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

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EgmatQuantExpert
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|x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and [#permalink] New post   26 May 2017, 05:21
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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|?


Answer Choices



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

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Gladiator59
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Re: |x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and [#permalink] New post   17 Dec 2018, 07:16
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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,
Gladi


|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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Re: |x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and [#permalink] New post   28 May 2017, 05:45
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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
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Re: |x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and [#permalink] New post   26 May 2017, 05:46
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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|?


Answer Choices



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

Thanks,
Saquib
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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.
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Re: |x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and [#permalink] New post   26 May 2017, 05:58
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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
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Re: |x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and [#permalink] New post   26 May 2017, 06:25
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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|?


Answer Choices



    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
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Re: |x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and [#permalink] New post   19 Jun 2017, 16:08
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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
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Re: |x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and [#permalink] New post   16 Dec 2018, 12:07
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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|?

|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


Answer A.-12
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Re: |x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and [#permalink] New post   17 Dec 2018, 09:29
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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!
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|x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and [#permalink] New post   17 Jan 2019, 04:32
|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.
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Re: |x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and [#permalink] New post   17 Jan 2019, 04:45
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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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|x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and [#permalink] New post   29 Mar 2019, 16:54
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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
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|x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and [#permalink] New post   27 Apr 2019, 05:29
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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
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Re: |x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and [#permalink] New post   01 Nov 2019, 03:13
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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|?


Answer Choices



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

Thanks,
Saquib
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Re: |x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and [#permalink] New post   12 May 2023, 03:09
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Re: |x + 3| = |y -4|, where x and y are non-zero integers. If |x| < 5 and [#permalink]
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