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TAGS: Retired Moderator Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 175

Kudos [?]: 3029  , given: 394

x > 0 > y [#permalink]
1
KUDOS
Expert's post 00:00

Question Stats: 61% (01:01) correct 38% (00:53) wrong based on 110 sessions
$$x > 0 > y$$

 Quantity A Quantity B $$x - y$$ $$(x + y)^{2}$$

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

_________________

Sandy
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GRE Instructor Joined: 10 Apr 2015
Posts: 3905
Followers: 163

Kudos [?]: 4760 , given: 70

Re: x > 0 > y [#permalink]
Expert's post
sandy wrote:
$$x > 0 > y$$

 Quantity A Quantity B $$x - y$$ $$(x + y)^{2}$$

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

I can't think of any useful algebraic manipulations that will help me, so let's test some possible cases...

ASIDE: The given information tells us that x is POSITIVE and y is NEGATIVE

Case 1: x = 1 and y = -1
We get:
QUANTITY A: x - y = 1 - (-1) = 2
QUANTITY B: (x + y)² = (1 + -1)² = 0² = 0
In this case, Quantity A is greater

Case 2: x = 10 and y = -1
We get:
QUANTITY A: x - y = 10 - (-1) = 11
QUANTITY B: (x + y)² = (10 + -1)² = 9² = 81
In this case, Quantity B is greater

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com Manager Joined: 29 Nov 2017
Posts: 190
Location: United States
GRE 1: Q142 V146 WE: Information Technology (Computer Software)
Followers: 1

Kudos [?]: 94 , given: 99

Re: x > 0 > y [#permalink]
GreenlightTestPrep wrote:
sandy wrote:
$$x > 0 > y$$

 Quantity A Quantity B $$x - y$$ $$(x + y)^{2}$$

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

I can't think of any useful algebraic manipulations that will help me, so let's test some possible cases...

ASIDE: The given information tells us that x is POSITIVE and y is NEGATIVE

Case 1: x = 1 and y = -1
We get:
QUANTITY A: x - y = 1 - (-1) = 2
QUANTITY B: (x + y)² = (1 + -1)² = 0² = 0
In this case, Quantity A is greater

Case 2: x = 10 and y = -1
We get:
QUANTITY A: x - y = 10 - (-1) = 11
QUANTITY B: (x + y)² = (10 + -1)² = 9² = 81
In this case, Quantity B is greater

Cheers,
Brent

I expanded option B and equated to A(LHS) and the LHS went 0 and then the whole equation stopped making sense and chooce D.

I am wondering why did you not expanded x+y whole square equation? GRE Instructor Joined: 10 Apr 2015
Posts: 3905
Followers: 163

Kudos [?]: 4760  , given: 70

Re: x > 0 > y [#permalink]
1
KUDOS
Expert's post
[/quote]

I expanded option B and equated to A(LHS) and the LHS went 0 and then the whole equation stopped making sense and chooce D.

I am wondering why did you not expanded x+y whole square equation?[/quote]

Let's see what happens if we expand

Given:
QUANTITY A: x - y
QUANTITY B: (x + y)²

Expand Quantity B to get:
QUANTITY A: x - y
QUANTITY B: x² + 2xy + y²

Now what can we do?

Whatever we do from here seems more likely to make matters more confusing.
For example, we COULD add y to both quantities to get:
QUANTITY A: x
QUANTITY B: x² + 2xy + y + y²
This doesn't help.

What if we subtract x from both quantities? We get:
QUANTITY A: 0
QUANTITY B: x² + 2xy + y - x + y²
Yikes!!

At this point, we should probably start considering a different approach.

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com Intern Joined: 21 Mar 2019
Posts: 10
Followers: 0

Kudos [?]: 12 , given: 11

Re: x > 0 > y [#permalink]
The statement say: y < 0 < x

I will pick two numbers and test:

Case 1: x=10, y=-3

Quantity A
x-y =
10-(-3)=
13

Quantity B
(x+y)^2=
(10-3)^2
49

Therefore, B > A

Case 2: x=1/4, y=-1/2

Quantity A
x-y =
1/4 - (-1/2)=
3/4

Quantity B
(x+y)^2=
(1/4-1/2)^2
1/4

Therefore, A > B

_________________

Diana

If you found this post useful, please let me know by pressing the Kudos Button Re: x > 0 > y   [#permalink] 25 Mar 2019, 18:17
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