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Set A consists of a set of n consecutive integers. Is the sum of all the integers in set A even?
(1) If -5 is added to set A, the set would become symmetric about 0
(2) If the largest integer of set A is removed, the sum of the remaining integers is even
- 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?
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Set A consists of a set of n consecutive integers. Is the sum of all t...
Steps 1 & 2: Understand Question and Draw Inferences
- Let the smallest integer be in set A be a. So, the other integers in set A will be a+1, a+2….a+n-1
- Sum of all integers in set
Step 3: Analyze Statement 1 independently
(1) If -5 is added to set A, the set would become symmetric about 0
- As the set becomes symmetric about 0, that would mean that there will be (upon the inclusion of -5 in set A) an equal number of terms on either side of 0 with the same magnitude (but opposite signs).
- Let’s call this new set as A’
- So, the mean of (Set A’) = 0
- So, the sum of (All the integers in set A’) = 0
- Hence, the sum of all the integers in set A is odd.
- Sufficient to answer.
Step 4: Analyze Statement 2 independently
(2) If the largest integer of set A is removed, the sum of the remaining integers is even.
- The largest integer of Set A = a +n -1.
- So, (Sum of all the terms in set A – largest integer of set A) = even
- Let’s think of the possible ways in which difference of two integers is even:
- Case-I: even – even = even
- So, if the largest integer removed is even, the sum of all the integers in set A would be even.
- Hence
will be even - Case-II: odd – odd = even
- So, if the largest integer removed is odd, the sum of all the integers in set A would be odd.
- Hence
will be odd - As we do not have a unique answer, the statement is insufficient to answer.
- Case-I: even – even = even
Step 5: Analyze Both Statements Together (if needed)
- As we have a unique answer from step-3, this step is not required.
Answer: A
Most Upvoted Answer
Set A consists of a set of n consecutive integers. Is the sum of all t...
Statement 1: If -5 is added to set A, the set would become symmetric about 0.
Adding -5 to set A would shift the entire set to the left by 5 units, making it symmetric about 0.
- Let's assume the set A consists of n consecutive integers starting from x. So, the set A would be {x, x+1, x+2, ..., x+n-1}.
- If we add -5 to each integer in set A, the new set would be {x-5, x-4, x-3, ..., x+n-6, x+n-5}.
- Since the new set is symmetric about 0, we can conclude that the average of the integers in the set is 0.
- The sum of n consecutive integers can be calculated using the formula: sum = (first term + last term) * (number of terms) / 2.
- In this case, the sum of the integers in set A would be (x + x+n-1) * n / 2.
- From the given information, we know that the average of the integers in set A is 0. So, (x + x+n-1) * n / 2 = 0.
From statement 1, we can conclude that the sum of all the integers in set A is 0. Since 0 is an even number, the answer to the question is YES.
Statement 2: If the largest integer of set A is removed, the sum of the remaining integers is even.
Let's assume the largest integer in set A is x+n-1.
- The sum of the integers in set A would be (x + x+n-1) * n / 2.
- If we remove the largest integer x+n-1, the sum of the remaining integers would be (x + x+n-1) * (n-1) / 2.
- From this information, we cannot determine if the sum of the remaining integers is even or odd.
Since statement 2 alone is not sufficient to answer the question, the answer is (A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
Adding -5 to set A would shift the entire set to the left by 5 units, making it symmetric about 0.
- Let's assume the set A consists of n consecutive integers starting from x. So, the set A would be {x, x+1, x+2, ..., x+n-1}.
- If we add -5 to each integer in set A, the new set would be {x-5, x-4, x-3, ..., x+n-6, x+n-5}.
- Since the new set is symmetric about 0, we can conclude that the average of the integers in the set is 0.
- The sum of n consecutive integers can be calculated using the formula: sum = (first term + last term) * (number of terms) / 2.
- In this case, the sum of the integers in set A would be (x + x+n-1) * n / 2.
- From the given information, we know that the average of the integers in set A is 0. So, (x + x+n-1) * n / 2 = 0.
From statement 1, we can conclude that the sum of all the integers in set A is 0. Since 0 is an even number, the answer to the question is YES.
Statement 2: If the largest integer of set A is removed, the sum of the remaining integers is even.
Let's assume the largest integer in set A is x+n-1.
- The sum of the integers in set A would be (x + x+n-1) * n / 2.
- If we remove the largest integer x+n-1, the sum of the remaining integers would be (x + x+n-1) * (n-1) / 2.
- From this information, we cannot determine if the sum of the remaining integers is even or odd.
Since statement 2 alone is not sufficient to answer the question, the answer is (A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
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Set A consists of a set of n consecutive integers. Is the sum of all the integers in set A even?(1) If -5 is added to set A, the set would become symmetric about 0(2) If the largest integer of set A is removed, the sum of the remaining integers is evena)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?
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Set A consists of a set of n consecutive integers. Is the sum of all the integers in set A even?(1) If -5 is added to set A, the set would become symmetric about 0(2) If the largest integer of set A is removed, the sum of the remaining integers is evena)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? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Set A consists of a set of n consecutive integers. Is the sum of all the integers in set A even?(1) If -5 is added to set A, the set would become symmetric about 0(2) If the largest integer of set A is removed, the sum of the remaining integers is evena)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? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Set A consists of a set of n consecutive integers. Is the sum of all the integers in set A even?(1) If -5 is added to set A, the set would become symmetric about 0(2) If the largest integer of set A is removed, the sum of the remaining integers is evena)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?.
Set A consists of a set of n consecutive integers. Is the sum of all the integers in set A even?(1) If -5 is added to set A, the set would become symmetric about 0(2) If the largest integer of set A is removed, the sum of the remaining integers is evena)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? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Set A consists of a set of n consecutive integers. Is the sum of all the integers in set A even?(1) If -5 is added to set A, the set would become symmetric about 0(2) If the largest integer of set A is removed, the sum of the remaining integers is evena)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? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Set A consists of a set of n consecutive integers. Is the sum of all the integers in set A even?(1) If -5 is added to set A, the set would become symmetric about 0(2) If the largest integer of set A is removed, the sum of the remaining integers is evena)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?.
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Set A consists of a set of n consecutive integers. Is the sum of all the integers in set A even?(1) If -5 is added to set A, the set would become symmetric about 0(2) If the largest integer of set A is removed, the sum of the remaining integers is evena)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?, a detailed solution for Set A consists of a set of n consecutive integers. Is the sum of all the integers in set A even?(1) If -5 is added to set A, the set would become symmetric about 0(2) If the largest integer of set A is removed, the sum of the remaining integers is evena)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? has been provided alongside types of Set A consists of a set of n consecutive integers. Is the sum of all the integers in set A even?(1) If -5 is added to set A, the set would become symmetric about 0(2) If the largest integer of set A is removed, the sum of the remaining integers is evena)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? theory, EduRev gives you an
ample number of questions to practice Set A consists of a set of n consecutive integers. Is the sum of all the integers in set A even?(1) If -5 is added to set A, the set would become symmetric about 0(2) If the largest integer of set A is removed, the sum of the remaining integers is evena)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? tests, examples and also practice GMAT tests.
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