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

 It is currently 11 Dec 2019, 12:37

### 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

# |x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and

Author Message
TAGS:

### Hide Tags

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3158
|x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and  [#permalink]

### Show Tags

26 May 2017, 05:21
1
26
00:00

Difficulty:

95% (hard)

Question Stats:

36% (02:43) correct 64% (02:28) wrong based on 364 sessions

### HideShow timer Statistics

|x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and |y| < 5, what is the maximum possible value of -|xy|?

A. -12
B. -6
C. -4
D. -2
E. 0

Thanks,
Saquib
Quant Expert
e-GMAT

Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts

_________________
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3158
Re: |x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and  [#permalink]

### Show Tags

26 May 2017, 05:43
Intern
Status: GMAT tutor
Joined: 20 Apr 2017
Posts: 20
GMAT 1: 770 Q49 V47
Re: |x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and  [#permalink]

### Show Tags

26 May 2017, 05:46
3
EgmatQuantExpert wrote:
Q.

|x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and |y| < 5, what is the maximum possible value of -|xy|?

A.-12
B. -6
C. -4
D. -2
E. 0

Thanks,
Saquib
Quant Expert
e-GMAT

Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts

Well, I don't 100% understand the question, but I'll take a stab at it.

Since y<5, 1 is a possible value for y. Since |1-4|=3, x would have to be 0 or 6 and that's not possible.

So I'm going to try -1, which yields |-1-4|=5 so x could be 2. That will yield answer choice (D), and I don't see how you can reach zero since neither x nor y can be zero. I'm going with D.
_________________
Elias Latour
Verbal Specialist @ ApexGMAT
blog.apexgmat.com
+1 (646) 736-7622
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3158
Re: |x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and  [#permalink]

### Show Tags

26 May 2017, 05:58
eliaslatour wrote:
Well, I don't 100% understand the question, but I'll take a stab at it.

Since y<5, 1 is a possible value for y. Since |1-4|=3, x would have to be 0 or 6 and that's not possible.

So I'm going to try -1, which yields |-1-4|=5 so x could be 2. That will yield answer choice (D), and I don't see how you can reach zero since neither x nor y can be zero. I'm going with D.

Nice try eliaslatour.

Though I won't comment whether is correct or not, as I want the others to also give it a shot. I just wanted to point out one error in your analysis.

When we write |y| < 5 and we remove the modulus from y, the range of y is not y < 5, but -5 < y < 5.

Apart from that, kudos to your observation that since x and y are non-zero integers, the value of -|xy| can never be 0.

Thanks,
Saquib
Quant Expert
e-GMAT

Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts

_________________
Current Student
Joined: 18 Aug 2016
Posts: 593
Concentration: Strategy, Technology
GMAT 1: 630 Q47 V29
GMAT 2: 740 Q51 V38
Re: |x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and  [#permalink]

### Show Tags

26 May 2017, 06:25
1
EgmatQuantExpert wrote:
Q.

|x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and |y| < 5, what is the maximum possible value of -|xy|?

A.-12
B. -6
C. -4
D. -2
E. 0

Thanks,
Saquib
Quant Expert
e-GMAT

Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts

|x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and |y| < 5, what is the maximum possible value of -|xy|

-5<x<5, -5<y<5

We need to solve for values of x & y to keep XY to minimum using |x + 3| = |y -4|

by value substitution x =2 and y=-1 fits the criteria keeping XY to minimum

hence option D
_________________
We must try to achieve the best within us

Thanks
Luckisnoexcuse
Manager
Joined: 03 Jan 2016
Posts: 57
Location: India
WE: Engineering (Energy and Utilities)
Re: |x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and  [#permalink]

### Show Tags

28 May 2017, 05:45
2
I tried as mentioned below

Given :

-5<x<5, -5<y<5 & x and y are non zero integers.

Therefore; x = {-4,-3,-2,-1,1,2,3,4} & y = {-4,-3,-2,-1,1,2,3,4}

|x + 3| = |y -4|

Try plugging above values
&
above equation holds when
1. x=-4 & y = 3
2. x=-3 & y= 4
3. x=2 & y =-1
4. x = 3 & y=-2
5. x=4 & y = -3.

- |xy| will be max when x=2 & y = -1

Option D

This is how i arrived.

Thanx
Narayana raju
Retired Moderator
Joined: 19 Mar 2014
Posts: 915
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.5
Re: |x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and  [#permalink]

### Show Tags

19 Jun 2017, 16:08
1
1
This is a good and tricky question.

Given: lx+3l = ly-4l - x & y are non-zero integers.

lxl < 5
lyl < 5

Max of -lxyl = ?

As we have to find the max value, and the final max number will be negative as -lxyl will be negative, we need to ensure that we get smallest value of negative possible which satisfies given equation.

