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Is the positive integer 'x' divisible by 12?
Statement 1: x is divisible by 6
Statement 2: x is divisible by 8
- 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 'C'. Can you explain this answer?
Verified Answer
Is the positive integer x divisible by 12?Statement 1:x is divisible b...
Step 1: 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 is the test of divisibility for 12?
The test of divisibility for 12 is that the number should be divisible by both 3 and 4. Essentially, x should be divisible by 3 and 22.
The test of divisibility for 12 is that the number should be divisible by both 3 and 4. Essentially, x should be divisible by 3 and 22.
Step 2: Evaluate Statement (1) ALONE: x is divisible by 6
Approach: Look for a counter example
Example: x = 6. It is divisible by 6. However, it is NOT divisible by 12.
Counter Example: x = 12. It is divisible by 6. It is divisible by 12 as well.
Knowing that x is divisible by 6 is not enough to answer the question.
Counter Example: x = 12. It is divisible by 6. It is divisible by 12 as well.
Knowing that x is divisible by 6 is not enough to answer the question.
If x is divisible by 6, we can infer that it is divisible by 3 and 2. But we cannot deduce whether it is also divisible by 22 - which is essential to deduce that x is divisible by 12.
Statement 1 ALONE is NOT sufficient.
Eliminate choices A and D. Choices narrow down to B, C, or E.
Eliminate choices A and D. Choices narrow down to B, C, or E.
Step 3: Evaluate Statement (2) ALONE: x is divisible by 8
If x is divisible by 8, then x will definitely be divisible by 4.
However, from statement (2) alone we do not know if x is divisible by 3.
Alternative Approach: Look for a counter example
However, from statement (2) alone we do not know if x is divisible by 3.
Alternative Approach: Look for a counter example
Example: x = 8. It is divisible by 8. However, it is NOT divisible by 12.
Counter Example:x = 24. It is divisible by 8. It is divisible by 12 as well.
Knowing that x is divisible by 8 is not enough to answer the question.
Counter Example:x = 24. It is divisible by 8. It is divisible by 12 as well.
Knowing that x is divisible by 8 is not enough to answer the question.
Statement 2 ALONE is NOT sufficient.
Eliminate choice B. Choices narrow down to C or E.
Eliminate choice B. Choices narrow down to C or E.
Step 4: Evaluate Statements (1) & (2) Together: x is divisible by 6 & x is divisible by 8
From statement 1, if x is divisible by 6, it is definitely divisible by 3.
From statement 2, if x is divisible by 8, it is definitely divisible by 4.
So, by combining the two statements, we can conclude that x is divisible by 3 and by 4.
Or that x is divisible by 12.
From statement 2, if x is divisible by 8, it is definitely divisible by 4.
So, by combining the two statements, we can conclude that x is divisible by 3 and by 4.
Or that x is divisible by 12.
Statement TOGETHER are sufficient. Choice C is the answer.
Most Upvoted Answer
Is the positive integer x divisible by 12?Statement 1:x is divisible b...
Statement Analysis:
Statement 1:
- x is divisible by 6.
Statement 2:
- x is divisible by 8.
Combined Analysis:
- From statement 1, we know that x is divisible by 6, which means x can be written as 6a, where a is an integer.
- From statement 2, we know that x is divisible by 8, which means x can be written as 8b, where b is an integer.
- To find if x is divisible by 12, we need to find the least common multiple of 6 and 8, which is 24.
- Since 24 is the least common multiple, x must be divisible by 24, and therefore divisible by 12 as well.
- Both statements together are sufficient to determine that x is divisible by 12.
Therefore, the correct answer is option 'C'. Both statements together are sufficient, but neither statement alone is sufficient to determine if x is divisible by 12.
Statement 1:
- x is divisible by 6.
Statement 2:
- x is divisible by 8.
Combined Analysis:
- From statement 1, we know that x is divisible by 6, which means x can be written as 6a, where a is an integer.
- From statement 2, we know that x is divisible by 8, which means x can be written as 8b, where b is an integer.
- To find if x is divisible by 12, we need to find the least common multiple of 6 and 8, which is 24.
- Since 24 is the least common multiple, x must be divisible by 24, and therefore divisible by 12 as well.
- Both statements together are sufficient to determine that x is divisible by 12.
Therefore, the correct answer is option 'C'. Both statements together are sufficient, but neither statement alone is sufficient to determine if x is divisible by 12.
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Is the positive integer x divisible by 12?Statement 1:x is divisible by 6Statement 2:x is divisible by 8a)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 'C'. 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 Is the positive integer x divisible by 12?Statement 1:x is divisible by 6Statement 2:x is divisible by 8a)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 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Is the positive integer x divisible by 12?Statement 1:x is divisible by 6Statement 2:x is divisible by 8a)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 'C'. Can you explain this answer?.
Is the positive integer x divisible by 12?Statement 1:x is divisible by 6Statement 2:x is divisible by 8a)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 'C'. 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 Is the positive integer x divisible by 12?Statement 1:x is divisible by 6Statement 2:x is divisible by 8a)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 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Is the positive integer x divisible by 12?Statement 1:x is divisible by 6Statement 2:x is divisible by 8a)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 'C'. Can you explain this answer?.
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