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

 It is currently 08 Dec 2019, 04:07 ### 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.  # Is |x – 3| > |y – 3|?

Author Message
TAGS:

### Hide Tags

Manager  Joined: 10 Feb 2011
Posts: 103
Is |x – 3| > |y – 3|?  [#permalink]

### Show Tags

4
11 00:00

Difficulty:

(N/A)

Question Stats: 74% (01:31) correct 26% (01:28) wrong based on 487 sessions

### HideShow timer Statistics

Is |x – 3| > |y – 3|?

(1) x > y.
(2) xу is not equal to 0.

Originally posted by banksy on 15 Feb 2011, 13:28.
Last edited by Bunuel on 25 Jul 2013, 02:13, edited 2 times in total.
Retired Moderator Joined: 20 Dec 2010
Posts: 1546
Re: 180. Is Ix – 3I > Iy – 3I? (1) x > y. (2) xу is not equal  [#permalink]

### Show Tags

4
Is |x – 3| > |y – 3|?

x-3 > -(y-3)
x-3 > -y+3
x+y > 6
or
x-3 > y-3
x-y > 0
x>y

so; if x>y and x+y>6; we can be sure that |x-3| > |y-3|

(1) x > y.
But we don't know whether x+y>6. Not sufficient.

x=2
y=1
1<2

x=5
y=2
2>1

(2) xу is not equal to 0.
We don't know whether x>y or x+y>6. Not sufficient.
Same sample set from 1 can be used;

Together;
We don't know whether x+y>6. Not sufficient.

Same sample set from 1 can be used.

Ans: "E"
Math Expert V
Joined: 02 Sep 2009
Posts: 59592
Re: 180. Is Ix – 3I > Iy – 3I? (1) x > y. (2) xу is not equal  [#permalink]

### Show Tags

banksy wrote:
180. Is |x – 3| > |y – 3|?
(1) x > y.
(2) xу is not equal to 0.

Is |x – 3| > |y – 3|?

You need no algebra for this one. Question basically asks whether point x on the number line is further from 3 than point y (as |x-3| is the distance between points x and 3 on the number line and |y-3| is the distance between y and 3).

(1) x > y. Totally irrelevant.

(2) xу is not equal to 0. Also irrelevant, it just means that neither x nor y equals to zero.

(1)+(2) Two useless statements. Not sufficient.

_________________
Intern  Joined: 26 Oct 2013
Posts: 20
Re: Is |x – 3| > |y – 3|?  [#permalink]

### Show Tags

1
Is |x – 3| > |y – 3|?

To make true the statement we have to alternatives:
x>y (both x and y positives)
x<y (both x and y negatives)

(1) x > y. If both are positive the answer will be YES but if they are negatives the answer will be NO
(2) xу is not equal to 0. This statement is irrelevant.

(1)+(2) We can not determine. Not sufficient.
Manager  B
Joined: 10 Mar 2013
Posts: 168
GMAT 1: 620 Q44 V31 GMAT 2: 690 Q47 V37 GMAT 3: 610 Q47 V28 GMAT 4: 700 Q50 V34 GMAT 5: 700 Q49 V36 GMAT 6: 690 Q48 V35 GMAT 7: 750 Q49 V42 GMAT 8: 730 Q50 V39 GPA: 3
Re: Is |x – 3| > |y – 3|?  [#permalink]

### Show Tags

E

Picking smart numbers is the best approach for this problem:
(1)
N: x=6, y=-6
Y: x=6, y=5
NS

(2)
Same numbers as (1)
NS

(1)+(2)
NS
Intern  Joined: 23 Oct 2014
Posts: 10
Re: Is |x – 3| > |y – 3|?  [#permalink]

### Show Tags

Hello Experts,
Since both sides of the eqn are positive I assumed we can approach the problem as below:
(x-3)^2 - (y-3)^2 >0 which leads to (x-3-y-3)(x-3-y+3)>0 and further (x-y-6)(x-y)>0 ie, we get 2 solutions : x>y or (x-y)>6.

Because I saw Option 1 has one of these solutions ie.x>y I chose (A). Is it incorrect to choose an option if it is partially satisfied? Kindly help me understand.

