jen6 wrote:
So when we plug in numbers it's actually okay to test X and Y using the exact same number such as 1? I've always assumed that we have to use two different numbers to represent X and Y.
Hello jen6,
The question did not mention that x and y are "distinct" numbers. So, it's okay to pick numbers for x and y such that x = y. By picking the easiest cases {x & y = 0 and x &y = 1}, we could easily see that no relationship could be determined. And as long as you get the answer, it's fine. You do not have to show computer what numbers you have checked for
.
Having said that, you have raised a valid question. Should I always substitute same numbers for x and y? It worked well for this question, but what about for other questions? Although number substitution is very useful for easy questions; but for hard questions, you may fall into a thoughtfully designed trap by the test-maker. You may end up consuming a lot of time by picking numbers.
So, what is the alternative?
Always remember that, your solid understanding of concepts, in this case "numbers" is being tested. Developing a solid understanding will give you the confidence in narrowing down to your answer without number picking.
For example, you could look at the question this way:
Qty A is (x + y), let's say some number "A"
Qty B is (x +y)^2, "square of the number "A"
Per our conceptual understanding, we know that
When A = 0 or 1
Square of a A is equal to A
When
A < 0 (i.e. When A is negative)
Square of a A is greater than A (Square of any negative number is always positive, and of course we know "positive" is greater than "negative"
)
When
0 < A < 1 (This is very important to note, as many students miss this point, a trap that ETS love to use!!)
Square of a A is less than A (eg: A = 0.5 ; A^2 = 0.25)
When
A > 1Square of a A is greater than ASince we completely scanned the entire number line, we now do not have to pick any number. We could easily see that there is no fixed relationship that you can determine.
The point that I want to reiterate here is developing a solid conceptual understanding will not only help us answer questions efficiently, but will also help develop an appreciation towards the concepts.
Isn't that a fun way to learn?
Hope this helps