what is the value of

[bajwa2307]

what is the value of x^3 - y^3?

1. x^6 - y^6 = 0
2. y=0



if we take option 1. we get x^6=y^6, which gives x=y so that gives x^3 - y^3 = 0

and if we take 2. we get x^3, which is insufficient

according to me, using 1 alone we can answer this question but my guide says that he answer is C, ie the you can get the answer by taking both 1 and 2 together but not from 1 and 2 alone

please explain?

[maihuna]

Using 1 (X^3+y^3)(X^3-y^3) = 0 so x=y or x = -y

Using 2, y=0, if x=y=0 or x=-y=-0=0 both are same so C

[bajwa2307]

Thanks for that Maihuna. My doubt is cleared now

[aleph777]

Another nice way to think about a problem such as this is on a number theory level.

Statement 1 shows us that x^6 - y^6 = 0, and it's trying to trick us into thinking that x and y must, therefore be equal. And they may very well be. If x = 2 and y = 2, then 64 - 64 = 0. And that means that x^3 - y^3 = 0, too. But remember that anything raised to an even exponent, such as 2, 4, or 6, will always be positive, whereas raising an exponent to an odd number reveals the number's 'true' sign. In other words, what if x = 2 and y = -2? You still end up with 64 - 64 = 0 for statement 1, but you get 8 - (-8) = 16 for the original question. Therefore, INSUFFICIENT.

And if you just remember that even exponents hide the sign, and the initial question is asking us for values of cubed exponents, then you don't even need to compute.

Statement 2 tells us nothing about x. Therefore, INSUFFICIENT.

Combined, the two statements tell us x^6 - 0 = 0. Therefore, x^6 = 0. And, thus x = 0, too. Thus, SUFFICIENT. C