If x

Question

If x < 0 , which of the following is NOT necessarily true? (A) x^2 + x^3 < 0 (B) x^5 < x^2 (C) x^2 > 0 (D) 1/x < 0 (E) 1/x^2 > 0

dave13 · Accepted Answer

let x = - 1

(A) 1 + (-1) < 0 NOT necessarily true (B) -1 < 1 TRUE (C) 1 > 0 TRUE (D) 1/-1 < 0 TRUE (E) 1/1 > 0 TRUE IMO: A

u1983 · Answer

When  x=-1 ,  x^2 = 1  &  x^3 = -1  Thus  x^2 + x^3 =   1+(-1) = 0  !<0
All other options are always true.... Thus  ans A

KSBGC · Answer

x^2  will always be positive. Thus, eliminate options B, C, E.

x is negative thus  \frac{1}{x}  will yield a negative result. Cancel D.

Only option we left with is A .

This is our answer.

Farina · Answer

D- 1/x will also yield a negative result so why its not true? Am I missing something?

Bunuel · Answer

The question asks: If  x < 0 , which of the following is  NOT  necessarily true?

So, all options but one are ALWAYS true and we should find that one, which is NOT always true.

Farina · Answer

Yeah so I was missing something. Thank you Bunuel for your help as usual

aa1090 · Answer

Take values 
As, x<0 ; let x=-1
Now, option A -> 1-1= 0 and not greater than 0 
Check other options, they are true.

So, option A.

IanStewart · Answer

Another way to do this: in option A, we can divide both by sides by x^2 without worrying about whether to reverse the inequality, because x^2 cannot be negative. Then A becomes 1 + x < 0, or x < -1. If we know x < 0, we can't be sure x < -1 (maybe x = -1/2), so A does not need to be true.

kungfury42 · Answer

(B) x^2 is always positive, while x^5 is negative for x<0 , therefore, x^2>x^5 is correct (C) As discussed above, x^2 is always positive, therefore x^2>0 is correct (D) Since x<0 , therefore 1/x will also be < 0 , correct (E) As discussed in B, if x^2>0 then 1/x^2 will also be > 0 , correct Hence, we arrive at A by POE.

ThatDudeKnows · Answer

A) A bunch of ways to show this isn't necessarily true, but even if you can't spot any of those, process of elimination on the other answer choices is pretty easy. B) - < + Always true. Eliminate. C) + > 0 Always true. Eliminate. D) - < 0 Always true. Eliminate. E) + > 0 Always true. Eliminate. Answer choice A.

bumpbot · Answer

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If x < 0, which of the following is NOT necessarily true?

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