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

 It is currently 20 Oct 2019, 04:26 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

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.  If xy > 0 and both x and y are even numbers, is x > y?

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

Hide Tags

Math Expert V
Joined: 02 Aug 2009
Posts: 7987
If xy > 0 and both x and y are even numbers, is x > y?  [#permalink]

Show Tags

12 00:00

Difficulty:   95% (hard)

Question Stats: 42% (02:29) correct 58% (02:30) wrong based on 204 sessions

HideShow timer Statistics

If xy > 0 and both x and y are even numbers, is x > y?

(1) x > y - 2
(2) |x - y| > 4

New question!!!..

_________________
Math Expert V
Joined: 02 Aug 2009
Posts: 7987
If xy > 0 and both x and y are even numbers, is x > y?  [#permalink]

Show Tags

chetan2u wrote:
If xy>0 and both x and y are even numbers, is x>y?
(I) x>y-2
(II) |x-y|>4

New question!!!..

OE to follow..

xy>0.....
x and y are even...

1) x>y-2
x+2>y
So y <x in all cases except when x=y..
Example say x=6, y<x+2 or y<6+2 that is y<8 but y cannot be 7 as y is even,
so (I) y will be 6 or x=y OR
(II) y can be 4,2 etc or X>y
Insufficient

2) |x-y|>4
We cannot say if y>x or x>y but surely $$x\neq{y}$$
Insufficient

Combined..
We know from statement I that either x=y or X>y
But statement II tells us that $$x\neq{y}$$
So only possibility x>y
Sufficient

C
_________________
Intern  G
Joined: 18 Nov 2013
Posts: 46
Re: If xy > 0 and both x and y are even numbers, is x > y?  [#permalink]

Show Tags

chetan2u wrote:
If xy>0 and both x and y are even numbers, is x>y?
(I) x>y-2
(II) |x-y|>4

New question!!!..

The answer is C . since xy>0; here is my list of values

from statement 1:
x=-2; y= -8
x=4; y =4

statement 1 is insufficient

from statement 2:
x=-2; y=-8
x=-8; y=-2
x=2; y=8
x=8; y=2

statement 2 is insufficient

combining both makes it sufficient. C
Intern  B
Joined: 23 Feb 2012
Posts: 42
Re: If xy > 0 and both x and y are even numbers, is x > y?  [#permalink]

Show Tags

Xy>0 means either x ND y r both -ve or both are positive.
1) not sufficient.as x can be bigger/smaller than y or equal
2) sufficient: x-y >4 or y-x <- 4; for both +ve ND -ve x> y

Sent from my Redmi 5 Plus using GMAT Club Forum mobile app
Math Expert V
Joined: 02 Aug 2009
Posts: 7987
Re: If xy > 0 and both x and y are even numbers, is x > y?  [#permalink]

Show Tags

deepverma wrote:
Xy>0 means either x ND y r both -ve or both are positive.
1) not sufficient.as x can be bigger/smaller than y or equal
2) sufficient: x-y >4 or y-x <- 4; for both +ve ND -ve x> y

Sent from my Redmi 5 Plus using GMAT Club Forum mobile app

you will have to recheck highlighted portion

|x-y|>4
two cases
1) $$x-y\geq{0}$$
x-y>0
2) $$x-y<{0}$$
-(x-y)>4.......y-x>4

both x-y >4 and y-x <- 4 are SAME
_________________
Retired Moderator G
Joined: 11 Aug 2016
Posts: 370
Re: If xy > 0 and both x and y are even numbers, is x > y?  [#permalink]

Show Tags

1
chetan2u wrote:
If xy>0 and both x and y are even numbers, is x>y?
(I) x>y-2
(II) |x-y|>4

New question!!!..

Given:
both x and y are even numbers
xy>0: This means both x & y have same sign.

Statement 1: x>y-2

Case 1 both x,y >0
eg 8>6-2
x>y Yes

Case 2: both x,y<0
eg -8>-8-2
x>y No
Hence Insuficient

Statement 1: |x-y|>4
that means the distance between x & y is 4, but we dont know their relative positions.
Hence Insufficient.

Considering both Statement 1 &2
10>6-2

Sufficient.

