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

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

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

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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]

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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]

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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.

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

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

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27 Jan 2019, 20:26
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.

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

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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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