Thanks & Regards,
Nab
Math Expert V
Joined: 02 Aug 2009
Posts: 8288
Re: Is |x – 3| > |y – 3|?  [#permalink]

### Show Tags

1
Nab77 wrote:
Hello Experts,
Since both sides of the eqn are positive I assumed we can approach the problem as below:
(x-3)^2 - (y-3)^2 >0 which leads to (x-3-y-3)(x-3-y+3)>0 and further (x-y-6)(x-y)>0 ie, we get 2 solutions : x>y or (x-y)>6.

Because I saw Option 1 has one of these solutions ie.x>y I chose (A). Is it incorrect to choose an option if it is partially satisfied? Kindly help me understand.

Thanks & Regards,
Nab

Hi Nab,
you have done two mistakes in the highlighted portion..

1) $$(x-3)^2 - (y-3)^2 >0.............. (x-3+y-3)(x-3(y-3))>0...... (x+y-6)(x-y)>0.....$$ and NOT (x-y-6)(x-y)>0

2) It is NOT x>y or (x-y)>6 BUT x>y and (x+y)>6 or x<y and (x+y)<6..
so two cases-
a) BOTH (x+y-6) and (x-y) are +ive or BOTh are -ive
_________________
Intern  Joined: 23 Oct 2014
Posts: 10
Is |x – 3| > |y – 3|?  [#permalink]

### Show Tags

chetan2u wrote:
Nab77 wrote:
Hello Experts,
Since both sides of the eqn are positive I assumed we can approach the problem as below:
(x-3)^2 - (y-3)^2 >0 which leads to (x-3-y-3)(x-3-y+3)>0 and further (x-y-6)(x-y)>0 ie, we get 2 solutions : x>y or (x-y)>6.

Because I saw Option 1 has one of these solutions ie.x>y I chose (A). Is it incorrect to choose an option if it is partially satisfied? Kindly help me understand.

Thanks & Regards,
Nab

Hi Nab,
you have done two mistakes in the highlighted portion..

1) $$(x-3)^2 - (y-3)^2 >0.............. (x-3+y-3)(x-3(y-3))>0...... (x+y-6)(x-y)>0.....$$ and NOT (x-y-6)(x-y)>0

2) It is NOT x>y or (x-y)>6 BUT x>y and (x+y)>6 or x<y and (x+y)<6..
so two cases-
a) BOTH (x+y-6) and (x-y) are +ive or BOTh are -ive

Hi Chetan,
Oops yes I'm sorry that was a typo, i did get (x+y-6)(x-y)>0.
From 2) Do you mean that it is not an OR condition but an AND condition? I didn't understand that quite well, can you please explain again. Especially the part BUT x>y and (x+y)>6 or x<y and (x+y)<6. I didn't understand how the equality signs changed.

Regards,
Nab
Math Expert V
Joined: 02 Aug 2009
Posts: 8288
Re: Is |x – 3| > |y – 3|?  [#permalink]

### Show Tags

1
Nab77 wrote:
chetan2u wrote:
Nab77 wrote:
Hello Experts,
Since both sides of the eqn are positive I assumed we can approach the problem as below:
(x-3)^2 - (y-3)^2 >0 which leads to (x-3-y-3)(x-3-y+3)>0 and further (x-y-6)(x-y)>0 ie, we get 2 solutions : x>y or (x-y)>6.

Because I saw Option 1 has one of these solutions ie.x>y I chose (A). Is it incorrect to choose an option if it is partially satisfied? Kindly help me understand.

Thanks & Regards,
Nab

Hi Nab,
you have done two mistakes in the highlighted portion..

1) $$(x-3)^2 - (y-3)^2 >0.............. (x-3+y-3)(x-3(y-3))>0...... (x+y-6)(x-y)>0.....$$ and NOT (x-y-6)(x-y)>0

2) It is NOT x>y or (x-y)>6 BUT x>y and (x+y)>6 or x<y and (x+y)<6..
so two cases-
a) BOTH (x+y-6) and (x-y) are +ive or BOTh are -ive

Hi Chetan,
Oops yes I'm sorry that was a typo, i did get (x+y-6)(x-y)>0.
From 2) Do you mean that it is not an OR condition but an AND condition? I didn't understand that quite well, can you please explain again. Especially the part BUT x>y and (x+y)>6 or x<y and (x+y)<6. I didn't understand how the equality signs changed.

Regards,
Nab

Hi,

the equation is-

$$(x+y-6)(x-y)>0$$...

