It is currently 18 Oct 2017, 02:39

### 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
Your Progress

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:

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Intern
Joined: 02 Jan 2011
Posts: 9

Kudos [?]: 27 [1], given: 0

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

### Show Tags

03 Jul 2012, 21:27
1
This post received
KUDOS
12
This post was
BOOKMARKED
00:00

Difficulty:

5% (low)

Question Stats:

87% (00:41) correct 13% (00:52) wrong based on 970 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, 01:35, edited 1 time in total.
Edited the question.

Kudos [?]: 27 [1], given: 0

Math Expert
Joined: 02 Sep 2009
Posts: 41886

Kudos [?]: 128668 [15], given: 12181

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

### Show Tags

04 Jul 2012, 01:37
15
This post received
KUDOS
Expert's post
16
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: $$(a+b)^2=(a-b)^2$$ --> $$a^2+2ab+b^2=a^2-2ab+b^2$$ --> $$4ab=0$$ --> $$ab=0$$.

Answer: C.

Hope it's clear.

P.S. Please read and follow: rules-for-posting-please-read-this-before-posting-133935.html
_________________

Kudos [?]: 128668 [15], given: 12181

Current Student
Joined: 08 Jan 2009
Posts: 323

Kudos [?]: 158 [1], given: 7

GMAT 1: 770 Q50 V46
Re: If |a+b|=|a-b|, then a*b must be equal to: [#permalink]

### Show Tags

04 Jul 2012, 02:47
1
This post received
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 $$ab = 0$$

Kudos [?]: 158 [1], given: 7

Director
Joined: 22 Mar 2011
Posts: 610

Kudos [?]: 1057 [1], given: 43

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

### Show Tags

07 Sep 2012, 14:48
1
This post received
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 $$0.$$

Answer C
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Kudos [?]: 1057 [1], given: 43

Math Expert
Joined: 02 Sep 2009
Posts: 41886

Kudos [?]: 128668 [1], given: 12181

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

### Show Tags

08 Sep 2012, 02:54
1
This post received
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.

Check this post: elimination-of-radials-confused-138409.html

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.
_________________

Kudos [?]: 128668 [1], given: 12181

Current Student
Joined: 25 Jun 2012
Posts: 141

Kudos [?]: 20 [1], given: 18

Location: United States
GMAT 1: 700 Q47 V40
GMAT 2: 740 Q48 V44
GPA: 3.48
Re: If |a+b|=|a-b|, then a*b must be equal to: [#permalink]

### Show Tags

09 Sep 2012, 00:59
1
This post received
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?

Kudos [?]: 20 [1], given: 18

Director
Joined: 17 Dec 2012
Posts: 608

Kudos [?]: 516 [1], given: 16

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

### Show Tags

04 Jul 2013, 03:28
1
This post received
KUDOS
Expert's post
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/regularcourse.php

Pay After Use
Standardized Approaches

Kudos [?]: 516 [1], given: 16

Intern
Joined: 14 Apr 2012
Posts: 11

Kudos [?]: 5 [0], given: 0

Re: Absolute number. [#permalink]

### Show Tags

03 Jul 2012, 21:40
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

Kudos [?]: 5 [0], given: 0

Intern
Joined: 31 May 2012
Posts: 11

Kudos [?]: 13 [0], given: 8

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

### Show Tags

07 Sep 2012, 13:39
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.

Kudos [?]: 13 [0], given: 8

Director
Joined: 22 Mar 2011
Posts: 610

Kudos [?]: 1057 [0], given: 43

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

### Show Tags

08 Sep 2012, 03:26
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.

Kudos [?]: 1057 [0], given: 43

Director
Joined: 22 Mar 2011
Posts: 610

Kudos [?]: 1057 [0], given: 43

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

### Show Tags

09 Sep 2012, 06:56
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.

Kudos [?]: 1057 [0], given: 43

Current Student
Joined: 25 Jun 2012
Posts: 141

Kudos [?]: 20 [0], given: 18

Location: United States
GMAT 1: 700 Q47 V40
GMAT 2: 740 Q48 V44
GPA: 3.48
Re: If |a+b|=|a-b|, then a*b must be equal to: [#permalink]

### Show Tags

09 Sep 2012, 14:14
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

Kudos [?]: 20 [0], given: 18

Intern
Joined: 27 Aug 2012
Posts: 6

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

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

### Show Tags

09 Sep 2012, 15:33
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.

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

Current Student
Joined: 25 Jun 2012
Posts: 141

Kudos [?]: 20 [0], given: 18

Location: United States
GMAT 1: 700 Q47 V40
GMAT 2: 740 Q48 V44
GPA: 3.48
Re: If |a+b|=|a-b|, then a*b must be equal to: [#permalink]

### Show Tags

09 Sep 2012, 16:03
ravipprasad wrote:
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

Kudos [?]: 20 [0], given: 18

Intern
Joined: 27 Aug 2012
Posts: 6

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

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

### Show Tags

09 Sep 2012, 21:30
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

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

Senior Manager
Joined: 13 Aug 2012
Posts: 458

Kudos [?]: 540 [0], given: 11

Concentration: Marketing, Finance
GPA: 3.23
Re: If |a+b|=|a-b|, then a*b must be equal to: [#permalink]

### Show Tags

05 Dec 2012, 02:04
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

Answer: 0
_________________

Impossible is nothing to God.

Kudos [?]: 540 [0], given: 11

Senior Manager
Status: Prevent and prepare. Not repent and repair!!
Joined: 13 Feb 2010
Posts: 253

Kudos [?]: 124 [0], given: 282

Location: India
Concentration: Technology, General Management
GPA: 3.75
WE: Sales (Telecommunications)
Re: If |a+b|=|a-b|, then a*b must be equal to: [#permalink]

### Show Tags

07 Dec 2012, 23:59
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+

Kudos [?]: 124 [0], given: 282

Math Expert
Joined: 02 Sep 2009
Posts: 41886

Kudos [?]: 128668 [0], given: 12181

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

### Show Tags

04 Jul 2013, 01:44
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

_________________

Kudos [?]: 128668 [0], given: 12181

Senior Manager
Joined: 13 May 2013
Posts: 463

Kudos [?]: 197 [0], given: 134

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

### Show Tags

09 Jul 2013, 17:02
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)

Kudos [?]: 197 [0], given: 134

Intern
Joined: 23 Aug 2013
Posts: 4

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

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

### Show Tags

21 Dec 2014, 15:38
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

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

Re: If |a+b|=|a-b|, then a*b must be equal to:   [#permalink] 21 Dec 2014, 15:38

Go to page    1   2    Next  [ 25 posts ]

Display posts from previous: Sort by

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 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®.