If x and y are distinct positive integers, what is the value of x^4 - y^4?

(y^2 + x^2)(y + x)(x - y) = 240
x^y = y^x and x > y

A) Statement one ALONE is sufficient, but statement other alone is not sufficient.
B) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
C) EACH statement ALONE is sufficient.
D) Statement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

• Use the formula for a difference of squares (a^2 - b^2) = (a + b)(a - b). However, let x^2 equal a, meaning a^2 = x^4.
  x^4 - y^4 = (x^2 + y^2)(x^2 - y^2)
  Recognize that the expression contains another difference of squares and can be simplified even further.
  (x^2 + y^2)(x^2 – y^2) = (x^2 + y^2)(x – y)(x + y)
  The question can now be simplified to: "If x and y are distinct positive integers, what is the value of (x^2 + y^2)(x – y)(x + y)?" If you can find the value of (x^2 + y^2)(x - y)(x + y) or x^4 - y^4, you have sufficient data.
  Evaluate Statement (1) alone.
  Statement (1) says (y^2 + x^2)(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 x^y = y^x 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 n^2 = 2^n, which is the condition that would be necessary for the equation to hold true.
  Observe that this is true: 4^2 = 2^4 = 16.
  Remember that x > y, so x = 4 and y = 2. Consequently, you know the value of x^4 - y^4 from Statement (2). So, Statement (2) is SUFFICIENT.
  Since Statement (1) alone is SUFFICIENT and Statement (2) alone is SUFFICIENT, answerC is correct.
• 8 years agoHelpfull: Yes(28) No(2)
• Correct answer is 'A'
• 8 years agoHelpfull: Yes(2) No(2)
• it may B
  both are true .
  one alone is sufficient .
  
• 8 years agoHelpfull: Yes(1) No(4)
• B
  4^2 = 2^4 => 16=16(condition satisfy )
  now solving the first equation , we get
  x^4 - y^4 = 240 (put the value of X and Y)
  4^4 - 2^4 = 240
• 7 years agoHelpfull: Yes(1) No(0)
• answer is A
  
• 8 years agoHelpfull: Yes(0) No(4)
• correct answer is A)
  simplification - (x^2+y^2)(x^2-y^2)=240---------------------using identity (a+b)(a-b)=a^2-b^2
  x^4-y^4=240
• 8 years agoHelpfull: Yes(0) No(3)
• (y^2+x^2)(x^2-y^2)=240
  =>((x^2)^2-(y^2)^2)=240
  therefore x^4-y^4=240
• 8 years agoHelpfull: Yes(0) No(3)
• option (A)
• 7 years agoHelpfull: Yes(0) No(1)
• Pritam Sinha i want to ask that untill and unless you dont know which is greater (X>Y or Y>X) then how you can subtract Y from X . IT should be require that which one is greater .So Statement 2 also required...
• 7 years agoHelpfull: Yes(0) No(0)
• Statement 1 alone is sufficient
  and Statement 2 alone is sufficient.
  Ans is option C
• 7 years agoHelpfull: Yes(0) No(0)
• A
  (y^2+x^2)(x^2-y^2)=(x^4-y^4)
• 7 years agoHelpfull: Yes(0) No(0)
• A:
  
  (a+b)(a-b)=a^2-b^2
  use this formula and solve
• 7 years agoHelpfull: Yes(0) No(0)
• its A because only 1 is suffi.
  n if we talk about B statement take an example of x=5,y=3
• 7 years agoHelpfull: Yes(0) No(0)
• answer c is correct
  because when we do hit and trial method on second equation then the equation full fill on x=2 and y=4
  and first equation is expedition of x^4 - y^4
• 7 years agoHelpfull: Yes(0) No(0)