If |a+b|=|a-b|, then a*b must be equal to: : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 23 Feb 2017, 20:44

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If |a+b|=|a-b|, then a*b must be equal to:

Author Message
TAGS:

### Hide Tags

Intern
Joined: 02 Jan 2011
Posts: 9
Followers: 0

Kudos [?]: 22 [1] , given: 0

If |a+b|=|a-b|, then a*b must be equal to: [#permalink]

### Show Tags

03 Jul 2012, 20:27
1
KUDOS
8
This post was
BOOKMARKED
00:00

Difficulty:

5% (low)

Question Stats:

88% (01:41) correct 12% (00:52) wrong based on 811 sessions

### HideShow timer Statistics

If |a+b|=|a-b|, then a*b must be equal to:

A. 1
B. -1
C. 0
D. 2
E. -2
[Reveal] Spoiler: OA

Last edited by Bunuel on 04 Jul 2012, 00:35, edited 1 time in total.
Edited the question.
Intern
Joined: 14 Apr 2012
Posts: 11
Followers: 0

Kudos [?]: 3 [0], given: 0

### Show Tags

03 Jul 2012, 20:40
This I solved by trial and error...with a logic that what RHS has (a - b) and LHS has addition of the same terms. So for this to be true one has to be be zero hence answer will be zero.

Regards,
Tushar
Math Expert
Joined: 02 Sep 2009
Posts: 37102
Followers: 7251

Kudos [?]: 96454 [13] , given: 10751

Re: If |a+b|=|a-b|, then a*b must be equal to: [#permalink]

### Show Tags

04 Jul 2012, 00:37
13
KUDOS
Expert's post
11
This post was
BOOKMARKED
If |a+b|=|a-b|, then a*b must be equal to:
A. 1
B. -1
C. 0
D. 2
E. -2

Square both sides: $$(a+b)^2=(a-b)^2$$ --> $$a^2+2ab+b^2=a^2-2ab+b^2$$ --> $$4ab=0$$ --> $$ab=0$$.

Hope it's clear.

_________________
Current Student
Joined: 08 Jan 2009
Posts: 326
GMAT 1: 770 Q50 V46
Followers: 25

Kudos [?]: 137 [1] , given: 7

Re: If |a+b|=|a-b|, then a*b must be equal to: [#permalink]

### Show Tags

04 Jul 2012, 01:47
1
KUDOS
1
This post was
BOOKMARKED
Clearly if $$a$$ or $$b$$ equal zero, $$ab = 0$$

so, let $$b\neq{0}$$
Distance of $$a$$ from $$b$$, equals the distance of $$a$$ from -$$b$$
Draw this on a number line, $$a$$ must equal zero

same logic holds for $$a\neq{0}$$

So either $$a$$ or $$b$$ = 0, $$ab = 0$$

or just solve using our normal absolute value method, two cases:

$$(a+b) = (a-b)$$
$$b = 0$$

$$-(a+b) = (a-b)$$
$$-a-b = a-b$$
$$a = 0$$

so $$ab = 0$$
Intern
Joined: 31 May 2012
Posts: 11
GMAT 1: Q45 V45
GMAT 2: Q51 V46
Followers: 0

Kudos [?]: 10 [0], given: 8

Re: If |a+b|=|a-b|, then a*b must be equal to: [#permalink]

### Show Tags

07 Sep 2012, 12:39
Bunuel,

Can you always just square absolute values like you did on this problem?
I am wondering if squaring is a valid operation on absolute values.
Director
Joined: 22 Mar 2011
Posts: 612
WE: Science (Education)
Followers: 101

Kudos [?]: 910 [1] , given: 43

Re: If |a+b|=|a-b|, then a*b must be equal to: [#permalink]

### Show Tags

07 Sep 2012, 13:48
1
KUDOS
SergeNew wrote:
If |a+b|=|a-b|, then a*b must be equal to:

A. 1
B. -1
C. 0
D. 2
E. -2

If $$b=0$$, the equality obviously holds.
$$|a+b|=|a-b|$$ means the distance between $$a$$ and -$$b$$ is the same as the distance between $$a$$ and $$b$$.
For $$b\neq0,$$ it means that $$a$$ is the average of -$$b$$ and $$b$$ (or the midpoint between -$$b$$ and $$b$$), so necessarily $$a=0.$$
Altogether, the product $$ab$$ must be $$0.$$

