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

 It is currently 20 Aug 2018, 08:06

### 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

# If x>0, y<0 and z<0, (|x|+|y|+|z|)^2=?

Author Message
TAGS:

### Hide Tags

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6040
GMAT 1: 760 Q51 V42
GPA: 3.82
If x>0, y<0 and z<0, (|x|+|y|+|z|)^2=?  [#permalink]

### Show Tags

Updated on: 01 Mar 2016, 15:48
14
00:00

Difficulty:

45% (medium)

Question Stats:

62% (01:04) correct 38% (00:52) wrong based on 444 sessions

### HideShow timer Statistics

If x>0, y<0 and z<0,$$(|x|+|y|+|z|)^2$$=?

A. $$x^2+y^2+z^2+2xy+2yz+2zx$$
B.$$x^2+y^2+z^2+2xy-2yz+2zx$$
C.$$x^2+y^2+z^2-2xy+2yz-2zx$$
D. $$x^2+y^2+z^2-2xy-2yz-2zx$$
E.$$x^2-y^2-z^2+2xy+2yz+2zx$$

* A solution will be posted in two days.

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Originally posted by MathRevolution on 18 Jan 2016, 21:50. Last edited by Bunuel on 01 Mar 2016, 15:48, edited 4 times in total. Edited the question. Math Expert Joined: 02 Aug 2009 Posts: 6559 Re: If x>0, y<0 and z<0, (|x|+|y|+|z|)^2=? [#permalink] ### Show Tags 19 Jan 2016, 01:41 4 MathRevolution wrote: If x>0, y<0 and z<0,$$(|x|+|y|+|z|)^2$$=? A. $$x^2+y^2+z^2+2xy+2yz+2zx$$ B.$$x^2+y^2+z^2+2xy-2yz+2zx$$ C.$$x^2+y^2+z^2-2xy+2yz-2zx$$ D. $$x^2+y^2+z^2-2xy-2yz-2zx$$ E.$$x^2-y^2-z^2+2xy+2yz+2zx$$ * A solution will be posted in two days. Hi, We do not require to know the formula for this but realize that there are two -ive qty,z and y.. the mod of x does not have any effect as it is positive.. lets see the eq.. $$(|x|+|y|+|z|)^2$$... all terms in the Eq when expanded should be +ive.. When we see the choices all terms are same except change in sign at few places.. What will be any term with single z and single y, 2yz, it will be +ive as y is -ive and z is -ive.. What will be any term with only one of single z or single y, 2yx or 2xz, it will be -ive as x is +ive and other y or z is -ive.. so for 2xz to be positive, it should be -2xz and 2xy should be -2xy.. So, we have to look for a choice where all terms are positive apart from terms containing single power of z or single power of y but not both.. lets see the choices A. $$x^2+y^2+z^2+2xy+2yz+2zx$$ --- all terms are +ive, making 2xz and 2xy negative.. eliminate B.$$x^2+y^2+z^2+2xy-2yz+2zx$$--------2xy, 2yz, 2zx all are -ive .. eliminate C.$$x^2+y^2+z^2-2xy+2yz-2zx$$ -----------2xy, 2yz, 2zx all are +ive .. CORRECT D. $$x^2+y^2+z^2-2xy-2yz-2zx$$-------- 2yz is -ive .. eliminate E.$$x^2-y^2-z^2+2xy+2yz+2zx$$--------2xy,y^2,z^2, 2zx all are -ive .. eliminate ans C _________________ 1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html GMAT online Tutor Manager Joined: 07 May 2015 Posts: 93 Re: If x>0, y<0 and z<0, (|x|+|y|+|z|)^2=? [#permalink] ### Show Tags 20 Jan 2016, 18:24 1 MathRevolution wrote: If x>0, y<0 and z<0,$$(|x|+|y|+|z|)^2$$=? A. $$x^2+y^2+z^2+2xy+2yz+2zx$$ B.$$x^2+y^2+z^2+2xy-2yz+2zx$$ C.$$x^2+y^2+z^2-2xy+2yz-2zx$$ D. $$x^2+y^2+z^2-2xy-2yz-2zx$$ E.$$x^2-y^2-z^2+2xy+2yz+2zx$$ * A solution will be posted in two days. Because all its the square of the sum of absolute values, it MUST be >=0. Only C is the option which has outcome of each combination as positive. So i went with C as answer. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6040 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If x>0, y<0 and z<0, (|x|+|y|+|z|)^2=? [#permalink] ### Show Tags 20 Jan 2016, 21:35 If x>0, y<0 and z<0, (|x|+|y|+|z|)^2=? A. x^2+y^2+z^2+2xy+2yz+2zx B. x^2+y^2+z^2+2xy-2yz+2zx C. x^2+y^2+z^2-2xy+2yz-2zx D. x^2+y^2+z^2-2xy-2yz-2zx E. x^2-y^2-z^2+2xy+2yz+2zx ==> |A|=A when A>0 ,and |A|=-A when A<0. So, (|x|+|y|+|z|)^2=(x-y-z)^2=x^2+(-y)^2+(-z)^2+2x(-y)+2(-y)(-z)+2(-z)x =x^2+y^2+z^2-2xy+2yz-2zx. Therefore, the answer is C. _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Intern
Joined: 08 Dec 2015
Posts: 2
Re: If x>0, y<0 and z<0, (|x|+|y|+|z|)^2=?  [#permalink]

