Latest Elitmus Aptitude Question SOLUTION: 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

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.

Correct answer is 'A'

it may B
both are true .
one alone is sufficient .

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

answer is A

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

(y^2+x^2)(x^2-y^2)=240
=>((x^2)^2-(y^2)^2)=240
therefore x^4-y^4=240

option (A)

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...

Statement 1 alone is sufficient
and Statement 2 alone is sufficient.
Ans is option C

A
(y^2+x^2)(x^2-y^2)=(x^4-y^4)

A:

(a+b)(a-b)=a^2-b^2
use this formula and solve

its A because only 1 is suffi.
n if we talk about B statement take an example of x=5,y=3

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