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What is the absolute difference between the cubes of two different non-negative integers?
(1) One of the integers is 2 greater than the other integer.
(2) The square of the sum of the integers is 49 greater than the product of the integers.
(2) The square of the sum of the integers is 49 greater than the product of the integers.
- 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?
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Most Upvoted Answer
What is the absolute difference between the cubes of two different non...
Statement (1): One of the integers is 2 greater than the other integer.
This statement tells us that the two integers have a difference of 2.
Let's assume the smaller integer is x, so the larger integer would be x + 2.
Let's assume the smaller integer is x, so the larger integer would be x + 2.
The absolute difference between the cubes of the two integers can be expressed as (x + 2)3 - x3.
Expanding this expression, we get (x3 + 6x2 + 12x + 8) - x3, which simplifies to 6x2 + 12x + 8.
We can see that the expression does not yield a unique value for the absolute difference between the cubes. For example, if x = 1, the expression becomes 26, but if x = 2, the expression becomes 56. Therefore, statement (1) alone is not sufficient to determine the absolute difference between the cubes of the two integers.
Statement (2): The square of the sum of the integers is 49 greater than the product of the integers.
This statement can be expressed as (x + (x + 2))2 = x(x + 2) + 49.
Simplifying this equation, we get (2x + 2)2 = x2 + 2x + 49.
Expanding and simplifying further, we have 4x2 + 8x + 4 = x2 + 2x + 49.
Rearranging terms, we get 3x2 + 6x - 45 = 0.
Factoring this quadratic equation, we have (x + 5)(3x - 9) = 0.
From this, we find two possible solutions: x = -5 and x = 3.
However, we are given that the integers are non-negative, so x = -5 is not a valid solution.
Thus, x = 3 is the valid solution.
However, we are given that the integers are non-negative, so x = -5 is not a valid solution.
Thus, x = 3 is the valid solution.
Now that we know x = 3, we can find the two integers: 3 and 5.
The absolute difference between the cubes of these integers is (53 - 33) = 122.
The absolute difference between the cubes of these integers is (53 - 33) = 122.
Therefore, statement (2) alone is sufficient to determine the absolute difference between the cubes of the two integers.
Combined sufficiency:
By combining both statements, we know that one integer is 2 greater than the other (statement 1) and the integers are 3 and 5 (statement 2).
With this information, we can calculate the absolute difference between the cubes, which is 122.
With this information, we can calculate the absolute difference between the cubes, which is 122.
Thus, both statements together are sufficient to determine the absolute difference between the cubes of the two integers.
The answer is (C) BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient.
Community Answer
What is the absolute difference between the cubes of two different non...
Statement 1: One of the integers is 2 greater than the other integer.
This statement alone is not sufficient to determine the absolute difference between the cubes of the two integers. We can demonstrate this by considering two scenarios:
Scenario 1: Let one integer be x and the other be x + 2. In this case, the absolute difference between the cubes would be (x + 2)^3 - x^3, which cannot be simplified further.
Scenario 2: Let one integer be x and the other be x - 2. In this case, the absolute difference between the cubes would be x^3 - (x - 2)^3, which also cannot be simplified further.
Therefore, statement 1 alone is not sufficient.
Statement 2: The square of the sum of the integers is 49 greater than the product of the integers.
Let the two integers be x and y.
The square of the sum of the integers is (x + y)^2.
The product of the integers is xy.
According to the given information, (x + y)^2 = xy + 49.
Expanding (x + y)^2, we have x^2 + 2xy + y^2 = xy + 49.
Rearranging the terms, we get x^2 + y^2 - xy = 49.
This equation can be simplified further using the formula for the sum and product of roots of a quadratic equation:
(x + y)^2 - 3xy = 49.
Since we know that (x + y)^2 = xy + 49, we can substitute this into the equation:
xy + 49 - 3xy = 49.
Simplifying, we have -2xy = 0, which implies xy = 0.
From this, we can conclude that either x or y must be equal to 0.
Combining the statements:
From statement 1, we know that one of the integers is 2 greater than the other integer. Let's assume that x = y + 2.
From statement 2, we know that xy = 0.
Substituting the value of x from statement 1 into the equation xy = 0, we have (y + 2)y = 0.
Expanding, we get y^2 + 2y = 0.
Factoring out y, we have y(y + 2) = 0.