### Show Tags

01 Mar 2016, 09:38
Are you sure C is the answer?
The question says that y and z are negative, agree. But here we need to find the square of the sm of three absolute values, not three integers. If the question asked for (x+y+z)^2 I would have agreed. But here we have three absolute values which are always positive or equal to zero by definition.
Probably I'm missing something...could you please explain?
Thanks
Current Student
Joined: 20 Mar 2014
Posts: 2643
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: If x>0, y<0 and z<0, (|x|+|y|+|z|)^2=?  [#permalink]

### Show Tags

01 Mar 2016, 10:20
elenap818 wrote:
Are you sure C is the answer?
The question says that y and z are negative, agree. But here we need to find the square of the sm of three absolute values, not three integers. If the question asked for (x+y+z)^2 I would have agreed. But here we have three absolute values which are always positive or equal to zero by definition.
Probably I'm missing something...could you please explain?
Thanks

You are correct in your definition of the absolute value but you can not have (|x|+|y|+|z|)^2 = 0 as x, y ,z are NON zero numbers. What should according to you be the answer if not for C?
Math Expert
Joined: 02 Aug 2009
Posts: 6559
Re: If x>0, y<0 and z<0, (|x|+|y|+|z|)^2=?  [#permalink]

### Show Tags

01 Mar 2016, 10:23
1
elenap818 wrote:
Are you sure C is the answer?
The question says that y and z are negative, agree. But here we need to find the square of the sm of three absolute values, not three integers. If the question asked for (x+y+z)^2 I would have agreed. But here we have three absolute values which are always positive or equal to zero by definition.
Probably I'm missing something...could you please explain?
Thanks

Hi,
you are correct it will not effect the mod values ..
But the choices are not in mod values but integers, and that i swhy we have to see if the choices match the given conditions..

_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Current Student
Joined: 04 Sep 2015
Posts: 26
Location: United Arab Emirates
GMAT 1: 600 Q50 V40
GPA: 3.21
Re: If x>0, y<0 and z<0, (|x|+|y|+|z|)^2=?  [#permalink]

### Show Tags

22 May 2016, 10:30
I am confused too!
How will I know whether or not to take mods seriously when the correct answer is otherwise!
The question says tis asking us to find the square of three absolute values, not three integers.
Where am i wrong here??
Math Expert
Joined: 02 Aug 2009
Posts: 6559
Re: If x>0, y<0 and z<0, (|x|+|y|+|z|)^2=?  [#permalink]

### Show Tags

22 May 2016, 10:40
2
smritidabas wrote:
chetan2u wrote:
elenap818 wrote:
Are you sure C is the answer?
The question says that y and z are negative, agree. But here we need to find the square of the sm of three absolute values, not three integers. If the question asked for (x+y+z)^2 I would have agreed. But here we have three absolute values which are always positive or equal to zero by definition.
Probably I'm missing something...could you please explain?
Thanks

Hi,
you are correct it will not effect the mod values ..
But the choices are not in mod values but integers, and that i swhy we have to see if the choices match the given conditions..