_________________
~R.
If my post was of any help to you, You can thank me in the form of Kudos!!
Applying to ISB ? Check out the ISB Application Kit.
Intern  B
Joined: 23 Feb 2012
Posts: 42
Re: If xy > 0 and both x and y are even numbers, is x > y?  [#permalink]

Show Tags

Ya got it. thanks. Should be x-y >4 or x-y < -4 ND not sufficient.
Combining 1)ND 2) gives ultimate x-y > 4 which means x>y . So answer is C

Sent from my Redmi 5 Plus using GMAT Club Forum mobile app
Manager  S
Joined: 01 Nov 2017
Posts: 95
GMAT 1: 700 Q50 V35 GMAT 2: 640 Q49 V28 GMAT 3: 680 Q47 V36 GMAT 4: 700 Q50 V35 GPA: 3.84
Re: If xy > 0 and both x and y are even numbers, is x > y?  [#permalink]

Show Tags

How does the "even" information come into play?

Once I consider 2 conditions together, it was hard to see if it satisfies x > y.
x -y > -2 AND |x- y| > 4

I had to guess it is C because I picked a pair of different sign x and y ( x=-5, y =1) and it could not satisfy both conditions -> probably they must be same sign. Kinda not sure about this one.
Intern  B
Joined: 17 May 2018
Posts: 7
Re: If xy > 0 and both x and y are even numbers, is x > y?  [#permalink]

Show Tags

In the posted solutions above where A is determined as insufficient, there was the assumption that X can equal y.
My question is , when you are told x and y are even number(s), doesn't that mean that these numbers are different numbers?
Manager  S
Joined: 21 Jul 2018
Posts: 186
Re: If xy > 0 and both x and y are even numbers, is x > y?  [#permalink]

Show Tags

chetan2u wrote:
If xy>0 and both x and y are even numbers, is x>y?
(I) x>y-2
(II) |x-y|>4

New question!!!..

Given:
both x and y are even numbers
xy>0: This means both x & y have same sign.

Statement 1: x>y-2

Case 1 both x,y >0
eg 8>6-2
x>y Yes

Case 2: both x,y<0
eg -8>-8-2
x>y No
Hence Insuficient

Statement 1: |x-y|>4
that means the distance between x & y is 4, but we dont know their relative positions.
Hence Insufficient.

Considering both Statement 1 &2
10>6-2

Sufficient.

Understood why A and B is not an answer but still not able to understand why C is an answer, GmatDaddy could you please elaborate how both equation together are sufficient.
_________________
______________________________
Press +1 Kudos if my post helped you a little and help me to ulcock the tests Wish you all success

I'd appreciate learning about the grammatical errors in my posts

Please let me know if I'm wrong somewhere and help me to learn Retired Moderator G
Joined: 11 Aug 2016
Posts: 370
Re: If xy > 0 and both x and y are even numbers, is x > y?  [#permalink]

Show Tags

1
parthos wrote:
Understood why A and B is not an answer but still not able to understand why C is an answer, GmatDaddy could you please elaborate how both equation together are sufficient.

We have to judge if X>Y such that both the conditions mentioned in Statement 1 and 2 are met..
If you will try to choose values accordingly, you will see that X>Y

Eg: We know from 2 that the difference between X and Y is 4.
Now select values of X and Y such that X>Y-2
ie Y<X+2

let y be 6
now x can take either 2 or 10
Lets try both the cases
6<10+2, the answer to our ultimate question X>Y is Yes
6<2+2, this equality is absurd.

similarly the other case when both X and Y are -ve
_________________
~R.
If my post was of any help to you, You can thank me in the form of Kudos!!
Applying to ISB ? Check out the ISB Application Kit.
Intern  B
Joined: 16 Jun 2018
Posts: 27
GMAT 1: 640 Q49 V29 GPA: 4
WE: Supply Chain Management (Energy and Utilities)
If xy > 0 and both x and y are even numbers, is x > y?  [#permalink]

Show Tags

Given xy>0 (Same signs). we have to check x>y or x-y>0?

St 1: x>y-2, x-y>-2. Insufficient as x-y could be negative, zero or greater than 0.

St 2: x-y>4 or x-y<-4. Insufficient as Inequality 1 gives us Yes answer while Inequality 2 gives us No Answer.

Combining st 1 & 2, we have three inequalities:
x-y>-2
x-y>4
x-y<-4

From here on, if anyone can explain how both statements together are sufficient it would help me in error correction. Please explain algebraic approach.
Math Expert V
Joined: 02 Aug 2009
Posts: 7987
If xy > 0 and both x and y are even numbers, is x > y?  [#permalink]

Show Tags

chetan2u wrote:
If xy > 0 and both x and y are even numbers, is x > y?

(1) x > y - 2
(2) |x - y| > 4

New question!!!..

xy>0.....
x and y are even...