_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Math Expert
Joined: 02 Sep 2009
Posts: 37102
Followers: 7251

Kudos [?]: 96454 [1] , given: 10751

Re: If |a+b|=|a-b|, then a*b must be equal to: [#permalink]

### Show Tags

08 Sep 2012, 01:54
1
KUDOS
Expert's post
2
This post was
BOOKMARKED
honggil wrote:
Bunuel,

Can you always just square absolute values like you did on this problem?
I am wondering if squaring is a valid operation on absolute values.

As for inequalities:

A. We can raise both parts of an inequality to an even power if we know that both parts of an inequality are non-negative (the same for taking an even root of both sides of an inequality).
For example:
$$2<4$$ --> we can square both sides and write: $$2^2<4^2$$;
$$0\leq{x}<{y}$$ --> we can square both sides and write: $$x^2<y^2$$;

But if either of side is negative then raising to even power doesn't always work.
For example: $$1>-2$$ if we square we'll get $$1>4$$ which is not right. So if given that $$x>y$$ then we can not square both sides and write $$x^2>y^2$$ if we are not certain that both $$x$$ and $$y$$ are non-negative.

B. We can always raise both parts of an inequality to an odd power (the same for taking an odd root of both sides of an inequality).
For example:
$$-2<-1$$ --> we can raise both sides to third power and write: $$-2^3=-8<-1=-1^3$$ or $$-5<1$$ --> $$-5^2=-125<1=1^3$$;
$$x<y$$ --> we can raise both sides to third power and write: $$x^3<y^3$$.

Hope it helps.
_________________
Director
Joined: 22 Mar 2011
Posts: 612
WE: Science (Education)
Followers: 101

Kudos [?]: 910 [0], given: 43

Re: If |a+b|=|a-b|, then a*b must be equal to: [#permalink]

### Show Tags

08 Sep 2012, 02:26
honggil wrote:
Bunuel,

Can you always just square absolute values like you did on this problem?
I am wondering if squaring is a valid operation on absolute values.

Absolute value is always non-negative, so if you have an equality between two absolute values, either they are both 0 or they are equal to the same positive number. Squared, they still remain equal.
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Current Student
Joined: 25 Jun 2012
Posts: 139
Location: United States
GMAT 1: 700 Q47 V40
GMAT 2: 740 Q48 V44
GPA: 3.48
Followers: 3

Kudos [?]: 19 [1] , given: 18

Re: If |a+b|=|a-b|, then a*b must be equal to: [#permalink]

### Show Tags

08 Sep 2012, 23:59
1
KUDOS
SergeNew wrote:
If |a+b|=|a-b|, then a*b must be equal to:

A. 1
B. -1
C. 0
D. 2
E. -2

I did this problem a little differently. Since both sides have absolute values, I used positives and negatives to get the following four possibilities:

a+b = a-b
a+b = -(a-b)
-(a+b) = a-b
-(a+b) = -(a-b)

Simplifying each equation gets:

b = -b
a = -a
-a = a
-b = b

From there, I concluded that a*b must be zero since the only way a = -a is if a = 0 and the only way b = -b is if b = 0. Did I do this problem incorrectly?
Director
Joined: 22 Mar 2011
Posts: 612
WE: Science (Education)
Followers: 101

Kudos [?]: 910 [0], given: 43

Re: If |a+b|=|a-b|, then a*b must be equal to: [#permalink]

### Show Tags

09 Sep 2012, 05:56
HImba88 wrote:
SergeNew wrote:
If |a+b|=|a-b|, then a*b must be equal to:

A. 1
B. -1
C. 0
D. 2
E. -2

I did this problem a little differently. Since both sides have absolute values, I used positives and negatives to get the following four possibilities:

a+b = a-b
a+b = -(a-b)
-(a+b) = a-b
-(a+b) = -(a-b)

Simplifying each equation gets:

b = -b
a = -a
-a = a
-b = b

From there, I concluded that a*b must be zero since the only way a = -a is if a = 0 and the only way b = -b is if b = 0. Did I do this problem incorrectly?

