GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 22 Oct 2019, 07:27

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Is xy < x^2*y^2? (1) xy > 0 (2) x + y = 1

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Manager
Manager
avatar
P
Joined: 28 May 2018
Posts: 144
Location: India
Schools: ISB '21 (II)
GMAT 1: 640 Q45 V35
GMAT 2: 670 Q45 V37
GMAT 3: 730 Q50 V40
CAT Tests
Is xy < x^2*y^2? (1) xy > 0 (2) x + y = 1  [#permalink]

Show Tags

New post 19 Oct 2018, 09:42
2
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

52% (01:38) correct 48% (01:46) wrong based on 61 sessions

HideShow timer Statistics

Is \(xy < x^2y^2\)?

(1) xy > 0
(2) x + y = 1

_________________
Please award KUDOS if my post helps. Thank you.
Director
Director
avatar
G
Joined: 19 Oct 2013
Posts: 516
Location: Kuwait
GPA: 3.2
WE: Engineering (Real Estate)
GMAT ToolKit User
Re: Is xy < x^2*y^2? (1) xy > 0 (2) x + y = 1  [#permalink]

Show Tags

New post 19 Oct 2018, 14:19
PriyankaPalit7 wrote:
Is \(xy < x^2y^2\)?

1) xy>0
2) x+y=1


X and Y are of the same sign.

If x = 2 and y = 2

Then 4 < 16 yes

If x = 1/2 and y = 1/2

1/4 < 1/16 no.

Insufficient.

Eliminate A/D

Statement 2)

If x = -1

Y= 1
Then the statement -1 < 1 yes

If x = 1/2 and y = 1/2

Then the answer is xy < x^2 y^2 is no

Combined it is sufficient.

1/4 < 1/16 no.

Posted from my mobile device
Director
Director
User avatar
S
Status: Come! Fall in Love with Learning!
Joined: 05 Jan 2017
Posts: 531
Location: India
Re: Is xy < x^2*y^2? (1) xy > 0 (2) x + y = 1  [#permalink]

Show Tags

New post 19 Oct 2018, 23:16
Hi,

Slightly tricky question.

We can solve this using either Plugging in values for x and y OR we can do the mathematical approach.

Let’s see the mathematical approach.

Question:

Is x * y < x^2 * y^ 2 ?

Let’s simplify the question a bit.

Is 0 < x^2 * y^ 2 - x * y?

Is 0 < x * y (x * y - 1)?

If M = x * y, then

Is 0 < M * (M - 1)?

Answer to the question would be YES if M < 0 or M > 1 i.e., “x” and “y” have alternate signs OR “x” and “y” both positive or both negative and their product greater than 1.

Answer to the question would be NO if 0 < M < 1 i.e., “x” and “y” both positive or both negative and their product less then 1.

Statement I is insufficient:

x*y >0

i.e., M > 0

Answer to the question, would be YES or NO.

If M = 1/4

i.e., let’s say X = ½ and Y = ½, then answer to the question would be NO.

If M = 2

i.e., let’s say X = 2 and Y = 1, then answer to the question would be YES.

So not sufficient.

Statement II is insufficient:

x+y=1

If M = 1/4

let’s say X = ½ and Y = ½, then answer to the question would be NO.

If M = -2

i.e., let’s say X = 2 and Y = -1, then answer to the question would be YES.

So not sufficient.

Together it is sufficient.

x*y > 0

and x+y = 1

Only way we could achieve this is,

x and y has to lie between 0 and 1.

i.e., M has to be between 0 and 1. So answer to the question would be NO.

So together it is sufficient.

Answer is C.

Hope it is clear.
_________________
GMAT Mentors
Image
Intern
Intern
avatar
B
Joined: 10 Feb 2017
Posts: 47
Location: India
Schools: Rotman '20
GMAT 1: 710 Q49 V37
GPA: 4
GMAT ToolKit User Reviews Badge CAT Tests
Is xy < x^2*y^2? (1) xy > 0 (2) x + y = 1  [#permalink]

Show Tags

New post 03 Jun 2019, 23:02
PriyankaPalit7 wrote:
Is \(xy < x^2y^2\)?

