GMAT Exam > GMAT Questions > a, b, and c are three distinct positive integ...
Start Learning for Free
a, b, and c are three distinct positive integers. What is the product abc?
(1) a + b + c = 7
(2) ab + bc + ca = 14
(2) ab + bc + ca = 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)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
- e)EACH statement ALONE is sufficient to answer the question asked
Correct answer is option 'E'. Can you explain this answer?
Verified Answer
a, b, and c are three distinct positive integers. What is the product ...
Statement (1): a + b + c = 7
This statement provides information about the sum of the three positive integers, but it does not provide any information about their product. Since there are multiple combinations of three positive integers that can add up to 7 (e.g., 1 + 2 + 4, 1 + 3 + 3, etc.), statement (1) alone is not sufficient to determine the product abc.
Statement (2): ab + bc + ca = 14
This statement provides information about the sum of the pairwise products of the three positive integers.
However, similar to statement (1), it does not directly provide information about the product abc. It is important to note that the pairwise products are not necessarily the same as the product abc.
For example, if a = 2, b = 3, and c = 4, we have ab + bc + ca = 2(3) + 3(4) + 4(2) = 6 + 12 + 8 = 26, which is not equal to 14.
Therefore, statement (2) alone is not sufficient to determine the product abc.
However, similar to statement (1), it does not directly provide information about the product abc. It is important to note that the pairwise products are not necessarily the same as the product abc.
For example, if a = 2, b = 3, and c = 4, we have ab + bc + ca = 2(3) + 3(4) + 4(2) = 6 + 12 + 8 = 26, which is not equal to 14.
Therefore, statement (2) alone is not sufficient to determine the product abc.
Now let's consider both statements together:
Combining the two statements, we have the following system of equations:
a + b + c = 7 (from statement 1)
ab + bc + ca = 14 (from statement 2)
ab + bc + ca = 14 (from statement 2)
From this system, we can deduce that:
(a + b + c)2 = (7)2 = 49
a2 + b2 + c2 + 2(ab + bc + ca) = 49
a2 + b2 + c2 + 2(14) = 49
a2 + b2 + c2 = 21
a2 + b2 + c2 + 2(ab + bc + ca) = 49
a2 + b2 + c2 + 2(14) = 49
a2 + b2 + c2 = 21
However, even with this additional equation, we still cannot determine the values of a, b, and c uniquely.
There are multiple sets of positive integers that satisfy the equation a2 + b2 + c2 = 21.
For example, a = 1, b = 2, and c = 4 or a = 1, b = 3, and c = 3 are both valid solutions.
Since we can't uniquely determine the values of a, b, and c, even when combining the two statements, the answer is that the statements together are not sufficient.
There are multiple sets of positive integers that satisfy the equation a2 + b2 + c2 = 21.
For example, a = 1, b = 2, and c = 4 or a = 1, b = 3, and c = 3 are both valid solutions.
Since we can't uniquely determine the values of a, b, and c, even when combining the two statements, the answer is that the statements together are not sufficient.
Therefore, the correct answer is (E) Statements (1) and (2) together are not sufficient to answer the question asked, and additional data are needed.
Most Upvoted Answer
a, b, and c are three distinct positive integers. What is the product ...
Statement (1): a + b + c = 7
This statement provides information about the sum of the three positive integers, but it does not provide any information about their product. Since there are multiple combinations of three positive integers that can add up to 7 (e.g., 1 + 2 + 4, 1 + 3 + 3, etc.), statement (1) alone is not sufficient to determine the product abc.
Statement (2): ab + bc + ca = 14
This statement provides information about the sum of the pairwise products of the three positive integers.
However, similar to statement (1), it does not directly provide information about the product abc. It is important to note that the pairwise products are not necessarily the same as the product abc.
For example, if a = 2, b = 3, and c = 4, we have ab + bc + ca = 2(3) + 3(4) + 4(2) = 6 + 12 + 8 = 26, which is not equal to 14.
Therefore, statement (2) alone is not sufficient to determine the product abc.
However, similar to statement (1), it does not directly provide information about the product abc. It is important to note that the pairwise products are not necessarily the same as the product abc.
For example, if a = 2, b = 3, and c = 4, we have ab + bc + ca = 2(3) + 3(4) + 4(2) = 6 + 12 + 8 = 26, which is not equal to 14.
Therefore, statement (2) alone is not sufficient to determine the product abc.
Now let's consider both statements together:
Combining the two statements, we have the following system of equations:
a + b + c = 7 (from statement 1)
ab + bc + ca = 14 (from statement 2)
ab + bc + ca = 14 (from statement 2)
From this system, we can deduce that:
(a + b + c)2 = (7)2 = 49
a2 + b2 + c2 + 2(ab + bc + ca) = 49
a2 + b2 + c2 + 2(14) = 49
a2 + b2 + c2 = 21
a2 + b2 + c2 + 2(ab + bc + ca) = 49
a2 + b2 + c2 + 2(14) = 49
a2 + b2 + c2 = 21
However, even with this additional equation, we still cannot determine the values of a, b, and c uniquely.
There are multiple sets of positive integers that satisfy the equation a2 + b2 + c2 = 21.
For example, a = 1, b = 2, and c = 4 or a = 1, b = 3, and c = 3 are both valid solutions.
Since we can't uniquely determine the values of a, b, and c, even when combining the two statements, the answer is that the statements together are not sufficient.
