A set consists of n distinct integers arranged in the order of increasing magnitude. Is the median of the n integers equal to thearithmetic mean of the n integers?(1) The sum of any 3 successive integers of the set is divisible by 3(2) The difference between any 2 successive integers of the set is 4a)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 'B'. Can you explain this answer?

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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 'B'. Can you explain this answer?

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Test: Statistics- 2

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A set consists of n distinct integers arranged in the order of increas...

Step 1 & 2: Understand Question and Draw Inference

Given: A set of n distinct integers, arranged in the order of increasing magnitude
To find: Is Median = Mean?
The median is equal to the mean if:

Either the given sequence is an Arithmetic progression
Or, It’s not an Arithmetic Progression but symmetric about a number.
- Like the set, {1, 2, 4, 6, 7}. This set is {4 – 3, 4 – 2, 4, 4 + 2, 4 + 3}, i.e. it is symmetric about 4.So, the sum of the terms = 4*5 And

Step 3 : Analyze Statement 1 independent

(1) The sum of any 3 successive integers of the set is divisible by 3

Statement 1 is fulfilled by more than one cases:
Case 1: The terms of the set are in arithmetic progression
- Example: 1, 2, 3, 4, 5
- In this case, as discussed in Step 1 and 2, Median = Mean (= 3 in the Example above)
- Case 2: The terms of the set are not in arithmetic progression
For example, a set of the form: {3k + 0, 3k + l, 3k + 5, 3k + 12, 3k + 16} where k is an integer
In this set,
But Median = 3k + 5
So, Median ≠ Mean
Thus, Statement 1 doesn’t give us a unique answer to the asked question. So, this statement is not sufficient

Step 4 : Analyze Statement 2 independent

(2) The difference between any 2 successive integers of the set is 4

Note that we are given that the integers are arranged in ascending order.
So, combining this fact with Statement 2, we can write that the numbers are of the form: {m, m + 4, m + 8, m + 12, . . . , m + (n-1)*4}
Thus, the given sequence is an Arithmetic Progression.
Therefore, the median of the sequence will definitely be equal to the mean of the sequence.

So Statement 2 is sufficient.

Step 5: Analyze Both Statements Together (if needed)

Since we’ve already arrived at a unique answer in Step 4, this step is not required
Answer: Option B

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A set consists of n distinct integers arranged in the order of increasing magnitude. Is the median of the n integers equal to thearithmetic mean of the n integers?(1) The sum of any 3 successive integers of the set is divisible by 3(2) The difference between any 2 successive integers of the set is 4a)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 'B'. Can you explain this answer?

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A set consists of n distinct integers arranged in the order of increasing magnitude. Is the median of the n integers equal to thearithmetic mean of the n integers?(1) The sum of any 3 successive integers of the set is divisible by 3(2) The difference between any 2 successive integers of the set is 4a)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 'B'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about A set consists of n distinct integers arranged in the order of increasing magnitude. Is the median of the n integers equal to thearithmetic mean of the n integers?(1) The sum of any 3 successive integers of the set is divisible by 3(2) The difference between any 2 successive integers of the set is 4a)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 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A set consists of n distinct integers arranged in the order of increasing magnitude. Is the median of the n integers equal to thearithmetic mean of the n integers?(1) The sum of any 3 successive integers of the set is divisible by 3(2) The difference between any 2 successive integers of the set is 4a)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 'B'. Can you explain this answer?.

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