Great question!!
If two values are represented by two different variables (e.g., x and y) that doesn't mean those two values cannot be equal.

Cheers,
Brent

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 > 1
Square of a A is greater than A

Since 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

Unless mentioned, nothing can be assumed in GRE. All those assumptions are traps GRE use to test us!!

Explanation

Plug In! If x = 2 and y = 3, then Quantity A is 5 and Quantity B is 25.

Quantity B is greater, so eliminate choices (A) and (C).

Next, make x and y both 0. Both Quantities A and B are now 0, thus, they are equal. Eliminate choice (B), and you’re left with choice (D).

Or you could proceed this way.

If x and y are equal then both quantities are equal. Now see below

Case 1:

In addition of being zero, x+ y can be positive. There are three cases,
1) Positive proper fraction
2)positive improper fraction.
3)Positive integer

if it is positive proper fraction, x+ y is greater, if it is an improper fraction or an integer quantity B will be greater.

Case 2:

x + Y can also be negative. So, we have three cases

1) Negative proper fraction
2) Negative improper fraction
3)Negative integer

In all the cases, quantity B will be larger because its raised to an even exponent.


It could have been a fun question if original question would have stated x not equaly y.

This question is real simple.

for A and B when X and Y are = 0 then both are equal.

and

when when X and Y are equal to 2 then B is greater.

hence we have 2 situation and therefore the relation is uncertain because X and Y can be anything.

AND - D

did these and got D. can we change the "official" answer?

x=0 y=2: x+y = 2, (x+y)^2 = 4
x=2, y=-2: x+y = 0, (x+y)^2 = 0

The official answer is D.

Oh sorry. I didn't click the 'show' button. thanks