It is absolutely correct.
Good job!
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Current Student
Joined: 25 Jun 2012
Posts: 139
Location: United States
GMAT 1: 700 Q47 V40
GMAT 2: 740 Q48 V44
GPA: 3.48
Followers: 3

Kudos [?]: 19 [0], given: 18

Re: If |a+b|=|a-b|, then a*b must be equal to: [#permalink]

### Show Tags

09 Sep 2012, 13:14
EvaJager wrote:
HImba88 wrote:
SergeNew wrote:
If |a+b|=|a-b|, then a*b must be equal to:

A. 1
B. -1
C. 0
D. 2
E. -2

I did this problem a little differently. Since both sides have absolute values, I used positives and negatives to get the following four possibilities:

a+b = a-b
a+b = -(a-b)
-(a+b) = a-b
-(a+b) = -(a-b)

Simplifying each equation gets:

b = -b
a = -a
-a = a
-b = b

From there, I concluded that a*b must be zero since the only way a = -a is if a = 0 and the only way b = -b is if b = 0. Did I do this problem incorrectly?

It is absolutely correct.
Good job!

Thanks Eva. I didn't even think initially to square both sides. That way seems much more efficient than the way I approached the problem. Guess my brain is wired differently
Intern
Joined: 27 Aug 2012
Posts: 8
Followers: 0

Kudos [?]: 0 [0], given: 1

Re: If |a+b|=|a-b|, then a*b must be equal to: [#permalink]

### Show Tags

09 Sep 2012, 14:33
I found the right answer. But not sure if the procedure is right
|a+b| = |a-b|

|a| + |b| = |a| -|b|

|b| = -|b| this is possible only with 0. So it is possible in only 2 cases. 1 and 0. But if it is 1, a+b neq to a-b. so b=0 and a*b = 0. Please let me know if this is a right approach.
Current Student
Joined: 25 Jun 2012
Posts: 139
Location: United States
GMAT 1: 700 Q47 V40
GMAT 2: 740 Q48 V44
GPA: 3.48
Followers: 3

Kudos [?]: 19 [0], given: 18

Re: If |a+b|=|a-b|, then a*b must be equal to: [#permalink]

### Show Tags

09 Sep 2012, 15:03
I found the right answer. But not sure if the procedure is right
|a+b| = |a-b|

|a| + |b| = |a| -|b|

|b| = -|b| this is possible only with 0. So it is possible in only 2 cases. 1 and 0. But if it is 1, a+b neq to a-b. so b=0 and a*b = 0. Please let me know if this is a right approach.

Not sure if you can split the absolute value that way. For example:

a = -5
b = 3

|a+b| gets you 2 while |a| + |b| gets you 8.

That approach does get you the correct answer though so I may be incorrect
Intern
Joined: 27 Aug 2012
Posts: 8
Followers: 0

Kudos [?]: 0 [0], given: 1

Re: If |a+b|=|a-b|, then a*b must be equal to: [#permalink]

### Show Tags

09 Sep 2012, 20:30
Then definitely my approach is wrong. But looking at the answer choices we can find that it should be 0.

Posted from my mobile device
Senior Manager
Joined: 13 Aug 2012
Posts: 464
Concentration: Marketing, Finance
GMAT 1: Q V0
GPA: 3.23
Followers: 26

Kudos [?]: 443 [0], given: 11

Re: If |a+b|=|a-b|, then a*b must be equal to: [#permalink]

### Show Tags

05 Dec 2012, 01:04
Solution 1: Distance perspective

|a-b| = |a+b| ==> The distance of a and b is equal to the distance of a and -b.

<=======(-b)=======0=======(b)======>

Only 0 is the value that has a distance equal to b and -b.

Solution 2:

|a-b| = |a+b| (square both)
a^2 -2ab + b^2 = a^2 + 2ab + b^2
4ab = 0
ab = 0

_________________

Impossible is nothing to God.