1) x>y-2
x+2>y
So y <x in all cases except when x=y..
Example say x=6, y<8 but y cannot be 7 as y is even, so y will be 6 or <6..
Insufficient as x can be y AND X can be >y

2) |x-y|>4
We cannot say if y>x or x>y but $$x\neq{y}$$
Insufficient

Combined..
We know from statement I that either x=y or X>y
But statement II tells us that $$x\neq{y}$$
So only possibility x>y
Sufficient

C
_________________
Intern  B
Joined: 14 Mar 2018
Posts: 22
Location: India
Concentration: Finance, Marketing
GPA: 3.55
If xy > 0 and both x and y are even numbers, is x > y?  [#permalink]

Show Tags

chetan2u wrote:
chetan2u wrote:
If xy > 0 and both x and y are even numbers, is x > y?

(1) x > y - 2
(2) |x - y| > 4

New question!!!..

xy>0.....
x and y are even...

1) x>y-2
x+2>y
So y <x in all cases except when x=y..
Example say x=6, y<8 but y cannot be 7 as y is even, so y will be 6 or <6..
Insufficient as x can be y AND X can be >y

2) |x-y|>4
We cannot say if y>x or x>y but $$x\neq{0}$$
Insufficient

Combined..
We know from statement I that either x=y or X>y
But statement II tells us that $$x\neq{0}$$
So only possibility x>y
Sufficient

C

Hi chetan2u
From St.2, how did you derive x<>0?
If x = 0 & y = -6,
Modulus (0-(-6)) = 6 ==> 6>4

x<>0 can be derived from the question stem itself, because xy>0.
So what value is statement 2 adding here?
Didn't quite get it...
Thanks.
Also, is this a 700+ level question?
Math Expert V
Joined: 02 Aug 2009
Posts: 7987
Re: If xy > 0 and both x and y are even numbers, is x > y?  [#permalink]

Show Tags

ankitamundhra28 wrote:
chetan2u wrote:
chetan2u wrote:
If xy > 0 and both x and y are even numbers, is x > y?

(1) x > y - 2
(2) |x - y| > 4

New question!!!..

xy>0.....
x and y are even...

1) x>y-2
x+2>y
So y <x in all cases except when x=y..
Example say x=6, y<8 but y cannot be 7 as y is even, so y will be 6 or <6..
Insufficient as x can be y AND X can be >y

2) |x-y|>4
We cannot say if y>x or x>y but $$x\neq{0}$$
Insufficient

Combined..
We know from statement I that either x=y or X>y
But statement II tells us that $$x\neq{0}$$
So only possibility x>y
Sufficient

C

Hi chetan2u
From St.2, how did you derive x<>0?
If x = 0 & y = -6,
Modulus (0-(-6)) = 6 ==> 6>4

x<>0 can be derived from the question stem itself, because xy>0.
So what value is statement 2 adding here?
Didn't quite get it...
Thanks.
Also, is this a 700+ level question?

Hi...
Although combined too I have worked on $$x\neq{y}$$ but have mentioned 0 instead of y...
$$x\neq{y}$$ is correct as x-y cannot be 0
_________________
Intern  B
Joined: 15 Oct 2018
Posts: 14
Re: If xy > 0 and both x and y are even numbers, is x > y?  [#permalink]

Show Tags

amresh09 wrote:
Given xy>0 (Same signs). we have to check x>y or x-y>0?

St 1: x>y-2, x-y>-2. Insufficient as x-y could be negative, zero or greater than 0.

St 2: x-y>4 or x-y<-4. Insufficient as Inequality 1 gives us Yes answer while Inequality 2 gives us No Answer.

Combining st 1 & 2, we have three inequalities:
x-y>-2
x-y>4
x-y<-4

From here on, if anyone can explain how both statements together are sufficient it would help me in error correction. Please explain algebraic approach.

I arrived in the same point with the 3 equations and I combined the two first equations:
x-y>-2
x-y>4

>>> 2x - 2y > 2
>>> x - y > 1
>>> x > y +1

The only way to satisfy x > y +1 is when x>y.

I think I didn't use those information: x and y are even and xy > 0, so we know y and x are different to zero and or both are positive or both are negative.

Or am I missing some step and should I had used ? Re: If xy > 0 and both x and y are even numbers, is x > y?   [#permalink] 21 Oct 2018, 07:05
Display posts from previous: Sort by

If xy > 0 and both x and y are even numbers, is x > y?

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

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