kabilank87 wrote:
Is x < y ?
(1) 2x < 3y
(2) xy > 0
Statement 1:
In this type of question, I test whether the variables have any ability to change the inequality sign.
How i test:
(a) Take a same positive integer for both variables.
[*]If the inequality holds true (normal case), the variables have no ability to change the inequality sign [all credit goes the given constants]
in that situation, three scenarios are possible. (i) both variables are equal, (ii) first variable is greater than second variable, (iii) second variable is greater than first variable
[*]If the inequality does not hold true (abnormal case), the variables are playing the main role to change the inequality sign [ the given constants have no ability to change the inequality sign]. in that situation, only a fixed role is possible [either first variable is greater than second variable or second variable is greater than first variable] as stated in the inequality.
(b) Take a same negative integer for both variables.
[*]If the inequality holds true (normal case), the variables have no ability to change the inequality sign [all credit goes the given constants]
in that situation, three scenarios are possible. (i) both variables are equal, (ii) first variable is greater than second variable, (iii) second variable is greater than first variable
[*]If the inequality does not hold true (abnormal case), the variables are playing the main role to change the inequality sign [ the given constants have no ability to change the inequality sign]. in that situation, only a fixed role is possible [either first variable is greater than second variable or second variable is greater than first variable] as stated in the inequality.
back to the main question: Take a same positive integer [2] for both variables.
4<6. Here, the inequality holds true (normal case). i.e. the variables have no ability to change the inequality sign [all credit goes the given constants]
in that situation, three scenarios are possible. (i) both variables are equal [x=y], (ii) first variable is greater than second variable (x>y), (iii) second variable is greater than first variable (x<Y).
So statement 1 is insufficient. However, if you take a same negative integer [-2] for both variables, [-4<-6] the inequality would not hold true (abnormal case), i.e. the variables are playing the main role to change the inequality sign [ the given constants have no ability to change the inequality sign]. in that situation, only a fixed role is possible [either first variable is greater than second variable or second variable is greater than first variable] as stated in the inequality [x<y].
Statement 2: xy>0. in other words x and y are both positive or both negative. i.e. (2,3) or (3,2) or (-2,-3) or (-3,-2).
Thus,
So statement 2 is insufficient. Combining: if x and y are positives, three scenarios are possible. (i) both variables are equal [x=y], (ii) first variable is greater than second variable (x>y), (iii) second variable is greater than first variable (x<Y).
So, C is cancelled out. answer E. However, if x and y are negatives, x<y.
Since statement 2 says both positive and both negatives are possible to exist. C is cancelled out.