Bunuel wrote:
LM wrote:
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?