An arithmetic sequence is a sequence in which each term after the first is equal to the sum of the preceding term and a constant, which is also known as the common difference of that arithmetic sequence. An increasing arithmetic sequence N consists of a set of distinct negative integers and an increasing arithmetic sequence P consists of a set of distinct positive integers. The sequence C contains all the terms of arithmetic sequences N and P such that the number of terms in sequence C is equal to the number of terms in arithmetic sequences N and P. Is sequence C an arithmetic sequence?(1) The sum of the largest term of the sequence N and the smallest term of the sequence P is zero.(2) For every integer in sequence N, there exists an integer in sequence P with the same magnitude.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 askedc)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 'E'. Can you explain this answer?

EduRev

All Courses

Explore Courses UPSC Exam UPSC Test Series Free Notes EduRev Infinity

Open App

GMAT Exam > GMAT Questions > An arithmetic sequence is a sequence in which...

Join the Discussion on the App

(1) The sum of the largest term of the sequence N and the smallest term of the sequence P is zero.

(2) For every integer in sequence N, there exists an integer in sequence P with the same magnitude.

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 'E'. Can you explain this answer?

FREE This question is part of

Test: Sequences

Attempt Test

Attempt this Test

Verified Answer

An arithmetic sequence is a sequence in which each term after the firs...

Steps 1 & 2: Understand Question and Draw Inferences

Increasing arithmetic sequence N consist of distinct negative integers with common difference n
Increasing arithmetic sequence P consist of distinct positive integers with common difference m.
Sequence C consist of terms of sequences N and P only.

To Find: Is sequence C an arithmetic sequence?

As sequence C consists of terms of arithmetic sequences N and P only, for sequence C to be arithmetic, sequences N and P should have the same common difference.

Also, sequences N and P will not have any common terms (as sequence N has all negative integers and sequence P has only positive integers), for sequence C to be arithmetic, the difference between the largest term of sequence N and the smallest term of sequence P should be equal to the common difference of the sequences.

For ex: Consider N = { -10, -9, -8……-1) and P = { 2, 3, 4, 5, ….}. In this case, both the sequences N and P have the same common difference but combining their terms does not result in an arithmetic sequence because the difference between -1 and 2 is not equal to the common difference of the sequences.

Consider N = { -14, -10, -6, -2} and P = {2, 6, 10}. In this case, as the difference between -2 and 2 is equal to the common differences of the sequences(i.e. 4), combining the terms of both the sequences results in an arithemetic sequence.

Step 3: Analyze Statement 1 independently

(1) The sum of the largest term of the sequence N and the smallest term of the sequence P is zero.

Let the largest term of sequence N be x and the smallest term of the sequence P be y.
So, x + y = 0
- x = -y
- So, difference between y and x = y – x = 2y

However we do not know the value of the common differences of the sequences as well as we do not know the value of y.

Insufficient to answer.

Step 4: Analyze Statement 2 independently

(2) For every integer in sequence N, there exists an integer in sequence P with the same magnitude.

It tells us that integers in sequence P consist of negative of all the integers in sequence N. Following cases are possible:
- Number of terms of sequence N and P are the same. For ex: N= {-8, -6, -4} and P = {4, 6, 8}. In this case the common difference of both the sequences will be equal.
- Number of terms in sequence P is greater than the number of terms in sequence N. For ex: N = {-8, -6, -4} and P = {3, 4, 5, 6, 7, 8, 9} or { 4, 6, 8, 10, 12}. In this case the common difference may or may not be equal.

Also, as we do not know the difference between the largest term of sequence N and the smallest term of sequence P, the statement is insufficient to answer.

Step 5: Analyze Both Statements Together (if needed)

Difference between the largest term of sequence N( i.e. x) and the smallest term of sequence P(i.e. y) is equal to 2y.
For every integer in sequence N, there exists an integer in sequence P with the same magnitude

Combining both the statements tell us that the largest term of sequence N (i.e. x) and the smallest term of sequence P(i.e. y ) have the same magnitude.

However it does not tell us:

the value of y and
if the sequences have the same common difference

Hence, combining the statements is also insufficient to answer.

