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

 It is currently 14 Dec 2019, 12:00

### 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

# Suppose that |x + y| + |x -y| = 2. What is the maximum possible value

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 59725
Suppose that |x + y| + |x -y| = 2. What is the maximum possible value  [#permalink]

### Show Tags

31 Mar 2019, 22:15
00:00

Difficulty:

55% (hard)

Question Stats:

62% (02:30) correct 38% (02:20) wrong based on 117 sessions

### HideShow timer Statistics

Suppose that |x + y| + |x -y| = 2. What is the maximum possible value of x^2 - 6x + y^2?

A. 5
B. 6
C. 7
D. 8
E. 9

_________________
Senior Manager
Joined: 13 Jan 2018
Posts: 341
Location: India
Concentration: Operations, General Management
GMAT 1: 580 Q47 V23
GMAT 2: 640 Q49 V27
GPA: 4
WE: Consulting (Consulting)
Re: Suppose that |x + y| + |x -y| = 2. What is the maximum possible value  [#permalink]

### Show Tags

31 Mar 2019, 22:46
2
if we open mod there are 4 cases possible

Case 1) Both are positive

x + y + x - y = 2
2x = 2
x = 1

Case 2) |x + y| is negative

-x - y + x - y = 2
-2y = 2
y = -1

Case 3) |x - y| is negative
x + y - x + y = 2
2y = 2
y = 1

Case 4) Both are negative
- x - y - x + y = 2
-2x = 2
x = -1

So from the above 4 cases, we can say $$x = \pm{1}$$ and $$y = \pm{1}$$

Substituting in the eq: $$x^2 - 6x + y^2$$

$$1 - 6(\pm{1}) + 1$$

This value will be maximum when x = -1

=$$1 -6(-1) + 1$$

=8

OPTION: D
Math Expert
Joined: 02 Aug 2009
Posts: 8320
Re: Suppose that |x + y| + |x -y| = 2. What is the maximum possible value  [#permalink]

### Show Tags

01 Apr 2019, 00:25
1
Bunuel wrote:
Suppose that |x + y| + |x -y| = 2. What is the maximum possible value of x^2 - 6x + y^2?

A. 5
B. 6
C. 7
D. 8
E. 9

We can find our solution by logic.
(I) Both the terms |x + y| and |x -y| are at least 0, and cannot be more than 2 as their sum itself is given as 2.
(II) If you have to maximize $$x^2 - 6x + y^2$$, we will try to maximize -6x as that will be the largest value, so x should be negative.

Now |x| and |y| should not be greater than 1, so both can be 1..
x has to be negative, so x=-1, and y =1..
|x + y| + |x -y| =|-1+1|+|-1-1|= 2...Yes

Value of $$x^2 - 6x + y^2$$ will become $$(-1)^2 - 6(-1) + (-1)^2=1+6+1=8$$

D
_________________
Director
Joined: 09 Aug 2017
Posts: 632
Re: Suppose that |x + y| + |x -y| = 2. What is the maximum possible value  [#permalink]

### Show Tags

01 Apr 2019, 17:58
1
How I approached this question is as follows.
I know that every term in equation is positive. Therefore, I squared both sides.
And got (x^2 + y^2)= 2.

Now I have maximize the x^2 + y^2 - 6x
To maximize 2-6x, x must be negative and can be -1.
So, maximum value is 8.

I think my approach to such questions in which both sides are positive is correct.

chetan2u wrote:
Bunuel wrote:
Suppose that |x + y| + |x -y| = 2. What is the maximum possible value of x^2 - 6x + y^2?

A. 5
B. 6
C. 7
D. 8
E. 9

We can find our solution by logic.
(I) Both the terms |x + y| and |x -y| are at least 0, and cannot be more than 2 as their sum itself is given as 2.
(II) If you have to maximize $$x^2 - 6x + y^2$$, we will try to maximize -6x as that will be the largest value, so x should be negative.

Now |x| and |y| should not be greater than 1, so both can be 1..
x has to be negative, so x=-1, and y =1..
|x + y| + |x -y| =|-1+1|+|-1-1|= 2...Yes

Value of $$x^2 - 6x + y^2$$ will become $$(-1)^2 - 6(-1) + (-1)^2=1+6+1=8$$

D
Manager
Joined: 09 Jun 2017
Posts: 104
GMAT 1: 640 Q44 V35
Re: Suppose that |x + y| + |x -y| = 2. What is the maximum possible value  [#permalink]

### Show Tags

04 Apr 2019, 09:38
1
gvij2017 wrote:
How I approached this question is as follows.
I know that every term in equation is positive. Therefore, I squared both sides.
And got (x^2 + y^2)= 2.

Now I have maximize the x^2 + y^2 - 6x
To maximize 2-6x, x must be negative and can be -1.
So, maximum value is 8.

I think my approach to such questions in which both sides are positive is correct.

chetan2u wrote:

Hi , I'm curious , when you square both sides , you got 2 *|x + y| * |x -y| in your way , how you did deal with that?
Duke & Cornell Moderator
Joined: 29 May 2018
Posts: 102
Location: India
GMAT 1: 700 Q48 V38
GMAT 2: 720 Q49 V39
GPA: 4
Suppose that |x + y| + |x − y| = 2. What is the maximum possible value  [#permalink]

### Show Tags

10 May 2019, 22:43
1
(|x+y| + |x-y|) ^2 = 4
2(x^2 + y^2) + 2( x^2-y^2)=4
4x^2=4
x=+/- 1

to maximize, x must be -1

put this in original equation, y can be 0 or 1

since we are looking to maximize, choose 1

Suppose that |x + y| + |x − y| = 2. What is the maximum possible value   [#permalink] 10 May 2019, 22:43
Display posts from previous: Sort by