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If (x – a)/(z^2 + 1) > 0, then which of the following must be true?

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Bunuel
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If (x – a)/(z^2 + 1) > 0, then which of the following must be true? [#permalink] New post   23 Jan 2019, 02:42
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If \(\frac{x – a}{z^2 + 1} > 0\), then which of the following must be true?


A x > 0

B x < a

C x > a

D xa > 0

E x + a > 0
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C
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Re: If (x – a)/(z^2 + 1) > 0, then which of the following must be true? [#permalink] New post   27 Jan 2019, 20:26
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Bunuel wrote:
If \(\frac{x – a}{z^2 + 1} > 0\), then which of the following must be true?


A x > 0

B x < a

C x > a

D xa > 0

E x + a > 0


Since (x - a)/(z^2 + 1) > 0, and since z^2 + 1 is always positive, then (x - a) must be positive, and thus x must be greater than a.

Answer: C
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Re: If (x – a)/(z^2 + 1) > 0, then which of the following must be true? [#permalink] New post   23 Jan 2019, 03:08
\(\frac{x–a}{z^2+1} > 0\)
Denominator is > 0
Hence numerator must be > 0
\(x-a > 0\)
\(x > a\)
IMO C
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Re: If (x – a)/(z^2 + 1) > 0, then which of the following must be true? [#permalink] New post   23 Jan 2019, 03:28
If \(\frac{x – a}{z^2 + 1} > 0\), this means both numerator & denominator can be -ive or +ive.

Since there is a square(square is always > 0) in denominator this will mean that automatically the denominator will be > 0

So only C says that x-a > 0

IMO C
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Re: If (x – a)/(z^2 + 1) > 0, then which of the following must be true? [#permalink] New post   23 Jan 2019, 06:13
Bunuel wrote:
If \(\frac{x – a}{z^2 + 1} > 0\), then which of the following must be true?


A x > 0

B x < a

C x > a

D xa > 0

E x + a > 0



\(\frac{x – a}{z^2 + 1} > 0\)

\(z^2 + 1>0\). So, x-a>0.

x-a>0

x>a.

C is the correct answer.
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Re: If (x – a)/(z^2 + 1) > 0, then which of the following must be true? [#permalink] New post   23 Jan 2019, 06:51
Bunuel wrote:
If \(\frac{x – a}{z^2 + 1} > 0\), then which of the following must be true?


A x > 0

B x < a

C x > a

D xa > 0

E x + a > 0



from the given expression it can be said that
x-a would be +ve and x>a
x-a>z+1
nr >dr
out of given options
c stands out
IMO C

x>a would be only valid option
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If (x – a)/(z^2 + 1) > 0, then which of the following must be true? [#permalink] New post   04 Feb 2019, 07:14
\(\frac{x – a}{z^2 + 1} > 0\)

since \(z^2 + 1>0\)

=> x-a>0.

=> x>a.

Option C is correct
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If (x – a)/(z^2 + 1) > 0, then which of the following must be true? [#permalink]
04 Feb 2019, 07:14
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