There are multiple sets of positive integers that satisfy the equation a2 + b2 + c2 = 21.
For example, a = 1, b = 2, and c = 4 or a = 1, b = 3, and c = 3 are both valid solutions.
Since we can't uniquely determine the values of a, b, and c, even when combining the two statements, the answer is that the statements together are not sufficient.
Therefore, the correct answer is (E) Statements (1) and (2) together are not sufficient to answer the question asked, and additional data are needed.
Community Answer
a, b, and c are three distinct positive integers. What is the product ...
Statement 1:
The sum of a, b, and c is 7.
Statement 2:
The sum of the products of any two of the integers a, b, and c is 14.
Explanation:
Analyzing Statement 1:
- From statement 1, we know that a + b + c = 7.
- However, this information alone does not provide enough details to determine the product abc, as there are multiple combinations of three distinct positive integers that sum up to 7.
Analyzing Statement 2:
- From statement 2, we know that ab + bc + ca = 14.
- Again, this information alone is not sufficient to determine the product abc, as the product ab, bc, and ca can vary based on the values of a, b, and c.
Combining Both Statements:
- Even when we combine both statements, we still do not have enough information to uniquely determine the values of a, b, and c and subsequently find the product abc.
- Without additional data to narrow down the possible values of a, b, and c, the product abc cannot be calculated definitively.
Therefore, the correct answer is option 'E', which states that both statements together are not sufficient to answer the question, and additional data are needed to find the product abc.
The sum of a, b, and c is 7.
Statement 2:
The sum of the products of any two of the integers a, b, and c is 14.
Explanation:
Analyzing Statement 1:
- From statement 1, we know that a + b + c = 7.
- However, this information alone does not provide enough details to determine the product abc, as there are multiple combinations of three distinct positive integers that sum up to 7.
Analyzing Statement 2:
- From statement 2, we know that ab + bc + ca = 14.
- Again, this information alone is not sufficient to determine the product abc, as the product ab, bc, and ca can vary based on the values of a, b, and c.
Combining Both Statements:
- Even when we combine both statements, we still do not have enough information to uniquely determine the values of a, b, and c and subsequently find the product abc.
- Without additional data to narrow down the possible values of a, b, and c, the product abc cannot be calculated definitively.
Therefore, the correct answer is option 'E', which states that both statements together are not sufficient to answer the question, and additional data are needed to find the product abc.
|
Explore Courses for GMAT exam
|
|
Top Courses for GMATView all
Question Description
a, b, and c are three distinct positive integers. What is the product abc?(1) a + b + c = 7(2) ab + bc + ca = 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)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needede)EACH statement ALONE is sufficient to answer the question askedCorrect answer is option 'E'. 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 a, b, and c are three distinct positive integers. What is the product abc?(1) a + b + c = 7(2) ab + bc + ca = 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)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needede)EACH statement ALONE is sufficient to answer the question askedCorrect answer is option 'E'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for a, b, and c are three distinct positive integers. What is the product abc?(1) a + b + c = 7(2) ab + bc + ca = 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)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needede)EACH statement ALONE is sufficient to answer the question askedCorrect answer is option 'E'. Can you explain this answer?.
a, b, and c are three distinct positive integers. What is the product abc?(1) a + b + c = 7(2) ab + bc + ca = 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)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needede)EACH statement ALONE is sufficient to answer the question askedCorrect answer is option 'E'. 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 a, b, and c are three distinct positive integers. What is the product abc?(1) a + b + c = 7(2) ab + bc + ca = 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)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needede)EACH statement ALONE is sufficient to answer the question askedCorrect answer is option 'E'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for a, b, and c are three distinct positive integers. What is the product abc?(1) a + b + c = 7(2) ab + bc + ca = 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)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needede)EACH statement ALONE is sufficient to answer the question askedCorrect answer is option 'E'. Can you explain this answer?.
Solutions for a, b, and c are three distinct positive integers. What is the product abc?(1) a + b + c = 7(2) ab + bc + ca = 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)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needede)EACH statement ALONE is sufficient to answer the question askedCorrect 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 a, b, and c are three distinct positive integers. What is the product abc?(1) a + b + c = 7(2) ab + bc + ca = 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)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needede)EACH statement ALONE is sufficient to answer the question askedCorrect answer is option 'E'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
a, b, and c are three distinct positive integers. What is the product abc?(1) a + b + c = 7(2) ab + bc + ca = 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)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needede)EACH statement ALONE is sufficient to answer the question askedCorrect answer is option 'E'. Can you explain this answer?, a detailed solution for a, b, and c are three distinct positive integers. What is the product abc?(1) a + b + c = 7(2) ab + bc + ca = 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)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needede)EACH statement ALONE is sufficient to answer the question askedCorrect answer is option 'E'. Can you explain this answer? has been provided alongside types of a, b, and c are three distinct positive integers. What is the product abc?(1) a + b + c = 7(2) ab + bc + ca = 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)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needede)EACH statement ALONE is sufficient to answer the question askedCorrect answer is option 'E'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice a, b, and c are three distinct positive integers. What is the product abc?(1) a + b + c = 7(2) ab + bc + ca = 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)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needede)EACH statement ALONE is sufficient to answer the question askedCorrect answer is option 'E'. 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!
within 7 days!
Takes less than 10 seconds to signup