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Retired Moderator V
Joined: 27 Oct 2017
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|x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and  [#permalink]

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16 00:00

Difficulty:   95% (hard)

Question Stats: 29% (02:27) correct 71% (02:39) wrong based on 190 sessions

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GMATbuster's Weekly Quant Quiz#13 Ques #8

For Questions from earlier quizzes: Click Here

|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

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Senior PS Moderator D
Status: It always seems impossible until it's done.
Joined: 16 Sep 2016
Posts: 737
GMAT 1: 740 Q50 V40 GMAT 2: 770 Q51 V42 Re: |x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and  [#permalink]

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3
1
2
First of all, we need to realize this - Mod is always nonnegative, so maximum possible of Negative of a mod expression will be at the minimum possible value of the mod expression.

So we are looking at Min value of |xy|

|x| < 5 or
-5 < x < 5

|x| is also the distance of x from zero, and in general |x-a| is the distance of x from a.

Hence |x+3| would be the distance of x from -3: which would translate to x ranging from 5 units to left of-3 to 5 units to right of -3. Just imagine that we have shifted the origin to -3 and then applying mod function

therefore, -8 < x < 2

Similarly, -1 < y < 9

we also have |x+3| = |y-4| so this could happen at x = -1 and y = 2 or at any of the following (x,y) pairs = ( -2.3) (-3,4) (-4,5) (-5,6) ...( -7,8) you can check by putting the values in.

Min absolute value of xy would be when x = -1 and y = 2 as y is nonzero integer. Hence , max value of -|xy| will be -2.

Option (D) is our choice

Regards,

|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
_________________
Regards,

“Do. Or do not. There is no try.” - Yoda (The Empire Strikes Back)
General Discussion
Director  D
Joined: 13 Mar 2017
Posts: 728
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: |x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and  [#permalink]

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1
2
|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|?

|x| < 5
-5<x<5
-2<x+3<8
0<|x+3|<8

|y| < 5
-5<y<5
-9<y-4<1
0<=|y-4|<1
Now, |x+3| = |y-4|
Hence 0<=|x+3|<1
-1<x+3<1
-4<x<-2
x=-3
-5<y<5
y = -4,-3,-2...,3,4
-|xy| = -12

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Manager  G
Joined: 02 Aug 2015
Posts: 153
Re: |x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and  [#permalink]

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gmatbusters wrote:

GMATbuster's Weekly Quant Quiz#13 Ques #8

For Questions from earlier quizzes: Click Here

|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

The question is best solved by going through the options. Option E can be eliminated as x and y are non zero integers, so xy cannot be zero.

Choosing the next maximum value among the options, i.e -2

xy can be -2 or 2.

By plugging in values for xy to get -2, we can see x=-1 and y=2 solves the given equation. So -2 is the maximum value. No need to even check other options as they are lesser than -2 and question asks for the greatest value.

Hence D.

Cheers!
Senior PS Moderator D
Status: It always seems impossible until it's done.
Joined: 16 Sep 2016
Posts: 737
GMAT 1: 740 Q50 V40 GMAT 2: 770 Q51 V42 |x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and  [#permalink]

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1
Hi Diwakar003,

While plugging in values is a very common approach to solve questions quickly, I think it does not benefit the user much here. There would be too many possibilities and stumbling upon the answer without zeroing down the options is a gamble I would rather not take on the exam.

For ex. 0 can be eliminated trivially. Apart from that, it so happens that here the next largest option is the correcrt answer. However, if that would not be the case ( in some other scenario) the the number of values to be tested would grow substantially.

-2 = 2,-2 check x = 1 y = -2 and y = 1 x = -2

-4 = 4,-4 check x = 1 y =4 ; y = 1 x = 4 ; x = 2 y =2 and three more for negative possibility already 6 cases to test

-6 = 6,-6 check x = 1 y = 6; y = 1 x =6 ; (2,3) (3,2) and four more for negatives. Already 8 cases

By the time you have eliminated 3 options, you have already tested 16 cases.

This is definitely not recommended and is definitely not the best way to solve the question

Hope it makes sense.

Best,

Diwakar003 wrote:
gmatbusters wrote:

GMATbuster's Weekly Quant Quiz#13 Ques #8

For Questions from earlier quizzes: Click Here

|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

The question is best solved by going through the options.
Option E can be eliminated as x and y are non zero integers, so xy cannot be zero.

Choosing the next maximum value among the options, i.e -2

xy can be -2 or 2.

