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Is x>1? 1) 1/x<1 2)x>0

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Is x>1? 1) 1/x<1 2)x>0  [#permalink]

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New post 14 Dec 2018, 16:13
2
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

59% (00:57) correct 41% (00:35) wrong based on 59 sessions

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Is \(x>1\)?
1) \(\frac{1}{x}<1\)
2) \(x>0\)
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Re: Is x>1? 1) 1/x<1 2)x>0  [#permalink]

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New post 14 Dec 2018, 21:51
1
1) 1/X<1 -> 1/X could be positive or negative. If 1/X is negative, X is negative. And if 1/X is positive and minus than 1, X is major than 1. So (1) is insufficient.

2) X>0 -> X could be minus or major than 1. So (2) insufficient.

(1)+(2) if x>0, so 1/x>0. Finally 0<1/X<1, then 1/X>1
Both together are sufficient.

Answer (C)

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Re: Is x>1? 1) 1/x<1 2)x>0  [#permalink]

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New post 14 Dec 2018, 22:44
carlosesg92, just to clear up your terminology

x>y
x is greater than y

x<y
x is less than y
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Re: Is x>1? 1) 1/x<1 2)x>0  [#permalink]

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New post 15 Dec 2018, 00:14
1
St:1
1/x < 1
If x positive then yes
If x negative then no.
Not sufficient.

St:2
X >0
X positive greater than 1.. if x=2 then yes
If x is 0.5 then no
Not sufficient.

Combine: x is positive the we can cross multiply
Statement 1.
1/x< 1
1<x sufficient.
C.
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Is x>1? 1) 1/x<1 2)x>0  [#permalink]

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New post 15 Dec 2018, 12:10
The explanations above show statement 2 and the statements together clearly enough.
But for statement 1 both just say 'if positive yes, if negative no', but don't really prove it. Someone please properly explain it.
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Re: Is x>1? 1) 1/x<1 2)x>0  [#permalink]

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New post 15 Dec 2018, 19:36
St:1
If x positive suppose 2,
1/x = 1/2= 0.5 suffice 1/x <1
And x>1 answer yes

If x is negative suppose -2
1/x = -1/2= -0.5 suffice 1/x<1
Ans x <1 answer no

So st 1 not sufficient.
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Re: Is x>1? 1) 1/x<1 2)x>0  [#permalink]

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New post 17 Dec 2018, 12:11
Again, the above is an example, but does not in general prove.
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Is x>1? 1) 1/x<1 2)x>0  [#permalink]

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New post 17 Dec 2018, 12:32
Is x>1?

1) 1/x<1
x can equal -100 or 100, so insufficient
-100 > 1, Not true
100 > 1, True


2) x>0

x can equal .001 or 100,

.001 > 1, Not true
100 > 1, true

Combine, this is where it can get tricky, when you combine both statement, "X" has to be greater than 1, because if test 1 and plug back into statement 1, it reads as

1/1<1 or 1<1, which is not true. As such, when combined x is always > 1, sufficient

Answer D
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Re: Is x>1? 1) 1/x<1 2)x>0  [#permalink]

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New post 17 Dec 2018, 19:59
1
Is x > 1 ?

St 1 : (1/x) < 1

(1/x) - 1 < 0
(1-x)/x < 0
(x-1)/x > 0

x > 1 or x < 0

x > 1 Yes
x < 0 No

Not Sufficient

St 2 : x > 0
x = 2 Yes
x = 0.5 No
Not Sufficient

St 1 + St 2
x > 1
Sufficient
Choice C
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Re: Is x>1? 1) 1/x<1 2)x>0 &nbs [#permalink] 17 Dec 2018, 19:59
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