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LM
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If x and y are integers such that x<0<y, and z is non 24 Jan 2012, 09:49
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64% (01:22) correct 36% (01:14) wrong based on 484 sessions

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If x and y are integers such that x<0<y, and z is non negative integer then which of the following must be true?

A. \(x^2<y^2\)

B. \(x+y=0\)

C. \(xz<yz\)

D. \(xz=yz\)

E. \(\frac{x}{y}<z\)
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E
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Bunuel
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If x and y are integers such that x<0<y, and z is non 24 Jan 2012, 09:59
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LM
If x and y are integers such that \(x<0<y\),and z is non negative integer then which of the following must be true?

A) \(x^2<y^2\)

B) \(x+y=0\)

C) \(xz<yz\)

D)\(xz=yz\)

E) \(\frac{x}{y}<z\)
Show more

Note that we are asked "which of the following MUST be true, not COULD be true. For such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer.

Given: \(x<0<y\) and \({0}\leq{z}\).

Evaluate each option:

A. \(x^2<y^2\) --> not necessarily true, for example: \(x=-2\) and \(y=1\);

B. \(x+y=0\) --> not necessarily true, for example: \(x=-2\) and \(y=1\);

C. \(xz<yz\) --> not necessarily true, if \(z=0\) then \(xz=yz=0\);

D. \(xz=yz\) --> not necessarily true, it's true only for \(z=0\);

E. \(\frac{x}{y}<z\) --> as \(x<0<y\) then \(\frac{x}{y}=\frac{negative}{positive}=negative<0\) and as \({0}\leq{z}\) then \(\frac{x}{y}<0\leq{z}\) --> always true.

Answer: E.
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If x and y are integers such that x<0<y, and z is non 22 May 2012, 01:19
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If x and y are integers such that \(x<0<y\),and z is non negative integer then which of the following must be true?

A) \(x^2<y^2\)

B) \(x+y=0\)

C) \(xz<yz\)

D)\(xz=yz\)

E) \(\frac{x}{y}<z\)

Note that we are asked "which of the following MUST be true, not COULD be true. For such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer.

Given: \(x<0<y\) and \({0}\leq{z}\).

Evaluate each option:
A) \(x^2<y^2\) --> not necessarily true, for example: \(x=-2\) and \(y=1\);

B) \(x+y=0\) --> not necessarily true, for example: \(x=-2\) and \(y=1\);

C) \(xz<yz\) --> not necessarily true, if \(z=0\) then \(xy=yz=0\);

D)\(xz=yz\) --> not necessarily true, it's true only for \(z=0\);

E) \(\frac{x}{y}<z\) --> as \(x<0<y\) then \(\frac{x}{y}=\frac{negative}{positive}=negative<0\) and as \({0}\leq{z}\) then \(\frac{x}{y}<0\leq{z}\) --> always true.

Answer: E.
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amazing ! couldn't figure out how option 3 was not necessarily true , forgot that non negative could mean that 0 is possible ,folks : non negative does not mean only positive integers , it could be 0 as well

Hypothetically speaking, Bunuel so if a question says, non positive numbers can we consider 0 as well , rather than only negative numbers.

Set of Non positive numbers { 0,-1,-5,-9 }
Set of Non negative numbers { 0,1, 4, 7, }

is this correct?
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If x and y are integers such that x<0<y, and z is non 22 May 2012, 01:23
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Bunuel
LM
If x and y are integers such that \(x<0<y\),and z is non negative integer then which of the following must be true?

A) \(x^2<y^2\)

B) \(x+y=0\)

C) \(xz<yz\)

D)\(xz=yz\)

E) \(\frac{x}{y}<z\)

Note that we are asked "which of the following MUST be true, not COULD be true. For such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer.

Given: \(x<0<y\) and \({0}\leq{z}\).

Evaluate each option:
A) \(x^2<y^2\) --> not necessarily true, for example: \(x=-2\) and \(y=1\);

B) \(x+y=0\) --> not necessarily true, for example: \(x=-2\) and \(y=1\);

C) \(xz<yz\) --> not necessarily true, if \(z=0\) then \(xy=yz=0\);

D)\(xz=yz\) --> not necessarily true, it's true only for \(z=0\);

E) \(\frac{x}{y}<z\) --> as \(x<0<y\) then \(\frac{x}{y}=\frac{negative}{positive}=negative<0\) and as \({0}\leq{z}\) then \(\frac{x}{y}<0\leq{z}\) --> always true.

Answer: E.


amazing ! couldn't figure out how option 3 was not necessarily true , forgot that non negative could mean that 0 is possible ,folks : non negative does not mean only positive integers , it could be 0 as well

Hypothetically speaking, Bunuel so if a question says, non positive numbers can we consider 0 as well , rather than only negative numbers.

Set of Non positive numbers { 0,-1,-5,-9 }
Set of Non negative numbers { 0,1, 4, 7, }

is this correct?
Show more

Yes, a set of non-positive numbers consists of zero and negative numbers.
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If x and y are integers such that x<0<y, and z is non 24 May 2012, 02:08
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Bunuel

Yes, a set of non-positive numbers consists of zero and negative numbers.
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Isn't that one of the first few things one gets to learn when trying to read the number system. Thank you bunnel for reminding everyone about it :)
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If x and y are integers such that x<0<y, and z is non 25 May 2012, 22:34
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So 0 "Zero" is even
and can be part of both a NON Postive set and a NON negative set
Set of Non positive numbers { 0,-1,-5,-9 }
Set of Non negative numbers { 0,1, 4, 7, }
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If x and y are integers such that x<0<y, and z is non 14 Sep 2016, 07:09
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what a nice trap here!!!
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If x and y are integers such that x<0<y, and z is non 13 Mar 2024, 07:53
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