By plugging in values for xy to get -2, we can see x=-1 and y=2 solves the given equation. So -2 is the maximum value. No need to even check other options as they are lesser than -2 and question asks for the greatest value.

Hence D.

Cheers!

_________________
Regards,

“Do. Or do not. There is no try.” - Yoda (The Empire Strikes Back)
Director  D
Joined: 13 Mar 2017
Posts: 728
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: |x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and  [#permalink]

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The only question I did wrong Great going Gladiator59
_________________
CAT 2017 (98.95) & 2018 (98.91) : 99th percentiler
UPSC Aspirants : Get my app UPSC Important News Reader from Play store.

MBA Social Network : WebMaggu

Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)

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Intern  B
Status: when you say,"I can or I can't", Both times you are right!
Joined: 26 Nov 2018
Posts: 31
Location: India
|x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and  [#permalink]

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|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

would anyone please bring some light on this approach?

-5<x<5
hence, -2<x+3<8

-5<y<5
hence, -9<y-4<1

the question says, lx+3l=ly-4l; this relation is equal at 0 and -1

when we equate x+3 =0 or -1,we get -3 or -4 respectively
when we equate y-4 =0 or -1, we get 4 or 3 respectively

multiplying XY(in both cases) produces -12

Hence, It's A.
Math Expert V
Joined: 02 Sep 2009
Posts: 58434
Re: |x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and  [#permalink]

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Rupesh1Nonly 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

would anyone please bring some light on this approach?

-5<x<5
hence, -2<x+3<8

-5<y<5
hence, -9<y-4<1

the question says, lx+3l=ly-4l; this relation is equal at 0 and -1

when we equate x+3 =0 or -1,we get -3 or -4 respectively
when we equate y-4 =0 or -1, we get 4 or 3 respectively

multiplying XY(in both cases) produces -12

Hence, It's A.

You are missing cases there:

y - 4 is -1 and x + 3 is 1.
y - 4 is -2 and x + 3 is 2.
y - 4 is -3 and x + 3 is 3.
...
y - 4 is -7 and x + 3 is 7.

In all those cases |x + 3| = |y - 4|.
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Director  G
Joined: 09 Mar 2018
Posts: 994
Location: India
Re: |x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and  [#permalink]

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gmatbusters wrote:

GMATbuster's Weekly Quant Quiz#13 Ques #8

For Questions from earlier quizzes: Click Here

|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

If |x| < 5 and |y| < 5, from this you get to know the range of x and y
-5 < x < 5 & -5 < y < 5

If you can get -2 in some way, that will be the highest value, since you cannot get 0

x = - 1 and y = 2

will get you -2

Making D as answer.
_________________
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Quote which i can relate to.
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Manager  G
Joined: 19 Sep 2017
Posts: 204
Location: United Kingdom
GPA: 3.9
WE: Account Management (Other)
|x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and  [#permalink]

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First of all, we need to realize this - Mod is always nonnegative, so maximum possible of Negative of a mod expression will be at the minimum possible value of the mod expression.

So we are looking at Min value of |xy|

|x| < 5 or
-5 < x < 5

|x| is also the distance of x from zero, and in general |x-a| is the distance of x from a.

Hence |x+3| would be the distance of x from -3: which would translate to x ranging from 5 units to left of-3 to 5 units to right of -3. Just imagine that we have shifted the origin to -3 and then applying mod function

therefore, -8 < x < 2

Similarly, -1 < y < 9

we also have |x+3| = |y-4| so this could happen at x = -1 and y = 2 or at any of the following (x,y) pairs = ( -2.3) (-3,4) (-4,5) (-5,6) ...( -7,8) you can check by putting the values in.

Min absolute value of xy would be when x = -1 and y = 2 as y is nonzero integer. Hence , max value of -|xy| will be -2.

Option (D) is our choice

Regards,

|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

Hi,
How did you choose the pairs? ( -2.3) (-3,4) (-4,5) (-5,6) ...( -7,8)

Thanks.
_________________
Cheers!!
Intern  B
Joined: 16 Jul 2018
Posts: 1
Re: |x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and  [#permalink]

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Number line is the best approach.|y-4|is the distance of y from 4 and |x+3| is the distance of x from -3.The only value satisfying the equation is x=-1 and y=2.so the product -|xy|=-2

Posted from my mobile device Re: |x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and   [#permalink] 07 Jul 2019, 18:03
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