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Is 2-x<√(4-x^2)? 1) x^2<4 2) x>0

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Is 2-x<√(4-x^2)? 1) x^2<4 2) x>0  [#permalink]

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New post 01 Apr 2019, 09:18
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

19% (02:09) correct 81% (01:56) wrong based on 26 sessions

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Is \(2-x<√(4-x^2)?\)
1) \(x^2<4\)
2) \(x>0\)

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Is 2-x<√(4-x^2)? 1) x^2<4 2) x>0  [#permalink]

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New post 01 Apr 2019, 10:00
Working on question stem:
1) after squaring both sides we get (2-x)(2-x)<(2-x)(2+x)
2) after subtrackting we get: (2-x)(2-x)-(2-x)(2+x)<0
3) after factoring out 2-x we get: (2-x)(2-x-(2+x))<0
4) after simplification we get: 2\(x^2\)-4x<0
5) working further: x=0; x=2
6) range: 0<x<2

1 stm: -2<x<2 not sufficient
2 stm: x>0 not suff

Both statements: 0<x<2 sufficient

IMO
Ans: C
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Re: Is 2-x<√(4-x^2)? 1) x^2<4 2) x>0  [#permalink]

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New post 07 Apr 2019, 05:57
AsadAbu wrote:
Is \(2-x<√(4-x^2)?\)
1) \(x^2<4\)
2) \(x>0\)



IMO, ans should be C.

Considering only statement 2 (as per the OA), if \(x=3\), then
\(2-3<\sqrt{4-9}\)
Here comes the concept of complex number which is not valid for GMAT.

Hence, OA should C (\(0<x<2\))
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Re: Is 2-x<√(4-x^2)? 1) x^2<4 2) x>0  [#permalink]

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New post 07 Apr 2019, 06:09
B is not correct .

for x = 1 , it is true

but for x= 2 , it is false

0<0 not possible


but when we combine both,

we eliminat2 and we restrict the values between -2 and 2


So It should be C

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Is 2-x<√(4-x^2)? 1) x^2<4 2) x>0  [#permalink]

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New post 07 Apr 2019, 09:03
What I feel is... In Statement B ,X can take Values between 0 and 2..
0<X<2...

Here's why..

Look at RHS... Sqrt (4-x^2)
Now we all know that GMAT doesn't want us to take Sqrt of a negative value...

If i take X = 1
2-1 = 1 (LHS)
Sqrt (4-x^2) = 1.73
RHS > LHS , a definite yes

Let's take X = 1.5

2-1.5 = 0.5
Sqrt (4-x^2) = 1.33

RHS>LHS , again a definite yes..

Now the reason why I'm not willing to consider X = 2 is because I believe GMAT considers square root of positive numbers... Taking X= 2 will make RHS 0 And zero is neither negative nor positive..

I don't know whether my reasoning is right or wrong. . experts?? Might need your help ..

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Is 2-x<√(4-x^2)? 1) x^2<4 2) x>0   [#permalink] 07 Apr 2019, 09:03
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