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If x, y and z are non-zero integers

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If x, y and z are non-zero integers [#permalink] New post 09 Sep 2018, 01:41
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If x, y and z are non-zero integers, and if \(x > yz\), then which of the following statements must be true?

Indicate all such statements.

A) \(\frac{x}{y} > z\)

B) \(\frac{x}{z} > y\)

C) \(\frac{x}{yz} > 1\)

D) \(yz < x\)
[Reveal] Spoiler: OA
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Re: If x, y and z are non-zero integers [#permalink] New post 09 Sep 2018, 16:05
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WRONG SOLUTION MY MISTAKE! IGNORE THIS AND SCROLL DOWN


AchyuthReddy wrote:
If x, y and z are non-zero integers, and if \(x > yz\), then which of the following statements must be true?

Indicate all such statements.

A) \(\frac{x}{y} > z\)

B) \(\frac{x}{z} > y\)

C) \(\frac{x}{yz} > 1\)

d) \(yz < x\)


Since it is mentioned that x, y and z are positive you can divide them without flipping the inequality.

Given: \(x > yz\)

Dividing both sides with y

\(\frac{x}{y} > \frac{yz}{y}\) or \(\frac{x}{y} > z\)... So A is true

Dividing both sides with z

\(\frac{x}{z} > \frac{yz}{z}\) or \(\frac{x}{z} > y\)... So B is true

Dividing both sides with yy

\(\frac{x}{yz} > \frac{yz}{yz}\) or \(\frac{x}{yz} > 1\)... So C is true

Option D cant be true as it is a direct contradiction of the stement given in problem.
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Re: If x, y and z are non-zero integers [#permalink] New post 09 Sep 2018, 21:13
sandy wrote:
AchyuthReddy wrote:
If x, y and z are non-zero integers, and if \(x > yz\), then which of the following statements must be true?

Indicate all such statements.

A) \(\frac{x}{y} > z\)

B) \(\frac{x}{z} > y\)

C) \(\frac{x}{yz} > 1\)

d) \(yz < x\)


Since it is mentioned that x, y and z are positive you can divide them without flipping the inequality.

Given: \(x > yz\)

Dividing both sides with y

\(\frac{x}{y} > \frac{yz}{y}\) or \(\frac{x}{y} > z\)... So A is true

Dividing both sides with z

\(\frac{x}{z} > \frac{yz}{z}\) or \(\frac{x}{z} > y\)... So B is true

Dividing both sides with yy

\(\frac{x}{yz} > \frac{yz}{yz}\) or \(\frac{x}{yz} > 1\)... So C is true

Option D cant be true as it is a direct contradiction of the stement given in problem.


Non-Zero integer means we must exclude only zero so option D is correct

Set of Non-Zero numbers{ ......-3,-2,-1,1,2,3,4....}
This reply is basing on my knowledge if I am wrong please correct me.
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Re: If x, y and z are non-zero integers [#permalink] New post 10 Sep 2018, 08:46
We only know that the integers are non-negative. Hence, we don't know how the sign may change. Only D option is the correct one.

A: If y is negative, then it is false
B: If z is negative, then it is false
C: If x is positive and yz is negative, then it cannot be larger than 1.
Re: If x, y and z are non-zero integers   [#permalink] 10 Sep 2018, 08:46
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