From this equation, we can see that y = 0 or y = -2.
If y = 0, then x = 2, and the absolute difference between the cubes of the integers is 2^3 - 0^3 = 8.
If y = -2, then x = 0, and the absolute difference between the cubes of the integers is 0^3 - (-2)^3 = -8.
Therefore, by combining the information from both statements, we can determine the absolute difference between the cubes of the two integers.
Hence, the correct answer is option C.
This statement alone is not sufficient to determine the absolute difference between the cubes of the two integers. We can demonstrate this by considering two scenarios:
Scenario 1: Let one integer be x and the other be x + 2. In this case, the absolute difference between the cubes would be (x + 2)^3 - x^3, which cannot be simplified further.
Scenario 2: Let one integer be x and the other be x - 2. In this case, the absolute difference between the cubes would be x^3 - (x - 2)^3, which also cannot be simplified further.
Therefore, statement 1 alone is not sufficient.
Statement 2: The square of the sum of the integers is 49 greater than the product of the integers.
Let the two integers be x and y.
The square of the sum of the integers is (x + y)^2.
The product of the integers is xy.
According to the given information, (x + y)^2 = xy + 49.
Expanding (x + y)^2, we have x^2 + 2xy + y^2 = xy + 49.
Rearranging the terms, we get x^2 + y^2 - xy = 49.
This equation can be simplified further using the formula for the sum and product of roots of a quadratic equation:
(x + y)^2 - 3xy = 49.
Since we know that (x + y)^2 = xy + 49, we can substitute this into the equation:
xy + 49 - 3xy = 49.
Simplifying, we have -2xy = 0, which implies xy = 0.
From this, we can conclude that either x or y must be equal to 0.
Combining the statements:
From statement 1, we know that one of the integers is 2 greater than the other integer. Let's assume that x = y + 2.
From statement 2, we know that xy = 0.
Substituting the value of x from statement 1 into the equation xy = 0, we have (y + 2)y = 0.
Expanding, we get y^2 + 2y = 0.
Factoring out y, we have y(y + 2) = 0.
From this equation, we can see that y = 0 or y = -2.
If y = 0, then x = 2, and the absolute difference between the cubes of the integers is 2^3 - 0^3 = 8.
If y = -2, then x = 0, and the absolute difference between the cubes of the integers is 0^3 - (-2)^3 = -8.
Therefore, by combining the information from both statements, we can determine the absolute difference between the cubes of the two integers.
Hence, the correct answer is option C.
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What is the absolute difference between the cubes of two different non-negative integers?(1) One of the integers is 2 greater than the other integer.(2) The square of the sum of the integers is 49 greater than the product of the integers.a)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?
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What is the absolute difference between the cubes of two different non-negative integers?(1) One of the integers is 2 greater than the other integer.(2) The square of the sum of the integers is 49 greater than the product of the integers.a)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 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about What is the absolute difference between the cubes of two different non-negative integers?(1) One of the integers is 2 greater than the other integer.(2) The square of the sum of the integers is 49 greater than the product of the integers.a)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 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the absolute difference between the cubes of two different non-negative integers?(1) One of the integers is 2 greater than the other integer.(2) The square of the sum of the integers is 49 greater than the product of the integers.a)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 absolute difference between the cubes of two different non-negative integers?(1) One of the integers is 2 greater than the other integer.(2) The square of the sum of the integers is 49 greater than the product of the integers.a)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 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about What is the absolute difference between the cubes of two different non-negative integers?(1) One of the integers is 2 greater than the other integer.(2) The square of the sum of the integers is 49 greater than the product of the integers.a)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 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the absolute difference between the cubes of two different non-negative integers?(1) One of the integers is 2 greater than the other integer.(2) The square of the sum of the integers is 49 greater than the product of the integers.a)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?.
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What is the absolute difference between the cubes of two different non-negative integers?(1) One of the integers is 2 greater than the other integer.(2) The square of the sum of the integers is 49 greater than the product of the integers.a)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 absolute difference between the cubes of two different non-negative integers?(1) One of the integers is 2 greater than the other integer.(2) The square of the sum of the integers is 49 greater than the product of the integers.a)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 absolute difference between the cubes of two different non-negative integers?(1) One of the integers is 2 greater than the other integer.(2) The square of the sum of the integers is 49 greater than the product of the integers.a)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
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