Hi,
substitute x as 2 and y and z as -1 to check the answer..
If x>0, y<0 and z<0,$$(|x|+|y|+|z|)^2= (2+1+1)^2 = 16$$..

But lets substitute values in A.
$$x^2+y^2+z^2+2xy+2yz+2zx = 2^2+(-1)^2+(-1)^2+2*2*(-1)+2*(-1)*(-1)+2*2*(-1) = 4+1+1-4+2-4=0$$...NOT equal to 16..

lets see C
$$x^2+y^2+z^2-2xy+2yz-2zx = 2^2+(-1)^2+(-1)^2-2*2*(-1)+2*(-1)*(-1)-2*2*(-1) = 4+1+1+4+2+4=16$$... equal to 16..

So C is CORRECT
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Director
Joined: 04 Jun 2016
Posts: 603
GMAT 1: 750 Q49 V43
Re: If x>0, y<0 and z<0, (|x|+|y|+|z|)^2=?  [#permalink]

### Show Tags

25 Jul 2016, 00:32
1
MathRevolution wrote:
If x>0, y<0 and z<0,$$(|x|+|y|+|z|)^2$$=?

A. $$x^2+y^2+z^2+2xy+2yz+2zx$$
B.$$x^2+y^2+z^2+2xy-2yz+2zx$$
C.$$x^2+y^2+z^2-2xy+2yz-2zx$$
D. $$x^2+y^2+z^2-2xy-2yz-2zx$$
E.$$x^2-y^2-z^2+2xy+2yz+2zx$$

* A solution will be posted in two days.
s

Remember that these kind of question can be tricky if you don't apply the last trick after sorting your reasoning.
The reasoning is anything that comes out of mod is always positive . It can not be negative.
But the last part of the trick that many of us forget to apply is to check whether your answers depends on the absolute value (value that comes out of the mod) or on the "raw value" that is the original original value of the integer without the mod (values with original polarity -ve or +ve)

IN THIS QUESTION:- value of y and z are negative
SO the expression $$(|x|+|y|+|z|)^2$$ will always be positive
You don't have to worry about terms with square. because squaring kills negative polarity so x^2, y^2 and z^2 are not our worries.
Now to get a positive value from the options that contains "Raw values" and not the "absolute values" you must remember that x is +ve and y and z are -ve , so if they are multiplied with x their product will be negative. You have to remove that negative polarity . What is the easiest way of removing a negative polarity ? multiply it with -1 or simply -
Therefore all terms that contains either y or z should be multiplied with -1 to give us terms that are positive,
so our answer should contains -2xy and -2xz
Also because -y and -z will multiply to give +yz we don't have to multiply it with -1
finally our expression should look like
$$x^2+y^2+z^2 - 2xy +2yz-2xz$$

THAT IS OPTION C

_________________

Posting an answer without an explanation is "GOD COMPLEX". The world doesn't need any more gods. Please explain you answers properly.
FINAL GOODBYE :- 17th SEPTEMBER 2016. .. 16 March 2017 - I am back but for all purposes please consider me semi-retired.

Non-Human User
Joined: 09 Sep 2013
Posts: 7776
Re: If x>0, y<0 and z<0, (|x|+|y|+|z|)^2=?  [#permalink]

### Show Tags

29 Jul 2018, 02:46
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: If x>0, y<0 and z<0, (|x|+|y|+|z|)^2=? &nbs [#permalink] 29 Jul 2018, 02:46
Display posts from previous: Sort by

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.