Answer: E

View all questions of this test

View all answers Start learning for free

< Previous Question Next Question >

Explore Courses for GMAT exam

Similar GMAT Doubts

An arithmetic sequence is a sequence in which each term after the first is equal to the sum of the preceding term and a constant, which is also known as the common difference of that arithmetic sequence. The sequence S contains all the terms of two different increasing arithmetic sequences P and Q such that the number of terms in sequence S is equal to the sum of the number of terms in sequences P and Q. If each of the arithmetic sequences P and Q consists of 10 positive integral terms, how many distinct terms does sequence S have?(1) The least common multiple of the common differences of the sequences P and Q is 6(2) The third term of the sequence P is equal to the second term of the sequence Q

View answer

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 4

View answer

List A contains 16 distinct odd integers and 9 distinct even integers such that the average (arithmetic mean) of List A is 13.84. If each odd integer is doubled in magnitude, what is the new average (arithmetic mean) of List A?(1) The average (arithmetic mean) of the even integers in List A is 10(2) Before each odd integer is doubled in magnitude, the smallest odd integer in List A is 1 and the largest odd integer in List A is31.

View answer

A list contains 7 positive integers. What is the value of the smallest integer in the set?(1) The highest term in the set is 37(2) When arranged in increasing order, the difference between any two consecutive terms isat least6

View answer

NumbersAll numbers used are real numbers.FiguresA figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2).Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight.You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.All figures lie in a plane unless otherwise indicated.Q.A set S contains the following elements: {7, 11, 15, 19, 23, x}. What is the value of x?1.The elements are in arithmetic progression.2.x is prime.

View answer

Top Courses for GMATView all

GMAT Focus Edition Mock Test Series 2024

Top Courses for GMAT

View all

An arithmetic sequence is a sequence in which each term after the first is equal to the sum of the preceding term and a constant, which is also known as the common difference of that arithmetic sequence. An increasing arithmetic sequence N consists of a set of distinct negative integers and an increasing arithmetic sequence P consists of a set of distinct positive integers. The sequence C contains all the terms of arithmetic sequences N and P such that the number of terms in sequence C is equal to the number of terms in arithmetic sequences N and P. Is sequence C an arithmetic sequence?(1) The sum of the largest term of the sequence N and the smallest term of the sequence P is zero.(2) For every integer in sequence N, there exists an integer in sequence P with the same magnitude.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 askedc)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 'E'. Can you explain this answer?

Share with a Friend

Answer this doubt

Question Description
An arithmetic sequence is a sequence in which each term after the first is equal to the sum of the preceding term and a constant, which is also known as the common difference of that arithmetic sequence. An increasing arithmetic sequence N consists of a set of distinct negative integers and an increasing arithmetic sequence P consists of a set of distinct positive integers. The sequence C contains all the terms of arithmetic sequences N and P such that the number of terms in sequence C is equal to the number of terms in arithmetic sequences N and P. Is sequence C an arithmetic sequence?(1) The sum of the largest term of the sequence N and the smallest term of the sequence P is zero.(2) For every integer in sequence N, there exists an integer in sequence P with the same magnitude.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 askedc)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 'E'. 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 An arithmetic sequence is a sequence in which each term after the first is equal to the sum of the preceding term and a constant, which is also known as the common difference of that arithmetic sequence. An increasing arithmetic sequence N consists of a set of distinct negative integers and an increasing arithmetic sequence P consists of a set of distinct positive integers. The sequence C contains all the terms of arithmetic sequences N and P such that the number of terms in sequence C is equal to the number of terms in arithmetic sequences N and P. Is sequence C an arithmetic sequence?(1) The sum of the largest term of the sequence N and the smallest term of the sequence P is zero.(2) For every integer in sequence N, there exists an integer in sequence P with the same magnitude.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 askedc)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 'E'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An arithmetic sequence is a sequence in which each term after the first is equal to the sum of the preceding term and a constant, which is also known as the common difference of that arithmetic sequence. An increasing arithmetic sequence N consists of a set of distinct negative integers and an increasing arithmetic sequence P consists of a set of distinct positive integers. The sequence C contains all the terms of arithmetic sequences N and P such that the number of terms in sequence C is equal to the number of terms in arithmetic sequences N and P. Is sequence C an arithmetic sequence?(1) The sum of the largest term of the sequence N and the smallest term of the sequence P is zero.(2) For every integer in sequence N, there exists an integer in sequence P with the same magnitude.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 askedc)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 'E'. Can you explain this answer?.

Solutions for An arithmetic sequence is a sequence in which each term after the first is equal to the sum of the preceding term and a constant, which is also known as the common difference of that arithmetic sequence. An increasing arithmetic sequence N consists of a set of distinct negative integers and an increasing arithmetic sequence P consists of a set of distinct positive integers. The sequence C contains all the terms of arithmetic sequences N and P such that the number of terms in sequence C is equal to the number of terms in arithmetic sequences N and P. Is sequence C an arithmetic sequence?(1) The sum of the largest term of the sequence N and the smallest term of the sequence P is zero.(2) For every integer in sequence N, there exists an integer in sequence P with the same magnitude.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 askedc)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 'E'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT. Download more important topics, notes, lectures and mock test series for GMAT Exam by signing up for free.

Here you can find the meaning of An arithmetic sequence is a sequence in which each term after the first is equal to the sum of the preceding term and a constant, which is also known as the common difference of that arithmetic sequence. An increasing arithmetic sequence N consists of a set of distinct negative integers and an increasing arithmetic sequence P consists of a set of distinct positive integers. The sequence C contains all the terms of arithmetic sequences N and P such that the number of terms in sequence C is equal to the number of terms in arithmetic sequences N and P. Is sequence C an arithmetic sequence?(1) The sum of the largest term of the sequence N and the smallest term of the sequence P is zero.(2) For every integer in sequence N, there exists an integer in sequence P with the same magnitude.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 askedc)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 'E'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of An arithmetic sequence is a sequence in which each term after the first is equal to the sum of the preceding term and a constant, which is also known as the common difference of that arithmetic sequence. An increasing arithmetic sequence N consists of a set of distinct negative integers and an increasing arithmetic sequence P consists of a set of distinct positive integers. The sequence C contains all the terms of arithmetic sequences N and P such that the number of terms in sequence C is equal to the number of terms in arithmetic sequences N and P. Is sequence C an arithmetic sequence?(1) The sum of the largest term of the sequence N and the smallest term of the sequence P is zero.(2) For every integer in sequence N, there exists an integer in sequence P with the same magnitude.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 askedc)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 'E'. Can you explain this answer?, a detailed solution for An arithmetic sequence is a sequence in which each term after the first is equal to the sum of the preceding term and a constant, which is also known as the common difference of that arithmetic sequence. An increasing arithmetic sequence N consists of a set of distinct negative integers and an increasing arithmetic sequence P consists of a set of distinct positive integers. The sequence C contains all the terms of arithmetic sequences N and P such that the number of terms in sequence C is equal to the number of terms in arithmetic sequences N and P. Is sequence C an arithmetic sequence?(1) The sum of the largest term of the sequence N and the smallest term of the sequence P is zero.(2) For every integer in sequence N, there exists an integer in sequence P with the same magnitude.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 askedc)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 'E'. Can you explain this answer? has been provided alongside types of An arithmetic sequence is a sequence in which each term after the first is equal to the sum of the preceding term and a constant, which is also known as the common difference of that arithmetic sequence. An increasing arithmetic sequence N consists of a set of distinct negative integers and an increasing arithmetic sequence P consists of a set of distinct positive integers. The sequence C contains all the terms of arithmetic sequences N and P such that the number of terms in sequence C is equal to the number of terms in arithmetic sequences N and P. Is sequence C an arithmetic sequence?(1) The sum of the largest term of the sequence N and the smallest term of the sequence P is zero.(2) For every integer in sequence N, there exists an integer in sequence P with the same magnitude.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 askedc)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 'E'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice An arithmetic sequence is a sequence in which each term after the first is equal to the sum of the preceding term and a constant, which is also known as the common difference of that arithmetic sequence. An increasing arithmetic sequence N consists of a set of distinct negative integers and an increasing arithmetic sequence P consists of a set of distinct positive integers. The sequence C contains all the terms of arithmetic sequences N and P such that the number of terms in sequence C is equal to the number of terms in arithmetic sequences N and P. Is sequence C an arithmetic sequence?(1) The sum of the largest term of the sequence N and the smallest term of the sequence P is zero.(2) For every integer in sequence N, there exists an integer in sequence P with the same magnitude.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 askedc)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 'E'. Can you explain this answer? tests, examples and also practice GMAT tests.

Explore Courses for GMAT exam