As per given information values of x and y can range as per below:

-5 < x < 5
-5 < y < 5

As we have to take least numbers, we will plug numbers from this range.

Note we cannot take x & y as zero as per the given information, also it does not satisfy the given equation lx+3l = ly-4l.

Only values we can check for us -1 & 2 or 2 & -1

so maximum value we get is -2.

Hence, Answer is D = -2
_________________
"Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent."

Best AWA Template: https://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html#p470475
Director
Joined: 18 Feb 2019
Posts: 607
Location: India
GMAT 1: 460 Q42 V13
GPA: 3.6
|x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and  [#permalink]

### Show Tags

29 Mar 2019, 12:40
1
|x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and |y| < 5, what is the maximum possible value of -|xy|?

A. -12
B. -6
C. -4
D. -2
E. 0
Math Expert
Joined: 02 Aug 2009
Posts: 8302
|x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and  [#permalink]

### Show Tags

29 Mar 2019, 16:54
1
kiran120680 wrote:
|x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and |y| < 5, what is the maximum possible value of -|xy|?

A. -12
B. -6
C. -4
D. -2
E. 0

To maximize -|xy|, we have to minimize |xy|

Possible cases |x + 3| = |y -4|
(I) $$x+3=y-4....x=y-7$$........|xy|=|y(y-7)|... |y(y-7)| will be at least 6 even if we take y as 1.
(II) $$-(x+3)=y-4....-x-3=y-4................y+x=1$$.....let us take minimum possible value for this. Both are non-zero, so one of them 2 and other -1 will fit and |xy|=|2(-1)|=|2|

so maximum value of -|xy|=-|2|. No need to check further as in the options the max value is -2.
0 cannot be a value as both x and y are non-zero.

D
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 59674
Re: |x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and  [#permalink]

### Show Tags

30 Mar 2019, 00:29
kiran120680 wrote:
|x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and |y| < 5, what is the maximum possible value of -|xy|?

A. -12
B. -6
C. -4
D. -2
E. 0

Merging topics. Please search before posting.
_________________
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5470
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: |x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and  [#permalink]

### Show Tags

30 Mar 2019, 01:00
kiran120680 wrote:
|x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and |y| < 5, what is the maximum possible value of -|xy|?

A. -12
B. -6
C. -4
D. -2
E. 0

simplify the expression
|x + 3| = |y -4|
x+3= y-4
x-y=-7
or say
-x-3=y-4
-(x+y)=-1
x+y=1
so x=2 and y=-1
possible and it satisfies
|x + 3| = |y -4|
-lxyl ; -2
IMO D
Senior Manager
Joined: 09 Jun 2014
Posts: 351
Location: India
Concentration: General Management, Operations
Re: |x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and  [#permalink]

### Show Tags

27 Apr 2019, 03:13
Archit3110 wrote:
kiran120680 wrote:
|x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and |y| < 5, what is the maximum possible value of -|xy|?

A. -12
B. -6
C. -4
D. -2
E. 0

simplify the expression
|x + 3| = |y -4|
x+3= y-4
x-y=-7
or say
-x-3=y-4
-(x+y)=-1
x+y=1
so x=2 and y=-1
possible and it satisfies
|x + 3| = |y -4|
-lxyl ; -2
IMO D

correct me if am wrong but the solution of eqution in red is x=-3 and y=4

I tried a simlar approach and was struck for quite a bit .

Press kudos if it helps!!
Senior Manager
Joined: 09 Jun 2014
Posts: 351
Location: India
Concentration: General Management, Operations
Re: |x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and  [#permalink]

### Show Tags

27 Apr 2019, 03:19
chetan2u wrote:
kiran120680 wrote:
|x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and |y| < 5, what is the maximum possible value of -|xy|?

A. -12
B. -6
C. -4
D. -2
E. 0

To maximize -|xy|, we have to minimize |xy|

Possible cases |x + 3| = |y -4|
(I) $$x+3=y-4....x=y-7$$........|xy|=|y(y-7)|... |y(y-7)| will be at least 6 even if we take y as 1.
(II) $$-(x+3)=y-4....-x-3=y-4................y+x=1$$.....let us take minimum possible value for this. Both are non-zero, so one of them 2 and other -1 will fit and |xy|=|2(-1)|=|2|

so maximum value of -|xy|=-|2|. No need to check further as in the options the max value is -2.
0 cannot be a value as both x and y are non-zero.

D

hello Egmat/Chetan sir,

I tried solving the inequalities and landed up withe x=-3 and y=4.

