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# compare (x+y) and (x+y)^2

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Retired Moderator
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compare (x+y) and (x+y)^2 [#permalink]  02 Jul 2017, 15:37
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Question Stats:

81% (00:19) correct 18% (00:30) wrong based on 98 sessions
 Quantity A Quantity B $$(x+y)$$ $$(x+y)^2$$

A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.

Drill 1
Question: 4
Page: 352
[Reveal] Spoiler: OA

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Sandy
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Re: compare (x+y) and (x+y)^2 [#permalink]  03 Jul 2017, 08:20
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Expert's post
sandy wrote:
 Quantity A Quantity B $$(x+y)$$ $$(x+y)^2$$

A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.

Drill 1
Question: 4
Page: 352

Test some values

Case 1: x = 0 and y = 0
We get:
Quantity A: 0 + 0
Quantity B: (0 + 0)²

Evaluate:
Quantity A: 0
Quantity B: 0
The two quantities are EQUAL

Case 1: x = 1 and y = 1
We get:
Quantity A: 1 + 1
Quantity B: (1 + 1)²

Evaluate:
Quantity A: 2
Quantity B: 4
Quantities B is GREATER

[Reveal] Spoiler:
D

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Re: compare (x+y) and (x+y)^2 [#permalink]  18 Apr 2018, 17:05
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.
GRE Instructor
Joined: 10 Apr 2015
Posts: 3838
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Kudos [?]: 4499 [1] , given: 69

Re: compare (x+y) and (x+y)^2 [#permalink]  18 Apr 2018, 19:03
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Expert's post
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.

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
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Re: compare (x+y) and (x+y)^2 [#permalink]  18 Apr 2018, 19:16
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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 :D.

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
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Re: compare (x+y) and (x+y)^2 [#permalink]  19 Apr 2018, 04:59
1
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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.

Unless mentioned, nothing can be assumed in GRE. All those assumptions are traps GRE use to test us!!
Retired Moderator
Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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Kudos [?]: 2926 [0], given: 394

Re: compare (x+y) and (x+y)^2 [#permalink]  22 Apr 2018, 14:08
Expert's post
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).
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Re: compare (x+y) and (x+y)^2 [#permalink]  01 May 2018, 06:41
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.
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Re: compare (x+y) and (x+y)^2 [#permalink]  16 May 2018, 01:39
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
Re: compare (x+y) and (x+y)^2   [#permalink] 16 May 2018, 01:39
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