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Is the two digit positive integer P a prime number?
Statement 1: (P + 2) and (P - 2) are prime.
Statement 2: (P - 4) and (P + 4) are prime.
Statement 2: (P - 4) and (P + 4) are prime.
- 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 'D'. Can you explain this answer?
Verified Answer
Is the two digit positive integer P a prime number?Statement 1: (P + 2...
Step 1 of solving this GMAT DS question: Understand the Question Stem
What kind of an answer will the question fetch?
The question is an "Is" question. Answer to an "is" questions is either YES or NO.
The question is an "Is" question. Answer to an "is" questions is either YES or NO.
When is the data sufficient?
The data is sufficient if we are able to get a DEFINITE YES or a DEFINITE NO from the information given in the statements.
The data is sufficient if we are able to get a DEFINITE YES or a DEFINITE NO from the information given in the statements.
What additional information do we have about P from the question stem?
'P' is a 2-digit positive integer.
'P' is a 2-digit positive integer.
Step 2 of solving this GMAT DS question:
Evaluate Statement (1) ALONE: (P + 2) and (P - 2) are prime.
Evaluate Statement (1) ALONE: (P + 2) and (P - 2) are prime.
Inference: (P - 2), P and (P + 2) are 3 consecutive odd integers.
Why?
Because (P - 2) and (P + 2) are prime, both numbers have to be odd.
(P - 2), P, and (P + 2) are three numbers in an arithmetic progression with a common difference of 2.
So, the 3 numbers have to be 3 consecutive odd or consecutive even integers. If (P - 2) and (P + 2) are odd, then these 3 numbers have to be 3 consecutive odd integers.
Why?
Because (P - 2) and (P + 2) are prime, both numbers have to be odd.
(P - 2), P, and (P + 2) are three numbers in an arithmetic progression with a common difference of 2.
So, the 3 numbers have to be 3 consecutive odd or consecutive even integers. If (P - 2) and (P + 2) are odd, then these 3 numbers have to be 3 consecutive odd integers.
One out of 3 consecutive odd integers, (P - 2), P, and (P + 2) will definitely be a multiple of '3'.
If (P + 2) and (P - 2) are prime, then P has to be a multiple of '3', which is not prime.
If (P + 2) and (P - 2) are prime, then P has to be a multiple of '3', which is not prime.
The only exception is if the 3 consecutive odd numbers are 3, 5, and 7. However, we are dealing with two digit positive integers. So that possibility is ruled out.
Statement 1 ALONE is sufficient.
Eliminate choices B, C, and E. Choices narrow down to A or D.
Eliminate choices B, C, and E. Choices narrow down to A or D.
Step 3 of solving this GMAT DS question:
Evaluate Statement (2) ALONE: (P - 4) and (P + 4) are prime.
Evaluate Statement (2) ALONE: (P - 4) and (P + 4) are prime.
This is a brilliant statement.
1. The remainder when (P - 4) and (P - 1) are divided by 3 will be the same.
2. Similarly, the remainder when (P + 4) and (P + 1) are divided by 3 will be the same.
If (P - 4) and (P + 4) are prime, both (P - 4) and (P + 4) will leave a remainder when divided by 3.
1. The remainder when (P - 4) and (P - 1) are divided by 3 will be the same.
2. Similarly, the remainder when (P + 4) and (P + 1) are divided by 3 will be the same.
If (P - 4) and (P + 4) are prime, both (P - 4) and (P + 4) will leave a remainder when divided by 3.
Therefore, (P - 1) and (P + 1) will also leave a remainder when divided by 3. i.e., they are not divisible by 3.
(P - 1), P, (P + 1) are 3 consecutive positive integers.
One out of 3 consecutive integers, (P - 1), P, and (P + 1) will definitely be a multiple of '3'.
If (P - 1) and (P + 1) are not divisible by 3, then P has to be a multiple of '3'.
P cannot be 3 because P is a 2-digit number. So, that possiblity is ruled out.
Any 2-digit number that is a multiple of 3 cannot be prime.
Therefore, P is not prime.
(P - 1), P, (P + 1) are 3 consecutive positive integers.
