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If x and y are distinct positive integers, what is the value of x4-y4?
1)(y2+ x2)(y + x)(x -y) = 240
2)xy= yx and x > y
1)(y2+ x2)(y + x)(x -y) = 240
2)xy= yx and x > y
- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
- c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- d)EACH statement ALONE is sufficient.
- e)Statement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
If x and y are distinct positive integers, what is the value of x4-y4?...
Before even evaluating the statements, simplify the question. In a more complicated data sufficiency problem, it is likely that some rearranging of the terms will be necessary in order to see the correct answer.
Use the formula for a difference of squares (a2 - b2) = (a + b)(a - b). However, let x2 equal a, meaning a2 = x4.
x4 - y4 = (x2 + y2)(x2 - y2)
Recognize that the expression contains another difference of squares and can be simplified even further.
(x2 + y2)(x2 – y2) = (x2 + y2)(x – y)(x + y)
The question can now be simplified to: "If x and y are distinct positive integers, what is the value of (x2 + y2)(x – y)(x + y)?" If you can find the value of (x2 + y2)(x - y)(x + y) or x4 - y4, you have sufficient data.
Evaluate Statement (1) alone.
Statement (1) says (y2 + x2)(y + x)(x - y) = 240. The information in Statement (1) matches exactly the simplified question. Statement (1) is SUFFICIENT.
Evaluate Statement (2) alone.
Statement (2) says xy = yx and x > y. In other words, the product of multiplying x together y times equals the product of multiplying y together x times.
The differences in the bases must compensate for the fact that y is being multiplied more times than x (since x > y and y is being multiplied x times while x is being multiplied y times).
4 and 2 are the only numbers that work because only 4 and 2 satisfy the equation n2 = 2n, which is the condition that would be necessary for the equation to hold true.
Observe that this is true: 42 = 24 = 16.
Remember that x > y, so x = 4 and y = 2. Consequently, you know the value of x4 - y4 from Statement (2). So, Statement (2) is SUFFICIENT.
Since Statement (1) alone is SUFFICIENT and Statement (2) alone is SUFFICIENT
Use the formula for a difference of squares (a2 - b2) = (a + b)(a - b). However, let x2 equal a, meaning a2 = x4.
x4 - y4 = (x2 + y2)(x2 - y2)
Recognize that the expression contains another difference of squares and can be simplified even further.
(x2 + y2)(x2 – y2) = (x2 + y2)(x – y)(x + y)
The question can now be simplified to: "If x and y are distinct positive integers, what is the value of (x2 + y2)(x – y)(x + y)?" If you can find the value of (x2 + y2)(x - y)(x + y) or x4 - y4, you have sufficient data.
Evaluate Statement (1) alone.
Statement (1) says (y2 + x2)(y + x)(x - y) = 240. The information in Statement (1) matches exactly the simplified question. Statement (1) is SUFFICIENT.
Evaluate Statement (2) alone.
Statement (2) says xy = yx and x > y. In other words, the product of multiplying x together y times equals the product of multiplying y together x times.
The differences in the bases must compensate for the fact that y is being multiplied more times than x (since x > y and y is being multiplied x times while x is being multiplied y times).
4 and 2 are the only numbers that work because only 4 and 2 satisfy the equation n2 = 2n, which is the condition that would be necessary for the equation to hold true.
Observe that this is true: 42 = 24 = 16.
Remember that x > y, so x = 4 and y = 2. Consequently, you know the value of x4 - y4 from Statement (2). So, Statement (2) is SUFFICIENT.
Since Statement (1) alone is SUFFICIENT and Statement (2) alone is SUFFICIENT
Most Upvoted Answer
If x and y are distinct positive integers, what is the value of x4-y4?...
We can use the identity a^4 - b^4 = (a^2 + b^2)(a^2 - b^2) to solve the problem.
From statement 2, we know that xy = yx, which means x = y or xy = 0. Since x and y are distinct positive integers, we can eliminate the possibility of xy = 0 and conclude that x = y.
Using this information in statement 1, we can simplify the equation to:
(x^2 - y^2)(x^2 + y^2)(x - y) = 240
Since x and y are equal, we can substitute x for y:
(x^2 - x^2)(2x^2)(0) = 0
Therefore, x^4 - y^4 = 0.
The answer is 0.
From statement 2, we know that xy = yx, which means x = y or xy = 0. Since x and y are distinct positive integers, we can eliminate the possibility of xy = 0 and conclude that x = y.