The Left Hand Side can be >0 under two cases..

1) when both (x+y-6) and (x-y) are greater than 0... since Positive * Positive = Positive..
so x-y>0 or x>y................and x+y-6>0 or x+y>0.........
Example x = 5, y=2.. x>y and x+y>6 ... so (5+2-6)(5-2)>0.....1*3>0...YES

2) when both (x+y-6) and (x-y) are lesser than 0... since Negative * Negative = Positive..
so x-y<0 or x<y................and x+y-6<0 or x+y<6.........
x= 2 and y =3.....x<y and x+y<6 ... so (3+2-6)(2-3)>0.....(-1)(-1)>0..........1>0......YES
_________________
Intern  Joined: 23 Oct 2014
Posts: 10
Re: Is |x – 3| > |y – 3|?  [#permalink]

### Show Tags

Quote:
Hi,

the equation is-

$$(x+y-6)(x-y)>0$$...

The Left Hand Side can be >0 under two cases..

1) when both (x+y-6) and (x-y) are greater than 0... since Positive * Positive = Positive..
so x-y>0 or x>y................and x+y-6>0 or x+y>0.........
Example x = 5, y=2.. x>y and x+y>6 ... so (5+2-6)(5-2)>0.....1*3>0...YES

2) when both (x+y-6) and (x-y) are lesser than 0... since Negative * Negative = Positive..
so x-y<0 or x<y................and x+y-6<0 or x+y<6.........
x= 2 and y =3.....x<y and x+y<6 ... so (3+2-6)(2-3)>0.....(-1)(-1)>0..........1>0......YES

Yes i realize where I went wrong! Thanks a tonne for the explanation.

Thanks & Regards,
Nab
Current Student Joined: 18 Oct 2014
Posts: 796
Location: United States
GMAT 1: 660 Q49 V31 GPA: 3.98
Re: Is |x – 3| > |y – 3|?  [#permalink]

### Show Tags

2
banksy wrote:
Is |x – 3| > |y – 3|?

(1) x > y.
(2) xу is not equal to 0.

(1) x > y.
Let's say x=4 and y=3, then |x – 3| > |y – 3|
but it x=-3 and y=-4, then the aboveineqzuality will not hold true.
Insufficient
(2) xу is not equal to 0
This statement means either x or y is not equal to 0. It can be +ve or -ve. not sufficient.

Combining both statements doesn't give a unique answer. Hence E is the answer
_________________
I welcome critical analysis of my post!! That will help me reach 700+
Director  D
Joined: 13 Mar 2017
Posts: 730
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: Is |x – 3| > |y – 3|?  [#permalink]

### Show Tags

banksy wrote:
Is |x – 3| > |y – 3|?

(1) x > y.
(2) xу is not equal to 0.

DS: Is |x – 3| > |y – 3|?

Statement 1 : x>y
Lets say x =6 , y = 4 |x-3| = 3>|y-3| = 1
Lets say x = 1, y = -4 |x-3|= 2<|y-3| = 7

NOT SUFFICIENT

Statement 2 : xy is not equal to 0 . So, neither x nor y is not equal to 0 .
Lets say x =6 , y = 4 |x-3| = 3>|y-3| = 1
Lets say x = 1, y = -4 |x-3|= 2<|y-3| = 7
NOT SUFFICIENT

Combined : same examples
NOT SUFFICIENT

Intern  B
Joined: 28 Sep 2017
Posts: 23
Location: India
Concentration: Technology, General Management
GPA: 3.5
WE: Information Technology (Computer Software)
Re: Is |x – 3| > |y – 3|?  [#permalink]

### Show Tags

Is |x – 3| > |y – 3|?

(1) x > y.
(2) xу is not equal to 0

2. XY not equal to 0 we don't know the value of X and Y so Insufficient

2. If x =10 and Y = -100 then |Y-3| is greater if x=10 and Y= 5 then |X-3| is greater so insuffiecient

together the same example holds good, not sufficient hence Answer should be E
SC Moderator P
Status: GMAT - Pulling Quant and Verbal together
Joined: 04 Sep 2017
Posts: 243
Location: United States (OH)
GPA: 3.6
WE: Sales (Computer Software)
Is |x – 3| > |y – 3|?  [#permalink]

### Show Tags

banksy wrote:
Is |x – 3| > |y – 3|?