Senior Manager
Status: Prevent and prepare. Not repent and repair!!
Joined: 13 Feb 2010
Posts: 274
Location: India
Concentration: Technology, General Management
GPA: 3.75
WE: Sales (Telecommunications)
Followers: 9

Kudos [?]: 90 [0], given: 282

Re: If |a+b|=|a-b|, then a*b must be equal to: [#permalink]

### Show Tags

07 Dec 2012, 22:59
Can we plug in nos here? when we plug in random nos we realize that this can be equal only when a*b=0
_________________

I've failed over and over and over again in my life and that is why I succeed--Michael Jordan
Kudos drives a person to better himself every single time. So Pls give it generously
Wont give up till i hit a 700+

Math Expert
Joined: 02 Sep 2009
Posts: 37102
Followers: 7251

Kudos [?]: 96454 [0], given: 10751

Re: If |a+b|=|a-b|, then a*b must be equal to: [#permalink]

### Show Tags

04 Jul 2013, 00:44
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on Abolute Values: math-absolute-value-modulus-86462.html

DS Abolute Values Questions to practice: search.php?search_id=tag&tag_id=37
PS Abolute Values Questions to practice: search.php?search_id=tag&tag_id=58

Hard set on Abolute Values: inequality-and-absolute-value-questions-from-my-collection-86939.html

_________________
Senior Manager
Joined: 17 Dec 2012
Posts: 447
Location: India
Followers: 26

Kudos [?]: 407 [1] , given: 14

Re: If |a+b|=|a-b|, then a*b must be equal to: [#permalink]

### Show Tags

04 Jul 2013, 02:28
1
KUDOS
SergeNew wrote:
If |a+b|=|a-b|, then a*b must be equal to:

A. 1
B. -1
C. 0
D. 2
E. -2

Think the equation without "a". We know that -b and +b are equal in magnitude. We are adding "a" to each. That still doesn't change the equality of the magnitude. That is possible only when 0 is added or "a" is 0. We can say the reverse also and say that to a , we add b and -b and the equality still holds. In this case b is 0. Either a or b is 0. So a*b must be equal to 0.
_________________

Srinivasan Vaidyaraman
Sravna
http://www.sravnatestprep.com

Classroom and Online Coaching

Senior Manager
Joined: 13 May 2013
Posts: 472
Followers: 3

Kudos [?]: 165 [0], given: 134

Re: If |a+b|=|a-b|, then a*b must be equal to: [#permalink]

### Show Tags

09 Jul 2013, 16:02
If |a+b|=|a-b|, then a*b must be equal to:

|a+b|=|a-b|
(a+b)*(a+b) = (a-b)*(a-b)
a^2+2ab+b^2 = a^2-2ab+b^2
4ab=0
In other words, a or b must = 0, therefore, the product of a*b is 0 regardless of what a or b are...one of them is 0.

(C)
Intern
Joined: 23 Aug 2013
Posts: 4
Followers: 0

Kudos [?]: 0 [0], given: 9

Re: If |a+b|=|a-b|, then a*b must be equal to: [#permalink]

### Show Tags

21 Dec 2014, 14:38
I am very noob, please tell me whether this method is wrong or not

|a+b| = |a-b|

Think positive values
so,
a+b = a-b
2b=0 meaning b is 0

or

Think negative, then ,
a+b = - (a-b)
a+b= -a+b
2a=o
a=o

so a*b =0 either way
Re: If |a+b|=|a-b|, then a*b must be equal to:   [#permalink] 21 Dec 2014, 14:38

Go to page    1   2    Next  [ 24 posts ]

Similar topics Replies Last post
Similar
Topics:
If |ab| > ab, which of the following must be true? 2 19 Jan 2017, 19:22
1 If the operation $is defined such that a$b = (a/b)^(ab), what is the 2 07 Jan 2017, 02:52
1 If the operation # is defined such that a#b = (a/b)^(ab), what is the 1 02 Jan 2017, 04:43
2 If (a+b)/(a-b)=55/17 then what is a/b=? 6 06 Dec 2014, 09:32
If b#1, what is the value of a in terms of b if ab/(a-b)=1 ? 1 23 Mar 2012, 07:37
Display posts from previous: Sort by