Using this information in statement 1, we can simplify the equation to:
(x^2 - y^2)(x^2 + y^2)(x - y) = 240
Since x and y are equal, we can substitute x for y:
(x^2 - x^2)(2x^2)(0) = 0
Therefore, x^4 - y^4 = 0.
The answer is 0.
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Community Answer
If x and y are distinct positive integers, what is the value of x4-y4?...
We can use the identity x^4 - y^4 = (x^2 + y^2)(x^2 - y^2) to solve this problem.
From statement 2, we know that xy = yx, so x and y commute and we can write x^2 - y^2 = (x - y)(x + y). Thus, we have reduced the problem to finding the value of (x^2 + y^2)(x - y)(x + y).
From statement 1, we have (y^2 - x^2)(y - x)(x - y) = -240. Since x and y are distinct positive integers, we know that x - y cannot be 0, so we can divide both sides of the equation by (x - y) to get (y^2 - x^2)(y + x) = -240. We can rewrite this as (x^2 + y^2)(x - y)(x + y) - 2xy(x - y)(x + y) = -240.
Since xy = yx, we can simplify the second term on the left-hand side to get 2xy(x - y)(x + y) = 2x^2y^2 - 2xy^3. Substituting this into the equation above and rearranging, we get (x^2 + y^2)(x - y)(x + y) = 240 - 2x^2y^2 + 2xy^3.
We cannot simplify this expression further without more information about x and y, so the answer is E) insufficient information.
From statement 2, we know that xy = yx, so x and y commute and we can write x^2 - y^2 = (x - y)(x + y). Thus, we have reduced the problem to finding the value of (x^2 + y^2)(x - y)(x + y).
From statement 1, we have (y^2 - x^2)(y - x)(x - y) = -240. Since x and y are distinct positive integers, we know that x - y cannot be 0, so we can divide both sides of the equation by (x - y) to get (y^2 - x^2)(y + x) = -240. We can rewrite this as (x^2 + y^2)(x - y)(x + y) - 2xy(x - y)(x + y) = -240.
Since xy = yx, we can simplify the second term on the left-hand side to get 2xy(x - y)(x + y) = 2x^2y^2 - 2xy^3. Substituting this into the equation above and rearranging, we get (x^2 + y^2)(x - y)(x + y) = 240 - 2x^2y^2 + 2xy^3.
We cannot simplify this expression further without more information about x and y, so the answer is E) insufficient information.
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If x and y are distinct positive integers, what is the value of x4-y4?1)(y2+ x2)(y + x)(x -y) = 2402)xy= yxand x > ya)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, andadditional data are needed.Correct answer is option 'D'. 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 If x and y are distinct positive integers, what is the value of x4-y4?1)(y2+ x2)(y + x)(x -y) = 2402)xy= yxand x > ya)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, andadditional data are needed.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If x and y are distinct positive integers, what is the value of x4-y4?1)(y2+ x2)(y + x)(x -y) = 2402)xy= yxand x > ya)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, andadditional data are needed.Correct answer is option 'D'. Can you explain this answer?.
If x and y are distinct positive integers, what is the value of x4-y4?1)(y2+ x2)(y + x)(x -y) = 2402)xy= yxand x > ya)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, andadditional data are needed.Correct answer is option 'D'. 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 If x and y are distinct positive integers, what is the value of x4-y4?1)(y2+ x2)(y + x)(x -y) = 2402)xy= yxand x > ya)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, andadditional data are needed.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If x and y are distinct positive integers, what is the value of x4-y4?1)(y2+ x2)(y + x)(x -y) = 2402)xy= yxand x > ya)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, andadditional data are needed.Correct answer is option 'D'. Can you explain this answer?.
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If x and y are distinct positive integers, what is the value of x4-y4?1)(y2+ x2)(y + x)(x -y) = 2402)xy= yxand x > ya)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, andadditional data are needed.Correct answer is option 'D'. Can you explain this answer?, a detailed solution for If x and y are distinct positive integers, what is the value of x4-y4?1)(y2+ x2)(y + x)(x -y) = 2402)xy= yxand x > ya)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, andadditional data are needed.Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of If x and y are distinct positive integers, what is the value of x4-y4?1)(y2+ x2)(y + x)(x -y) = 2402)xy= yxand x > ya)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, andadditional data are needed.Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If x and y are distinct positive integers, what is the value of x4-y4?1)(y2+ x2)(y + x)(x -y) = 2402)xy= yxand x > ya)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, andadditional data are needed.Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice GMAT tests.
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