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If x, y and z are non-zero integers
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09 Sep 2018, 01:41
09 Sep 2018, 01:41
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Question Stats:
20% (00:43) correct
79% (00:36) wrong based on 81 sessions
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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) \(yz < x\)
Indicate all such statements.
A) \(\frac{x}{y} > z\)
B) \(\frac{x}{z} > y\)
C) \(\frac{x}{yz} > 1\)
D) \(yz < x\)
Re: If x, y and z are non-zero integers
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09 Sep 2018, 16:05
09 Sep 2018, 16:05
1
Expert Reply
WRONG SOLUTION MY MISTAKE! IGNORE THIS AND SCROLL DOWN
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.
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) \(yz < x\)
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.
Re: If x, y and z are non-zero integers
[#permalink]
09 Sep 2018, 21:13
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) \(yz < x\)
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.
