If x is a Positive Integer, Then is x Prime? 1) 3x + 1 is Prime 2) 5x GMAT Data Sufficiency

Question: If x is a positive integer, then is x prime?

1. 3x + 1 is prime
2. 5x + 1 is prime

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer:

Solution with Explanation:
Approach Solution (1):

We are given that x is a positive integer and must determine whether x is prime.

Statement 1 Alone:

3x + 1 is prime

Using the information in statement one, x does not necessarily have to be prime. For instance, if x = 2, then 3x + 1 = 7 is prime or if x = 4, then 3x + 1 = 13 is prime. In the former case, x = 2 is prime; however, in the latter case, x = 4 is not prime. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement 2 Alone:

5x + 1 is prime

Using the information in statement one, x does not necessarily have to be prime. For instance, if x = 2, then 5x + 1 = 11 is prime or if x = 6, then 5x + 1 = 31 is prime. In the former case, x = 2 is prime; however, in the latter case, x = 6 is not prime. Statement two alone is not sufficient to answer the question. We can eliminate answer choices B.

Statement 1 and 2 together:

Using the information from statements 1 and 2, we still cannot determine whether x is prime. For instance, if x = 2, then both 3x + 1 = 7 and 5x + 1 = 11 are prime, or if x = 12, then both 3x + 1 = 37 and 5x + 1 = 61 are prime. In the former case, x = 2 is prime; however, in the latter case, x = 12 is not prime.

Correct Option: E

Approach Solution (2):

There is one variable (x) in the original condition. So we need 1 equation. Since condition 1 and condition 2 each have 1 equation, there is a high chance that D is the correct answer.
The condition 1 has x = 2 yes, x = 6 no not sufficient
The condition 2 has x = 2 yes, x = 6 no not sufficient

Since the condition 1 and the condition 2 have x = 2 yes, x = 6 no not sufficient

Correct Option: E

Approach Solution (3):

x = positive integer

1) 3x + 1 is prime
If 3x + 1 = 7 = prime
x = 2, which is prime
If 3x + 1 = 19 = prime
x = 6, which is not a prime

Not sufficient

2) 5x + 1 is prime
If 5x + 1 = 11 = prime
x = 2, which is prime
If 5x + 1 = 31 = prime
x = 6, which is not a prime

Not sufficient

Combining 1 and 2, we will get:
Still not sufficient

Correct Option: E

“If x is a positive integer, then is x prime?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Suggested GMAT Data Sufficiency Samples

• What is the value of \(6x^2+9y^2\)? GMAT Data Sufficiency
• If x and y are integers and \(x=\frac{y}{5}+2\) , is xy even? GMAT Data Sufficiency
• If xy = - 6, What is the Value of xy(x + y)? GMAT Data Sufficiency
• A Drawer Contains 8 Socks, and 2 Socks are Selected at Random Without Replacement GMAT Data Sufficiency
• The Average Price of Three Stocks is $25 per Share GMAT Data Sufficiency
• Given k is a Nonzero Integer, is k>0? GMAT Data Sufficiency
• If J≠0, What Is The Value Of J? GMAT Data Sufficiency
• Paint X Costs $15 per Gallon, and Paint Y Costs $20 per Gallon GMAT Data Sufficiency
• What is the total value of Company H's stock? GMAT Data Sufficiency
• Is PQ > 1? GMAT Data Sufficiency
• How Many of the Students in a Certain Class are Taking Both a History and a Science Course? GMAT Data Sufficiency
• The Set S of Numbers has the following Properties GMAT Data Sufficiency
• A Contractor Combined x Tons of a Gravel Mixture that Contained 10 percent Gravel G GMAT Data Sufficiency
• If Jeff has four movies, and must choose to watch either 1, 2, or 3 different movies GMAT Data Sufficiency
• What is the probability that a student randomly selected from a class of 60 students will be a male who has brown hair? GMAT Data Sufficiency
• Does The Equation y = (x – p)(x – q) Intercept The x-axis At GMAT Data Sufficiency
• S is a Set of n Consecutive Positive Integers. Is the Mean of the Set GMAT Data Sufficiency
•  If |m + 4| = 2, what is the value of m? GMAT Data Sufficiency
• The Cardinality of a Finite Set is the Number of Elements in the Set., GMAT Data Sufficiency
• What is the Radius of the Circle above with Center O?, GMAT Data Sufficiency
• Is the Average of a Set of 5 Distinct Positive Integers {a, b, 6, 4, 2} Greater than the Median? GMAT Data Sufficiency
• If \(\sqrt{3+\sqrt{x-1}}=4\) , what is the value of x?, GMAT Data Sufficiency
• If There are 78 People Working at an Office, How Many of Them are Women Older than 40? GMAT Data Sufficiency
• From a Group of M Employees, N Will be Selected, at Random, GMAT Data Sufficiency
• If L \(\neq\) 0, is \(\frac{18K}{L}\) an Integer?
• If 0 < x < 53, What is the Value of Integer x? GMAT Data Sufficiency
• P and Q are Prime Numbers Less than 70. What is the Units Digit of P*Q?, GMAT Data Sufficiency
• Is P – 1 Even?, GMAT Data Sufficiency
• Buster Leaves the Trailer at Noon and Walks Towards the Studio at a Constant Rate of B Miles Per Hour., GMAT Data Sufficiency
• If ab = ac is b = 2?, GMAT Data Sufficiency
• The symbol ∆ Denotes One of The Four Arithmetic Operations GMAT DATA Sufficiency, GMAT Data Sufficiency
• Is Quadrilateral ABCD a Rectangle?, GMAT Data Sufficiency
• If \(x^2\)=\(2^x\), What is the Value of x ?, GMAT Data Sufficiency
• A Pentagon With 5 Sides Of Equal Length And 5 Interior Angles Of Equal measure is Inscribed in a Circle, GMAT Data Sufficiency
• If m is a positive integer, is \(\sqrt{m}>25\) ? , GMAT Data Sufficiency
• What is x? (1) |x| < 2 (2) |x| = 3x – 2 GMAT Data Sufficiency
• In the Picture Quadrilateral ABCD is a Parallelogram and Quadrilateral DEFG is a Rectangle GMAT Data Sufficiency
• What is the Remainder when 333^222 is Divided by 7? GMAT Data Sufficiency
• Is 1/(a - b) > b - a ? GMAT Data Sufficiency
• If x is the Product of Three Consecutive Positive Integers, Which of the Following Must be True? GMAT Data Sufficiency
• What is the value of 6x^2 + 9y^2 =? GMAT Data Sufficiency
• If x and y are integers and, is x=(y/5 +2) even? GMAT Data Sufficiency
• If m is a positive integer, is √m>25? GMAT Data Sufficiency
• If there are 78 people working at an office, how many of them are women older than 40? GMAT Data Sufficiency
• If ab = ac is b = 2? GMAT Data Sufficiency
• If x is a positive integer, what is the value of x? GMAT Data Sufficiency
• If 53 students are enrolled in both the CS103 (Algorithms and Data Structures) And M101 GMAT Data Sufficiency
• Buster leaves the trailer at noon and walks towards the studio at a constant rate of B miles per hour GMAT Data Sufficiency
• If sq rt{3+sq rt(x-1)} = 4, what is the value of x? GMAT Data Sufficiency
• What is the sum of a, b, and c? GMAT Data Sufficiency