(1) x > y.
(2) xу is not equal to 0.

For DS AbsValue questions I try to read the question and spend about 10 seconds to see if I can understand what it is asking before I even look at the statements.

Is |x – 3| > |y – 3|? When would this be true and when would it be not true?

Well, if they are both positive and x>y, then yes.

If they are both negative and x>y, then no.

Read statement (1) and (2), neither account for the option of a Negative Y. Example: x=1 y=-900, satisfies both statements, answer to question is no.

Yes/No= E
_________________
Would I rather be feared or loved? Easy. Both. I want people to be afraid of how much they love me.

How to sort questions by Topic, Difficulty, and Source:
https://gmatclub.com/forum/search.php?view=search_tags

Originally posted by MikeScarn on 13 Mar 2018, 05:38.
Last edited by MikeScarn on 13 Mar 2018, 13:57, edited 1 time in total.
Retired Moderator P
Joined: 22 Aug 2013
Posts: 1414
Location: India
Re: Is |x – 3| > |y – 3|?  [#permalink]

### Show Tags

msurls wrote:
banksy wrote:
Is |x – 3| > |y – 3|?

(1) x > y.
(2) xу is not equal to 0.

For DS AbsValue questions I try to read the question and spend about 10 seconds to see if I can understand what it is asking before I even look at the statements.

Is |x – 3| > |y – 3|? When would this be true and when would it be not true?

This is really the same as "Is |x|>|y|?"

Well, if they are both positive and x>y, then yes.

If x>y but Y has a greater magnitude than X, then no.

Read statement (1) and (2), neither account for the option of a Negative Y. Example: x=1 y=-900, satisfies both statements, answer to question is no.

Yes/No= E

Hello

You are correct that answer is E. However, I would like to point out the highlighted part in your analysis. (I have highlighted)

|x-3| > |y-3| is NOT the same as |x|>|y|.

Eg., if x=-1 and y=5, then |x-3| > |y-3| BUT |x| < |y|

Actually |x-3| > |y-3| means that the distance of 'x' and '3' is more than the distance of 'y' and '3'.
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8235
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Is |x – 3| > |y – 3|?  [#permalink]

### Show Tags

1
banksy wrote:
Is |x – 3| > |y – 3|?

(1) x > y.
(2) xу is not equal to 0.

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 2 variables (x and y) and 0 equations, C is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2):
x = 4, y = 3: Yes
x = 3, y = 2: No

Since we have two answer, "yes" and "no", both conditions together are not sufficient.

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.
_________________
Intern  B
Joined: 11 Feb 2018
Posts: 35
Re: Is |x – 3| > |y – 3|?  [#permalink]

### Show Tags

fluke wrote:
Is |x – 3| > |y – 3|?

x-3 > -(y-3)
x-3 > -y+3
x+y > 6
or
x-3 > y-3
x-y > 0
x>y

so; if x>y and x+y>6; we can be sure that |x-3| > |y-3|

(1) x > y.
But we don't know whether x+y>6. Not sufficient.

x=2
y=1
1<2

x=5
y=2
2>1

(2) xу is not equal to 0.
We don't know whether x>y or x+y>6. Not sufficient.
Same sample set from 1 can be used;

Together;
We don't know whether x+y>6. Not sufficient.

Same sample set from 1 can be used.

Ans: "E"

I got the solution explained above. My doubt is shouldn't be we checking the other 2 scenarios also which are
-(x-3)>(y-3) and
-(x-3) > -(y-3)

my thinking is as there are two modulus involved we should check all the 4 possible scenario
x-3 > y-3
x-3 > -(y-3)
-(x-3)>(y-3)
-(x-3) > -(y-3)
Senior Manager  B
Joined: 03 Sep 2018
Posts: 252
Location: Netherlands
GMAT 1: 710 Q48 V40 GMAT 2: 780 Q50 V49 GMAT 3: 760 Q49 V44 GPA: 4
Re: Is |x – 3| > |y – 3|?  [#permalink]

### Show Tags

Can anyone explain to me why |x-3| > |y-3| is only true if x>y AND 6>x+y? Why is it not sufficient to just have one of the conditions met?
_________________
Good luck to you. Re: Is |x – 3| > |y – 3|?   [#permalink] 06 Aug 2019, 00:51
Display posts from previous: Sort by

# Is |x – 3| > |y – 3|?  