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Set P contains 3 distinct positive integers: A, B and C. Is the average (arithmetic mean) of set P divisible by 3?
(1) The sum of A×104 , B×102 and C is divisible by 9
(2) The product of the range of Set P and the median of Set P is 18.
(1) The sum of A×104 , B×102 and C is divisible by 9
(2) The product of the range of Set P and the median of Set P is 18.
- 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 'A'. Can you explain this answer?
Verified Answer
Set P contains 3 distinct positive integers: A, B and C. Is the averag...
Step 1 & 2: Understand Question and Draw Inference
Given:
- Set P = {A, B, C} where A, B and C are distinct positive integers
- Average of Set P =
To find: Is divisible by 3?
divisible by 3?- If A + B + C divisible by 9?
- Is =
an integer? - Let A = 9m + a, where a is the remainder that A leaves with 9. So a lies between 0 and 8, inclusive
- Similarly let B = 9n + b
- And let C = 9p + c
- So, the question is to find: Is
an integer? - Is
an integer? - Since m + n + p is an integer, the question simplifies to find: is
Step 3 : Analyze Statement 1 independent
- So, the number 10,000a + 100b +c is divisible by 9
- By applying the divisibility rule of 9, we can say that the sum of the digits of the number 10,000a + 100b +c is divisible by 9
- Since a, b and c are each single-digit integers that lie between 0 and 8, inclusive, the number 10,000a + 100b +c is of the form a00b0c (that is, a is the ten-thousands digit of this number, b is the hundreds digit and c is the units digit).
- So, the sum of digits of 10,000a +100b+c (=a00b0c) = a+b+c
- So, a+b+c is divisible by 9
- So, is an integer
Sufficient.
Step 4 : Analyze Statement 2 independent
- The product of the range of Set P and the median of Set P is 18.
- (Range of Set P)*(Median of Set P) = 18
- Since Set P contains only integers, Range of Set P is an integer
- Since Set P contains an odd number of integers, Median of Set P is equal to the middle integer when A, B and C are arranged in ascending order. Thus, Median of Set P is an integer as well.
- Thus, the product of 2 integers is 18
- The number of ways to express 18 as a product of 2 integers:
- Case 1: 18 = 18*1
- Either Range = 18 and Median = 1
- Not possible – A, B and C are distinct, positive integers. So, minimum value of an integer in Set P is 1. The second integer in Set P cannot also be 1. So, Median cannot be 1
- Or Range = 1 and Median = 18
- Not possible – A, B and C are distinct integers. So, the minimum possible value of Range is 2 (happens if A, B and C are consecutive integers)
- Either Range = 18 and Median = 1
- Case 2: 18 = 9*2
- Either Range = 9 and Median = 2
- This means, Set P = {1, 2, 10}
- A + B + C = 1 + 2 +10 = 13, which is not divisible by 9.
- So, the answer to the question is NO
- Or Range = 2 and Median = 9
- This means, Set P = {8, 9, 10}
- A + B + C = 8 + 9 + 10 = 27, which is divisible by 9
- So, the answer to the question is YES
- Either Range = 9 and Median = 2
- Case 3: 18 = 6*3
- Since we’ve already seen that Case 2 leads to conflicting answers, we need not analyze Case 3.
- Case 1: 18 = 18*1
Thus, Statement 2 is not sufficient to provide a unique answer to the posed question.
Step 5: Analyze Both Statements Together (if needed)
Since we’ve already arrived at a unique answer in Step 3, this step is not required.
Answer: Option A
Answer: Option A
Most Upvoted Answer
Set P contains 3 distinct positive integers: A, B and C. Is the averag...
We can simplify the expression for the average of the set as (A+B+C)/3. We want to know if this expression is divisible by 3.
Statement 1: The sum of A, B, and C is divisible by 3.
If the sum of A, B, and C is divisible by 3, then we know that (A+B+C)/3 is also divisible by 3. Therefore, statement 1 is sufficient.
