Is x x^2?

Question

Is x > x^2?

(1) x > x^3
(2) x > x^4

Bunuel · Answer

Is x > x^2 --> is x(x-1)<0 ? --> is 0 x^3 --> x*(x^2-1)<0 --> (x+1)*x*(x-1)<0 --> 0 x^4 --> 0

brandy96 · Answer

Hi, can you explain how you came up with this? #1 above? specially the last part. I was solving the other way. x > x^3 can have negative as well as positive. Where as x>x^4 can only happen if 0

KarishmaB · Answer

A couple of things about x, x^2 and x^3: 1. x^2 > x when x > 1 or x < 0. This implies that x^2 < x when 0 < x< 1. At 0 and 1, x^2 = x (The relation is same for every positive even power.) 2. x^3 > x when x > 1 or -1 < x < 0 This implies that x^3 < x when x < -1 or 0 x^3 means either x < -1 or 0 x^2 only when 0 < x< 1 hence statement 1 alone is not sufficient. S2 x > x^4. This is obviously sufficient since the relation is same for every positive even power. Answer (B).

Bunuel · Answer

Check this: x2-4x-94661.html#p731476 or here: inequalities-trick-91482.html

brandy96 · Answer

Thanks, This is great!!!

MYWAY · Answer

to put it in words...

Question is actually whether x is a positive fraction (Simple Eg: 0.1 so that 0.1 > 0.01). So we need to find out if x is positive & if x lies between 0 & 1.

1) would hold good even when x is a negative integer => Not Suff
2) if x is greater than the  even  power of x it can only mean that x is positive and lies between 0 & 1 => Suff

So B.

thesfactor · Answer

Very simple question. Think about this:
Question asks is x>x^2?
so in order for this to be true, x must be a positive fraction.
1) x>x^3
This says that x could be a positive fraction OR a negative integer.
Plug values to check for yourself.
2) x>x^4
This says that x definitely has to be a positive fraction.
Hence B

subhashghosh · Answer

x > x^2 when x is a +ve fraction

(1) x > x^3

not enough as -2 > -8 (-2)^3, or x can be a +ve fraction too

(2) x > x^4 when x is a +ve fraction, so sufficient.

Answer B.

mvictor · Answer

the main question asks: is 0x^3. what if x=-3? then for sure x>x^3, but x is not > than x^2. in this case - the answer is no. we can have x=0.25, thus, x>x^3. and the answer to the question is x>x^2 is yes. since we have 2 outcomes, statement 1 alone is not sufficient. statement 2 tells that x>x^4. now, in this case, we know for sure that x is positive, and 0

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Is x > x^2?

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Is x > x^2?

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