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If a and b are positive integers, is (a + b) prime?
Statement 1: 13a = 43b
Statement 2: 8a = 15b
Statement 1: 13a = 43b
Statement 2: 8a = 15b
- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient
- c)Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
- d)EACH statement ALONE is sufficient
- e)Statements (1) and (2) TOGETHER are NOT sufficient
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
If a and b are positive integers, is (a + b) prime?Statement 1: 13a = ...
Step 1: Evaluate Statement 1 ALONE
Statement 1: 13a = 43b
a/b = 43/13
a : b :: 43 : 13
So, a = 43x and b = 13x
a + b = 43x + 13x = 56x
56 is not prime. Therefore, 56x cannot be prime.
We are able to answer the question with a DEFNITE NO.
Hence, statement 1 alone is sufficient.
Eliminate answer option B, C, and E.
Statement 1: 13a = 43b
a/b = 43/13
a : b :: 43 : 13
So, a = 43x and b = 13x
a + b = 43x + 13x = 56x
56 is not prime. Therefore, 56x cannot be prime.
We are able to answer the question with a DEFNITE NO.
Hence, statement 1 alone is sufficient.
Eliminate answer option B, C, and E.
Step 2: Evaluate Statement 2 ALONE
Statement 2: 8a = 15b
a/b = 15/8
a : b :: 15 : 8
So, a = 15x and b = 8x
a + b = 15x + 8x = 23x
23 is prime.
If x is 1, a + b will be prime. For other values of x, a + b will not be prime.
We are not able to answer the question with a DEFNITE Yes or No.
Hence, statement 2 alone is not sufficient.
Eliminate answer option D.
Statement 1 alone is sufficient. Statement 2 is NOT sufficient.
Choice A is the correct answer.
Statement 2: 8a = 15b
a/b = 15/8
a : b :: 15 : 8
So, a = 15x and b = 8x
a + b = 15x + 8x = 23x
23 is prime.
If x is 1, a + b will be prime. For other values of x, a + b will not be prime.
We are not able to answer the question with a DEFNITE Yes or No.
Hence, statement 2 alone is not sufficient.
Eliminate answer option D.
Statement 1 alone is sufficient. Statement 2 is NOT sufficient.
Choice A is the correct answer.
Most Upvoted Answer
If a and b are positive integers, is (a + b) prime?Statement 1: 13a = ...
To determine if (a + b) is prime, we need to find the values of a and b. Let's analyze each statement separately:
Statement 1: 13a = 43b
- This equation relates the values of a and b. We can rewrite it as a = (43b)/13.
- Since a and b are positive integers, the value of (43b)/13 must also be an integer.
- However, we can't determine if (a + b) is prime from this information alone. We don't have any specific values for a or b.
Statement 2: 8a = 15b
- This equation also relates the values of a and b. We can rewrite it as a = (15b)/8.
- Since a and b are positive integers, the value of (15b)/8 must also be an integer.
- Again, we can't determine if (a + b) is prime from this information alone. We don't have any specific values for a or b.
Now, let's consider both statements together:
From statement 1, we have a = (43b)/13, and from statement 2, we have a = (15b)/8.
- Since both expressions are equal to a, they must be equal to each other: (43b)/13 = (15b)/8.
- We can cross multiply to solve for b: 43b * 8 = 13 * 15b.
- Simplifying, we get 344b = 195b.
- Dividing both sides by b, we get 344 = 195.
- This is a contradiction, as 344 is not equal to 195.
- Therefore, the two statements together lead to an inconsistency, and we still can't determine if (a + b) is prime.
Since neither statement alone is sufficient to determine if (a + b) is prime and the two statements together are also not sufficient, the correct answer is option A: Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement 1: 13a = 43b
- This equation relates the values of a and b. We can rewrite it as a = (43b)/13.
- Since a and b are positive integers, the value of (43b)/13 must also be an integer.
- However, we can't determine if (a + b) is prime from this information alone. We don't have any specific values for a or b.
Statement 2: 8a = 15b
- This equation also relates the values of a and b. We can rewrite it as a = (15b)/8.
- Since a and b are positive integers, the value of (15b)/8 must also be an integer.
- Again, we can't determine if (a + b) is prime from this information alone. We don't have any specific values for a or b.
Now, let's consider both statements together:
From statement 1, we have a = (43b)/13, and from statement 2, we have a = (15b)/8.
- Since both expressions are equal to a, they must be equal to each other: (43b)/13 = (15b)/8.
- We can cross multiply to solve for b: 43b * 8 = 13 * 15b.
- Simplifying, we get 344b = 195b.
- Dividing both sides by b, we get 344 = 195.
- This is a contradiction, as 344 is not equal to 195.
- Therefore, the two statements together lead to an inconsistency, and we still can't determine if (a + b) is prime.
Since neither statement alone is sufficient to determine if (a + b) is prime and the two statements together are also not sufficient, the correct answer is option A: Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
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If a and b are positive integers, is (a + b) prime?Statement 1: 13a = 43bStatement 2: 8a = 15ba)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficientb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficientc)Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficiente)Statements (1) and (2) TOGETHER are NOT sufficientCorrect answer is option 'A'. 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 If a and b are positive integers, is (a + b) prime?Statement 1: 13a = 43bStatement 2: 8a = 15ba)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficientb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficientc)Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficiente)Statements (1) and (2) TOGETHER are NOT sufficientCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a and b are positive integers, is (a + b) prime?Statement 1: 13a = 43bStatement 2: 8a = 15ba)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficientb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficientc)Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficiente)Statements (1) and (2) TOGETHER are NOT sufficientCorrect answer is option 'A'. Can you explain this answer?.
If a and b are positive integers, is (a + b) prime?Statement 1: 13a = 43bStatement 2: 8a = 15ba)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficientb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficientc)Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficiente)Statements (1) and (2) TOGETHER are NOT sufficientCorrect answer is option 'A'. 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 If a and b are positive integers, is (a + b) prime?Statement 1: 13a = 43bStatement 2: 8a = 15ba)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficientb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficientc)Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficiente)Statements (1) and (2) TOGETHER are NOT sufficientCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a and b are positive integers, is (a + b) prime?Statement 1: 13a = 43bStatement 2: 8a = 15ba)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficientb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficientc)Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficiente)Statements (1) and (2) TOGETHER are NOT sufficientCorrect answer is option 'A'. Can you explain this answer?.
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ample number of questions to practice If a and b are positive integers, is (a + b) prime?Statement 1: 13a = 43bStatement 2: 8a = 15ba)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficientb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficientc)Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficiente)Statements (1) and (2) TOGETHER are NOT sufficientCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice GMAT tests.
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