Statement 2: The sum of A and B is divisible by 3.
We cannot determine if the average of the set is divisible by 3 based on this statement alone. For example, if A=1, B=2, and C=4, then the average of the set is (1+2+4)/3 = 7/3, which is not divisible by 3. However, if A=3, B=6, and C=9, then the average of the set is (3+6+9)/3 = 6, which is divisible by 3. Therefore, statement 2 is not sufficient.
Answer: A (Statement 1 alone is sufficient, but statement 2 alone is not sufficient.)
Statement 1: The sum of A, B, and C is divisible by 3.
If the sum of A, B, and C is divisible by 3, then we know that (A+B+C)/3 is also divisible by 3. Therefore, statement 1 is sufficient.
Statement 2: The sum of A and B is divisible by 3.
We cannot determine if the average of the set is divisible by 3 based on this statement alone. For example, if A=1, B=2, and C=4, then the average of the set is (1+2+4)/3 = 7/3, which is not divisible by 3. However, if A=3, B=6, and C=9, then the average of the set is (3+6+9)/3 = 6, which is divisible by 3. Therefore, statement 2 is not sufficient.
Answer: A (Statement 1 alone is sufficient, but statement 2 alone is not sufficient.)
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Set P contains 3 distinct positive integers: A, B and C. Is the average (arithmetic mean) of set P divisible by 3?(1) The sum of A×104 , B×102 and C is divisible by 9(2) The product of the range of Set P and the median of Set P is 18.a)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct 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 Set P contains 3 distinct positive integers: A, B and C. Is the average (arithmetic mean) of set P divisible by 3?(1) The sum of A×104 , B×102 and C is divisible by 9(2) The product of the range of Set P and the median of Set P is 18.a)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct 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 Set P contains 3 distinct positive integers: A, B and C. Is the average (arithmetic mean) of set P divisible by 3?(1) The sum of A×104 , B×102 and C is divisible by 9(2) The product of the range of Set P and the median of Set P is 18.a)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'A'. Can you explain this answer?.
Set P contains 3 distinct positive integers: A, B and C. Is the average (arithmetic mean) of set P divisible by 3?(1) The sum of A×104 , B×102 and C is divisible by 9(2) The product of the range of Set P and the median of Set P is 18.a)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct 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 Set P contains 3 distinct positive integers: A, B and C. Is the average (arithmetic mean) of set P divisible by 3?(1) The sum of A×104 , B×102 and C is divisible by 9(2) The product of the range of Set P and the median of Set P is 18.a)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct 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 Set P contains 3 distinct positive integers: A, B and C. Is the average (arithmetic mean) of set P divisible by 3?(1) The sum of A×104 , B×102 and C is divisible by 9(2) The product of the range of Set P and the median of Set P is 18.a)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'A'. Can you explain this answer?.
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Set P contains 3 distinct positive integers: A, B and C. Is the average (arithmetic mean) of set P divisible by 3?(1) The sum of A×104 , B×102 and C is divisible by 9(2) The product of the range of Set P and the median of Set P is 18.a)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'A'. Can you explain this answer?, a detailed solution for Set P contains 3 distinct positive integers: A, B and C. Is the average (arithmetic mean) of set P divisible by 3?(1) The sum of A×104 , B×102 and C is divisible by 9(2) The product of the range of Set P and the median of Set P is 18.a)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of Set P contains 3 distinct positive integers: A, B and C. Is the average (arithmetic mean) of set P divisible by 3?(1) The sum of A×104 , B×102 and C is divisible by 9(2) The product of the range of Set P and the median of Set P is 18.a)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Set P contains 3 distinct positive integers: A, B and C. Is the average (arithmetic mean) of set P divisible by 3?(1) The sum of A×104 , B×102 and C is divisible by 9(2) The product of the range of Set P and the median of Set P is 18.a)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice GMAT tests.
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