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A, B, C, D, E, and F are six consecutive positive odd integers in increasing order. What is the value of the median of these six integers?
(1) The sum of the two smallest integers is greater than the largest integer by 13
(2) The average (arithmetic mean) of these integers is 26
- 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 'D'. Can you explain this answer?
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Verified Answer
A, B, C, D, E, and F are six consecutive positive odd integers in incr...
Steps 1 & 2: Understand Question and Draw Inferences
We are given six consecutive positive odd integers. We have to find the median of this set of integers.
Since the integers are consecutive odd integers, they can be represented with the help of a positive integer n, as follows:
A = 2*n + 1
B = 2*n + 3
C = 2*n + 5
D = 2*n + 7
E = 2*n + 9
F = 2*n + 11
Now, we know that, for a series in increasing order, the median is the middle number in case of odd number of integers and the average of the middle two numbers in case of even number of integers.
Since there are even number (6) of integers in this series, the median will be the average of the 3rd and 4th number:
Thus, in order to find the value of the median, we need to know the value of n. So, the question becomes “what is the value of n?”
Step 3: Analyze Statement 1
The sum of the two smallest integers is greater than the largest integer by 13 ?
Now, the two smallest integers in the sequence are 2n+1 and 2n+3 and their sum = 4n+4
The largest integer in the sequence is 2n+11.
Per statement (1), the difference between these two should be 13. So,
(4n+4) – (2n+11) = 13
2n-7 = 13
2n = 20
Thus, n =10.
Now, since we have found the value of n, we can find the median.
Hence, statement (1) is sufficient to find a unique value of the median.
Step 4: Analyze Statement 2
The average (arithmetic mean) of these integers is 26
Thus:
Now, since we have found the value of n, we can find the median.
Hence, statement (2) is sufficient to find a unique value of the median
Step 5: Analyze Both Statements Together (if needed)
Since statement (1) and (2) alone are sufficient to answer the question, we don’t need to perform this step.
Answer: Option (D)
Most Upvoted Answer
A, B, C, D, E, and F are six consecutive positive odd integers in incr...
Solution:
Let's represent the six integers as A, B, C, D, E, and F.
From the given information, we know that:
B = A + 2
C = A + 4
D = A + 6
E = A + 8
F = A + 10
The median of these six integers is the fourth integer, which is D.
Statement 1: The sum of the two smallest integers is greater than the largest integer by 13.
A + B > F + 13
Substituting the values of A and B from above, we get:
A + (A + 2) > (A + 10) + 13
Simplifying, we get:
2A - 1 > 23
2A > 24
A > 12
This tells us that A is greater than 12, and therefore, the value of the median (D) is greater than 18. This statement alone is sufficient.
Statement 2: The average (arithmetic mean) of these integers is 26.
The sum of the six integers is:
A + (A + 2) + (A + 4) + (A + 6) + (A + 8) + (A + 10) = 6A + 30
Since the average is 26, we have:
(6A + 30)/6 = 26
Simplifying, we get:
A = 16
This tells us the value of A, but we still need to calculate the value of the median (D). Using the values of A and D from above, we get:
D = A + 6 = 16 + 6 = 22
Therefore, this statement alone is also sufficient.
Both statements together provide the value of A and confirm that A > 12, which means that the median (D) is greater than 18. This makes statement 1 sufficient and statement 2 confirms the value of the median. Therefore, the correct answer is option D.
Let's represent the six integers as A, B, C, D, E, and F.
From the given information, we know that:
B = A + 2
C = A + 4
D = A + 6
E = A + 8
F = A + 10
The median of these six integers is the fourth integer, which is D.
Statement 1: The sum of the two smallest integers is greater than the largest integer by 13.
A + B > F + 13
Substituting the values of A and B from above, we get:
A + (A + 2) > (A + 10) + 13
Simplifying, we get:
2A - 1 > 23
2A > 24
A > 12
This tells us that A is greater than 12, and therefore, the value of the median (D) is greater than 18. This statement alone is sufficient.
Statement 2: The average (arithmetic mean) of these integers is 26.
The sum of the six integers is:
A + (A + 2) + (A + 4) + (A + 6) + (A + 8) + (A + 10) = 6A + 30
Since the average is 26, we have:
(6A + 30)/6 = 26
Simplifying, we get:
A = 16
This tells us the value of A, but we still need to calculate the value of the median (D). Using the values of A and D from above, we get:
D = A + 6 = 16 + 6 = 22
Therefore, this statement alone is also sufficient.
Both statements together provide the value of A and confirm that A > 12, which means that the median (D) is greater than 18. This makes statement 1 sufficient and statement 2 confirms the value of the median. Therefore, the correct answer is option D.
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A, B, C, D, E, and F are six consecutive positive odd integers in increasing order. What is the value of the median of these six integers?(1) The sum of the two smallest integers is greater than the largest integer by 13(2) The average (arithmetic mean) of these integers is 26a)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 'D'. Can you explain this answer?
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A, B, C, D, E, and F are six consecutive positive odd integers in increasing order. What is the value of the median of these six integers?(1) The sum of the two smallest integers is greater than the largest integer by 13(2) The average (arithmetic mean) of these integers is 26a)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 'D'. 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, B, C, D, E, and F are six consecutive positive odd integers in increasing order. What is the value of the median of these six integers?(1) The sum of the two smallest integers is greater than the largest integer by 13(2) The average (arithmetic mean) of these integers is 26a)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 'D'. 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, B, C, D, E, and F are six consecutive positive odd integers in increasing order. What is the value of the median of these six integers?(1) The sum of the two smallest integers is greater than the largest integer by 13(2) The average (arithmetic mean) of these integers is 26a)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 'D'. Can you explain this answer?.
A, B, C, D, E, and F are six consecutive positive odd integers in increasing order. What is the value of the median of these six integers?(1) The sum of the two smallest integers is greater than the largest integer by 13(2) The average (arithmetic mean) of these integers is 26a)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 'D'. 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, B, C, D, E, and F are six consecutive positive odd integers in increasing order. What is the value of the median of these six integers?(1) The sum of the two smallest integers is greater than the largest integer by 13(2) The average (arithmetic mean) of these integers is 26a)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 'D'. 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, B, C, D, E, and F are six consecutive positive odd integers in increasing order. What is the value of the median of these six integers?(1) The sum of the two smallest integers is greater than the largest integer by 13(2) The average (arithmetic mean) of these integers is 26a)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 'D'. Can you explain this answer?.
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A, B, C, D, E, and F are six consecutive positive odd integers in increasing order. What is the value of the median of these six integers?(1) The sum of the two smallest integers is greater than the largest integer by 13(2) The average (arithmetic mean) of these integers is 26a)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 'D'. Can you explain this answer?, a detailed solution for A, B, C, D, E, and F are six consecutive positive odd integers in increasing order. What is the value of the median of these six integers?(1) The sum of the two smallest integers is greater than the largest integer by 13(2) The average (arithmetic mean) of these integers is 26a)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 'D'. Can you explain this answer? has been provided alongside types of A, B, C, D, E, and F are six consecutive positive odd integers in increasing order. What is the value of the median of these six integers?(1) The sum of the two smallest integers is greater than the largest integer by 13(2) The average (arithmetic mean) of these integers is 26a)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 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A, B, C, D, E, and F are six consecutive positive odd integers in increasing order. What is the value of the median of these six integers?(1) The sum of the two smallest integers is greater than the largest integer by 13(2) The average (arithmetic mean) of these integers is 26a)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 'D'. Can you explain this answer? tests, examples and also practice GMAT tests.
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