jabhatta@umail.iu.edu wrote:
If x and y are integers, and x + y < 0, is x — y > 0?
1) |x| + |y| > |x|
2) x^y = 1
The OA solution suggested testing cases ....Any suggestions on doing this via logic or critical thinking ?
You can imagine the numbers on the number line to solve it.
x and y are integers.
x + y < 0 implies at least one of x and y is negative and if there is one negative number and one positive, the negative one has higher absolute value. I imagine them placed on the number line.
Question: Is x - y > 0
This just means: "Is x to the right of y on the number line?"
1) |x| + |y| > |x|
If absolute value of the two is greater than the absolute value of x alone, it just means that y is not 0.
Not sufficient
2) x^y = 1
This can be done in 2 main ways: Either make y = 0 or make x = 1 (with y as any integer) / -1 (with y even)
If y is 0, x must be negative and answer would be "No"
If x = 1, y must be negative and answer would be "Yes"
Not sufficient
Using both statements, x = 1 (with y as any integer) / -1 (with y even)
If x is 1, answer is "Yes"
If x = -1, y is even. So y is one of -2, -4, -6 etc in which case answer is "Yes". y cannot be positive because the negative value must have higher absolute value.
Sufficient
Answer (C)
on the first highlight in red -- any reason why the following cases were not considered
Case 1, Scenario 1 when both variables are negative) |Y| > |x|
Case 1, Scenario 2 when both variables are negative) |x| > |Y|
Case 2, Scenario 2 y = 0 and X is negative