(1) xy > 0
(2) x + y = 1



Always we should use our basic inference from a qn stem.

qn is asking whether xy and (1-xy) are of opposite sign?
or the range of xy?
so as per modified qn stem in mind
option 1 says only one sided limit of xy
option 2 says the sum of x and y,however we need the range of xy,so again dillema in deriving the actual conclusion.
lets combine the upper limiting value can be judged from the 2nd statement,how? whether it is -19+20,or 0.5+0.5 ,the multiplication will result a value that is always <1
so the qn that whether xy(1-xy) is less than 0 will pop up in your mind as yes
because xy>0 and (1-xy) is positive (from 2nd statement) and the result is confirmed NO.
so OA-C
Manhattan Prep Instructor
User avatar
G
Joined: 04 Dec 2015
Posts: 832
GMAT 1: 790 Q51 V49
GRE 1: Q170 V170
Re: Is xy < x^2*y^2? (1) xy > 0 (2) x + y = 1  [#permalink]

Show Tags

New post 04 Jun 2019, 10:35
PriyankaPalit7 wrote:
Is \(xy < x^2y^2\)?

(1) xy > 0
(2) x + y = 1


I enjoyed this problem! It tests a lot of different Data Sufficiency skills in ways that aren't obvious at first.

First of all, understand the question stem.

There are a few different ways to handle the question stem, here. You could try to simplify it with math, but there's a trick. You can't just divide both sides by xy, because you don't know whether xy is positive or negative. If it's positive, you wouldn't have to flip the inequality sign. If it's negative, you would have to flip it. Since you don't know either way, you aren't allowed to do that division.

Instead, in this situation, try subtracting a term from both sides:

Is \(xy < x^2y^2\)?

Is \(0 < x^2y^2 - xy\)?

Is \(xy(xy-1) > 0\)?

OR, you can use a "decoding" kind of approach, and try to figure out what the question was asking you in plain English. When is xy less than (xy)^2? Well, if xy is negative, the answer would definitely be "yes". Also, if xy is a large positive number, the answer would be "yes" as well, because large positive numbers get bigger when you square them. In fact, the only situation where the answer would be "no" is if xy is between 0 and 1, inclusive. So the question is really asking, "is xy between 0 and 1?"

Now, approach the statements.

Statement 1: First, suppose that you used the math approach. You now know that xy is positive, so try plugging in some positive values for xy.

If xy = 0.5, then xy(xy-1) = 0.5(0.5-1) = -0.25, which is NOT greater than 0.
If xy = 100, then xy(xy-1) = 100(99) = 9900, which IS greater than 0.

So, the statement is insufficient.

Or, suppose that you used the "decoding" approach to the question. This statement tells you that xy is positive, but it doesn't tell you whether it's between 0 and 1, so it's not sufficient.

Statement 2: Similarly, suppose that you used the math approach. You know that x + y = 1. Try some values.

x = 0, y = 1: xy(xy-1) = 0(0-1) = 0, which is NOT greater than 0.
x = 0.5, y = 0.5: xy(xy-1) = 0.25(-0.75), which is NOT greater than 0.
x = 100, y = -99: xy(xy-1) = -9900(-9901), which IS greater than 0.

Or, suppose that you "decoded". Could xy be between 0 and 1? Yes, because x and y could both be decimals between 0 and 1. Or, xy could be negative, for instance if x is negative and y is positive. So, the answer could be yes or no, and the statement is insufficient.

Statements 1 and 2 together:

Things get a little simpler at this point! x and y can't both be negative, because then they can't sum to 1. So, x and y have to both be positive. They also have to be between 0 and 1, because their sum needs to be 1. So the answer to the question is "yes" and the statements are sufficient together.
_________________
Image

Chelsey Cooley | Manhattan Prep | Seattle and Online

My latest GMAT blog posts | Suggestions for blog articles are always welcome!
GMAT Club Bot
Re: Is xy < x^2*y^2? (1) xy > 0 (2) x + y = 1   [#permalink] 04 Jun 2019, 10:35
Display posts from previous: Sort by

Is xy < x^2*y^2? (1) xy > 0 (2) x + y = 1

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne