GMAT Exam > GMAT Questions > What is the average (arithmetic mean) of a, b...
Start Learning for Free
What is the average (arithmetic mean) of a, b, and c ?
(1) a + 2b + 3c = 10
(2) 3a + 2b + c = 14
(2) 3a + 2b + c = 14
- 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
- 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 are needed
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
What is the average (arithmetic mean) of a, b, and c ?(1) a + 2b + 3c ...
Understanding the Problem
To find the average (arithmetic mean) of a, b, and c, we need to calculate:
\[
\text{Average} = \frac{a + b + c}{3}
\]
This requires knowledge of the values of a, b, and c.
Analyzing Statement (1)
- Equation: a + 2b + 3c = 10
This equation relates a, b, and c but does not provide sufficient information to isolate \(a + b + c\) on its own. Thus, Statement (1) alone is insufficient.
Analyzing Statement (2)
- Equation: 3a + 2b + c = 14
Similar to Statement (1), this equation also involves a, b, and c but does not allow us to determine \(a + b + c\) directly. Hence, Statement (2) alone is also insufficient.
Combining Both Statements
Now, let's analyze both statements together:
1. From Statement (1): \(a + 2b + 3c = 10\)
2. From Statement (2): \(3a + 2b + c = 14\)
To solve for \(a + b + c\), we can manipulate these equations:
- Multiply Statement (1) by 3:
\[
3a + 6b + 9c = 30
\]
- Now we have two equations:
- \(3a + 2b + c = 14\)
- \(3a + 6b + 9c = 30\)
Subtract the second equation from the first to eliminate \(3a\):
\[
(3a + 6b + 9c) - (3a + 2b + c) = 30 - 14
\]
This simplifies to:
\[
4b + 8c = 16 \implies b + 2c = 4
\]
Now we can express \(b\) in terms of \(c\) and substitute back into either original equation to find \(a\), \(b\), and \(c\).
Thus, both statements together are sufficient to find \(a + b + c\).
Conclusion
Thus, the correct answer is:
Option C: BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient.
To find the average (arithmetic mean) of a, b, and c, we need to calculate:
\[
\text{Average} = \frac{a + b + c}{3}
\]
This requires knowledge of the values of a, b, and c.
Analyzing Statement (1)
- Equation: a + 2b + 3c = 10
This equation relates a, b, and c but does not provide sufficient information to isolate \(a + b + c\) on its own. Thus, Statement (1) alone is insufficient.
Analyzing Statement (2)
- Equation: 3a + 2b + c = 14
Similar to Statement (1), this equation also involves a, b, and c but does not allow us to determine \(a + b + c\) directly. Hence, Statement (2) alone is also insufficient.
Combining Both Statements
Now, let's analyze both statements together:
1. From Statement (1): \(a + 2b + 3c = 10\)
2. From Statement (2): \(3a + 2b + c = 14\)
To solve for \(a + b + c\), we can manipulate these equations:
- Multiply Statement (1) by 3:
\[
3a + 6b + 9c = 30
\]
- Now we have two equations:
- \(3a + 2b + c = 14\)
- \(3a + 6b + 9c = 30\)
Subtract the second equation from the first to eliminate \(3a\):
\[
(3a + 6b + 9c) - (3a + 2b + c) = 30 - 14
\]
This simplifies to:
\[
4b + 8c = 16 \implies b + 2c = 4
\]
Now we can express \(b\) in terms of \(c\) and substitute back into either original equation to find \(a\), \(b\), and \(c\).
Thus, both statements together are sufficient to find \(a + b + c\).
Conclusion
Thus, the correct answer is:
Option C: BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient.
|
Explore Courses for GMAT exam
|
|
Similar GMAT Doubts
Top Courses for GMATView all
What is the average (arithmetic mean) of a, b, and c ?(1) a + 2b + 3c = 10(2) 3a + 2b + c = 14a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)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 sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'C'. Can you explain this answer?
Question Description
What is the average (arithmetic mean) of a, b, and c ?(1) a + 2b + 3c = 10(2) 3a + 2b + c = 14a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)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 sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'C'. 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 What is the average (arithmetic mean) of a, b, and c ?(1) a + 2b + 3c = 10(2) 3a + 2b + c = 14a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)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 sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the average (arithmetic mean) of a, b, and c ?(1) a + 2b + 3c = 10(2) 3a + 2b + c = 14a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)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 sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'C'. Can you explain this answer?.
What is the average (arithmetic mean) of a, b, and c ?(1) a + 2b + 3c = 10(2) 3a + 2b + c = 14a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)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 sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'C'. 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 What is the average (arithmetic mean) of a, b, and c ?(1) a + 2b + 3c = 10(2) 3a + 2b + c = 14a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)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 sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the average (arithmetic mean) of a, b, and c ?(1) a + 2b + 3c = 10(2) 3a + 2b + c = 14a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)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 sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'C'. Can you explain this answer?.
Solutions for What is the average (arithmetic mean) of a, b, and c ?(1) a + 2b + 3c = 10(2) 3a + 2b + c = 14a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)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 sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'C'. 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 What is the average (arithmetic mean) of a, b, and c ?(1) a + 2b + 3c = 10(2) 3a + 2b + c = 14a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)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 sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
What is the average (arithmetic mean) of a, b, and c ?(1) a + 2b + 3c = 10(2) 3a + 2b + c = 14a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)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 sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for What is the average (arithmetic mean) of a, b, and c ?(1) a + 2b + 3c = 10(2) 3a + 2b + c = 14a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)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 sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of What is the average (arithmetic mean) of a, b, and c ?(1) a + 2b + 3c = 10(2) 3a + 2b + c = 14a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)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 sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice What is the average (arithmetic mean) of a, b, and c ?(1) a + 2b + 3c = 10(2) 3a + 2b + c = 14a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)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 sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice GMAT tests.
|
|
Explore Courses for GMAT exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup