If x + y >0, is x > |y|?
(1) x > y
(2) y < 0
Hi guys!
Let's use some critical reasoning and maybe a bit of picking numbers too. Let's first focus on the question stem and the info in the question stem, trying to make deductions.
The question tells us that the sum of x and y is positive. Therefore, either x or y (or both) is positive; at least one of them must be positive (as punitkaur pointed out). This must be true because if they were both negative, their sum would be negative. The question is asking:
Is x >|y|?
Or Is left side > right side?
Because the right hand side is an absolute value, it must be positive (or zero). Therefore, if the answer to the question is "yes" it would mean x is positive for sure. (Because absolute value is always positive or zero, if x is bigger than the absolute value of something, then x is necessarily positive).
Let's look at statement 2 first: it tells us y is negative; therefore, x must be positive (remember that at least one of them is positive). Furthermore, because their sum is positive, x must be larger than the absolutve value of y. Here, you can pick numbers quickly to confirm this. If x is 8 and y is -5, then their sum is positive. But if x is 5 and y is -8, their sum is negative, which would betray the information given in the question stem. (That is to say, it is impossible for x to be a "small" positive number and y a "large" negative number without violating "x+y>0" given in the question stem). So, the answer to the question is "definitely yes". Statement 2 is sufficient.
For statement 1: x is bigger than y. Remember our deduction that at least one out of x and y is positive. So if x is bigger than y, and at least one is positive, there are two possible cases:
case 1: x is positive and y is negative (ie, one positive and one negative)
This case is the same as statement 2: x must have a larger absolute value than y. (Again, x is positive and y is negative but because their sum is positive x must be bigger than y.) In this case, the answer to the question is "yes" x is bigger than the absolute value of y.
case 2: x is a larger positive number than y, which is also a positive number (ie, both positive)
In this case, x is clearly larger than the absolute value of y, and again the answer to the question is "yes".
Under both possible cases, we get a "yes" answer to the question. Therefore, statement 1 yields a "definitely yes" answer to the question. Statement 1 is sufficient.
Because both statements are independenly sufficient, we should choose D.