One out of 3 consecutive integers, (P - 1), P, and (P + 1) will definitely be a multiple of '3'.
If (P - 1) and (P + 1) are not divisible by 3, then P has to be a multiple of '3'.
P cannot be 3 because P is a 2-digit number. So, that possiblity is ruled out.
Any 2-digit number that is a multiple of 3 cannot be prime.
Therefore, P is not prime.
Statement 2 ALONE is also sufficient.
Eliminate choice A.
Eliminate choice A.
Each statement is INDEPENDENTLY sufficient. Choice D is the answer.
Most Upvoted Answer
Is the two digit positive integer P a prime number?Statement 1: (P + 2...
Statement Analysis:
Statement 1:
- (P + 2) and (P - 2) are prime numbers.
- This means that P is not divisible by 2 or 3 (since P + 2 and P - 2 are prime, they cannot be divisible by 2 or 3).
- Therefore, P does not have any factors other than 1 and itself, making it a prime number.
Statement 2:
- (P - 4) and (P + 4) are prime numbers.
- Similar to Statement 1, this implies that P is not divisible by 2 or 3.
- Again, P has no factors other than 1 and itself, indicating that it is a prime number.
Combining Statements:
- Both statements independently prove that P is a prime number.
- Each statement alone is sufficient to conclude that P is a prime number.
- Therefore, the correct answer is option 'D' as each statement alone is sufficient to answer the question.
Statement 1:
- (P + 2) and (P - 2) are prime numbers.
- This means that P is not divisible by 2 or 3 (since P + 2 and P - 2 are prime, they cannot be divisible by 2 or 3).
- Therefore, P does not have any factors other than 1 and itself, making it a prime number.
Statement 2:
- (P - 4) and (P + 4) are prime numbers.
- Similar to Statement 1, this implies that P is not divisible by 2 or 3.
- Again, P has no factors other than 1 and itself, indicating that it is a prime number.
Combining Statements:
- Both statements independently prove that P is a prime number.
- Each statement alone is sufficient to conclude that P is a prime number.
- Therefore, the correct answer is option 'D' as each statement alone is sufficient to answer the question.
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Is the two digit positive integer P a prime number?Statement 1: (P + 2) and (P - 2) are prime.Statement 2: (P - 4) and (P + 4) are prime.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 'D'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Is the two digit positive integer P a prime number?Statement 1: (P + 2) and (P - 2) are prime.Statement 2: (P - 4) and (P + 4) are prime.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 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Is the two digit positive integer P a prime number?Statement 1: (P + 2) and (P - 2) are prime.Statement 2: (P - 4) and (P + 4) are prime.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 'D'. Can you explain this answer?.
Is the two digit positive integer P a prime number?Statement 1: (P + 2) and (P - 2) are prime.Statement 2: (P - 4) and (P + 4) are prime.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 'D'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Is the two digit positive integer P a prime number?Statement 1: (P + 2) and (P - 2) are prime.Statement 2: (P - 4) and (P + 4) are prime.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 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Is the two digit positive integer P a prime number?Statement 1: (P + 2) and (P - 2) are prime.Statement 2: (P - 4) and (P + 4) are prime.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 'D'. Can you explain this answer?.
Solutions for Is the two digit positive integer P a prime number?Statement 1: (P + 2) and (P - 2) are prime.Statement 2: (P - 4) and (P + 4) are prime.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 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT.
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Is the two digit positive integer P a prime number?Statement 1: (P + 2) and (P - 2) are prime.Statement 2: (P - 4) and (P + 4) are prime.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 'D'. Can you explain this answer?, a detailed solution for Is the two digit positive integer P a prime number?Statement 1: (P + 2) and (P - 2) are prime.Statement 2: (P - 4) and (P + 4) are prime.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 'D'. Can you explain this answer? has been provided alongside types of Is the two digit positive integer P a prime number?Statement 1: (P + 2) and (P - 2) are prime.Statement 2: (P - 4) and (P + 4) are prime.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 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Is the two digit positive integer P a prime number?Statement 1: (P + 2) and (P - 2) are prime.Statement 2: (P - 4) and (P + 4) are prime.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 'D'. Can you explain this answer? tests, examples and also practice GMAT tests.
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