Is the negative number x less than –1?

Question

(1) 1/x < 1/2
(2) 1/x^2 < 1/2

gmatexam439 · Answer

E

1. stmt 1 will hold true for x=-2 and for x=-0.5
insufficient

2. for x<-2, the given condition holds true
for -2<x<-1, the given condition fails,
for -1<x<0, the condition condition fails
insufficient

1&2 clearly insufficient

varundixitmro2512 · Answer

IMO B

x has to be less than -1from statetment 2

waiting for the OA

sauravleo123 · Answer

Statement 1:
1/x-1/2<0
2-x/2x<0
As x<0
This gives us 
x<2
No new information
Insufficient
Statement 2:
1/x^2-1/2<0
x^2>2
This confirms x<-1
Sufficient
B

sananoor · Answer

For me its B
if 1/x^2 < 1/2 then we can write this as 
x^2 > 2...and it is only possible when x is > 1 and as we are given that x is negative this means x is negative number greater than 1

jedit · Answer

IMO its B -

1-  1/x < 1/2 
 2/x < 1 
 x < 2  -- we flip signs because we know X is negative and we're taking negative to the other side, or so I think we should do.

2-  1/x^2 < 1/2

flipping sides, sign remains the same since we're dealing with  x^2

x^2 > 2  taking under root, we will be flipping the sign since we know x is negative.
 x < 1.41  - Not sufficient.

Combining both, we know x < 2 and and less than 1.41 but its still not sufficient to determine if X is less than -1. Answer should be E IMO. I may be making a dumb mistake so would love it if someone can correct me.

gmatexam439 · Answer

I understand it should be "B" and not "E".

andreagonzalez2k · Answer

1- 1/x < 1/2
Using -1/2 and -3/2 both satisfy the inequality, so insufficient.

2- 1/x^2 < 1/2
x^2 > 2 -> |x| > sqrt(2) -> x > sqrt(2) or x < -sqrt(2)
As we know also that x is negative, sufficient.

Answer: B

Is the negative number x less than –1?

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