Can you please suggest the right line of thinking when seeing such questions..I see your approach is clear...But seeing inequalities like this general tendency is to jump into solving them.
Here after seeing the options it didnt help rather just plugging in values from options(assuming |x|<4 and |y|<5 wold have been far more beneficial)
Intern
Joined: 03 Jun 2014
Posts: 4
Location: Viet Nam
GPA: 3.3
WE: Research (Consulting)
|x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and  [#permalink]

### Show Tags

27 Apr 2019, 05:29
2
1
I think this type of question is not too difficult if we solve things step by step. Below is my approach:

First things first, we have |x| < 5 and |y| < 5, which mean -5 < x < 5 and -5 < y < 5

Then, solve the equation:|x + 3| = |y -4|

We apply this: |A| = |B| then A = B or A = -B

=> x+3 = y-4 or x+3 = 4-y
=> x - y = -7 or x + y = 1

The possible values of x and y may be:
1. x - y = -7 -> pairs of value (x,y) can be: (-4;3) or (-3;4)
2. x + y = 1 -> (-1;2) or (-2;3) or (-3;4)

Then -|xy| can get these following values: -2, -6, -12 => -2 is the highest => D
Intern
Joined: 08 Aug 2017
Posts: 1
Re: |x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and  [#permalink]

### Show Tags

24 Oct 2019, 22:34
Hi.. I think the question is tricky and twisted. However, the answer -2 is definitely incorrect.

Why?

Because -mod(xy) can have a maximum value of zero, right. Let's keep it as it will be useful.

Let's consider a pair of (x,y) as y=1, and x=0.

This pair definitely satisfies all the equations in the question.

So, a valid pair of (x,y) is (0,1), which will give a product of xy as zero.

Hence, -mod(x,y)=0, which is the maximum attainable value.

Any thoughts?
Manager
Joined: 06 Feb 2019
Posts: 112
Re: |x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and  [#permalink]

### Show Tags

27 Oct 2019, 06:19
Harshit Srivastava wrote:
Hi.. I think the question is tricky and twisted. However, the answer -2 is definitely incorrect.

Why?

Because -mod(xy) can have a maximum value of zero, right. Let's keep it as it will be useful.

Let's consider a pair of (x,y) as y=1, and x=0.

This pair definitely satisfies all the equations in the question.

So, a valid pair of (x,y) is (0,1), which will give a product of xy as zero.

Hence, -mod(x,y)=0, which is the maximum attainable value.

Any thoughts?

hi
it is given in the question that x and y are non-zero integers
Intern
Joined: 30 Sep 2018
Posts: 19
WE: Marketing (Consumer Products)
Re: |x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and  [#permalink]

### Show Tags

01 Nov 2019, 02:20
EgmatQuantExpert wrote:
|x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and |y| < 5, what is the maximum possible value of -|xy|?

A. -12
B. -6
C. -4
D. -2
E. 0

Thanks,
Saquib
Quant Expert
e-GMAT

Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts

Here is my approach to this question:

Information gathering:
We are given that the distance of x from -3 is equal to the distance of y from 4...(converting |x + 3| = |y -4| into a sentence)..(info 1)
We are also given that distance of x from 0 is less than 5..(|x| < 5)..means -5<x<5
and distance of y from 0 is less than 5...(|y| < 5) -5<y<5

To find: Maximum possible value of -|xy|

Method:
Plot points -5, -3, 0 , 4 and 5 on a number line...and start pairing numbers!
pair 1: x = -4..which is 1 distance away from -3..hence y would also be 1 distance away from 4 as per info 1. For (-4,3) -|xy| = -|12| = -12
Pair 2: x=-2...which is 1 distance away from -3..hence y would also be 1 distance away from 4 as per info 1. For (-2,3) -|xy| = -|6| = -6
Pair 3: x=-1.....which is 2 distance away from -3..hence y would also be 2 distance away from 4 as per info 1. For (-1,2) -|xy| = -|2| = -2
Since x and y are non-zero integers, there is no point testing x and y with 0 value. Among the 3 pairs, -2 is the greatest.
Attachments

File comment: For visualizing the Number line better.

NL.png [ 3.59 KiB | Viewed 344 times ]

VP
Joined: 19 Oct 2018
Posts: 1167
Location: India
Re: |x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and  [#permalink]

### Show Tags

01 Nov 2019, 03:13
This is 20 seconds problem imo

We need to maximize -|xy|; hence, check the given options from the bottom.

We know that x and y are nonzero integers, eliminate E

Now check for whether we can get -|xy|=-2, where -5<x<5 and -5<y<5

At x=-1 and y=2, |x + 3| = |y -4|

D

EgmatQuantExpert wrote:
|x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and |y| < 5, what is the maximum possible value of -|xy|?

A. -12
B. -6
C. -4
D. -2
E. 0

Thanks,
Saquib
Quant Expert
e-GMAT

Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts

Re: |x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and   [#permalink] 01 Nov 2019, 03:13
Display posts from previous: Sort by