a)*2.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 'B'. Can you explain this answer?

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A function f(x) is defined as f(x) = x + x² for an integer x. If a is an integer, is f(a) a prime number?

1. f(a)+f(a+1) is a prime number

2. The greatest common divisor of f(3) & f(4) is f(a)*2.

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 'B'. Can you explain this answer?

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A function f(x) is defined as f(x) = x + x2 for an integer x. If a is ...

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

Given Info:

A function f(x) is defined as f(x) = x + x² , where x is an integer.
So function f(x) is given as a quadratic function in x and can be written as
f(x) = x(x+1)

To find:

Is f(a) a prime number?
So f(a) = a(a+1)
Now f(a) is the product of two consecutive numbers.

Product of any two consecutive number will always have one even number and one odd number and thus the product will always be an even number. →
EvenNumber*OddNumber=EvenNumber

, and the only even number which is a prime number is 2.

So, f(a) will be prime only when f(a) = 2
So we have to find the values of a, for which f(a)=2, to determine whether f(a) is a prime number or not.

If f(a) = 2

Subtracting 2 from both sides of the equation, we get

So this gives either a=-2 or a=1

So for a = -2 or a=1 the above expression of f(a) will be a prime number otherwise it will be not. So from the given statements we will determine the value of a and then conclude whether f(a) is a prime number or not.

Step 3: Analyze statement 1 independently

Statement 1:

f(a)+f(a+1) is a prime number
We have, f(a)=a(a+1) (Already established above)

The above expression will be prime when (a+1)²=1 or f(a) + f(a+1) = 2 . This is so because multiplication of (a+1)² with 2 will always result in even number and the only even number which is prime is 2.

Subtracting 1 from both sides of the equation, we get

This means either a=0 or a=-2

Now f(a) will be prime in case when a=-2 but it will not be prime when a=0 (As already established above)
Hence statement 1 is not sufficient to answer the question

Step 4: Analyze statement 2 independently

Statement 2:

The greatest common divisor of f(3) & f(4) is f(a)*2.
Now, we know f(x)=x(x+1)
So,f(3)=3(3+1)=12
And,f(4)=4(4+1)=20

- Now 12 can be expressed in prime factors as → 12 = 3*2²
- And 20 can be expresses in prime factors as → 20 = 5*2²
- The greatest common factor of 12 and 20 is 2².
- So the greatest common divisor of f(3) and f(4) will be equal to 4.

Now we are given this greatest common divisor is equal to f(a) * 2
So we have, f(a) * 2 = 4

⇒ f(a) = 2

Now since f(a) = 2, we will have f(a) is a prime number, because 2 is a prime number.
Hence statement 2 is sufficient to arrive at a unique answer.

Step 5: Analyze the two statements together

Since from statement 2 we are able to arrive at a unique answer (as shown in step 4) combining and analysing both statements together is not required.

Hence the correct answer is option B- Only statement 2 is sufficient to arrive at a unique answer.

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A function f(x) is defined as f(x) = x + x2 for an integer x. If a is an integer, is f(a) a prime number?1. f(a)+f(a+1) is a prime number2. The greatest common divisor of f(3) & f(4) is f(a)*2.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 'B'. Can you explain this answer? for GMAT 2026 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about A function f(x) is defined as f(x) = x + x2 for an integer x. If a is an integer, is f(a) a prime number?1. f(a)+f(a+1) is a prime number2. The greatest common divisor of f(3) & f(4) is f(a)*2.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 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A function f(x) is defined as f(x) = x + x2 for an integer x. If a is an integer, is f(a) a prime number?1. f(a)+f(a+1) is a prime number2. The greatest common divisor of f(3) & f(4) is f(a)*2.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 'B'. Can you explain this answer?.

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