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

 It is currently 17 Aug 2019, 13:51 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. ### Request Expert Reply # Is |a^2 - b^2| < 10? (1) |a - b| < 5 (2) |a + b| < 2

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

### Hide Tags

Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7728
GMAT 1: 760 Q51 V42 GPA: 3.82
Is |a^2 - b^2| < 10? (1) |a - b| < 5 (2) |a + b| < 2  [#permalink]

### Show Tags 00:00

Difficulty:   45% (medium)

Question Stats: 61% (01:36) correct 39% (01:50) wrong based on 147 sessions

### HideShow timer Statistics

Is |a^2 - b^2| < 10?

(1) |a - b| < 5
(2) |a + b| < 2

*An answer will be posted in 2 days.

_________________
Manager  B
Joined: 06 Aug 2015
Posts: 55
Concentration: General Management, Entrepreneurship
GMAT Date: 10-30-2016
GRE 1: Q160 V135 GPA: 3.34
WE: Programming (Consulting)
Re: Is |a^2 - b^2| < 10? (1) |a - b| < 5 (2) |a + b| < 2  [#permalink]

### Show Tags

1
My Answer is C)

Below is my explanation, Please feel free to correct me, if wrong.
given |(a+b)(a-b)| < 10 --> A

a) |a-b| < 5
Let a = 10 , b = 7 : Above eq A is not satisfied
a = 3 , b = -2 : Above eq A is satisfied
Therefore, Not Suff.

b) |a+b| <2
If a = 1, b = 1/2 : Eq A is satisfied
a = 10 , b = -9 : Eq A is not satisfied.
Therefore, Not Suff.

a + b => Sufficient. Hence, C
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7728
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Is |a^2 - b^2| < 10? (1) |a - b| < 5 (2) |a + b| < 2  [#permalink]

### Show Tags

Since there are 2 variables in the original condition, the correct answer is C.

- Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.
_________________
Intern  Joined: 16 Jul 2016
Posts: 4
Re: Is |a^2 - b^2| < 10? (1) |a - b| < 5 (2) |a + b| < 2  [#permalink]

### Show Tags

Could I seperate the equation |(a+b)(a-b)|<10 as |a+b|*|a-b|<10?
Board of Directors V
Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3605
Re: Is |a^2 - b^2| < 10? (1) |a - b| < 5 (2) |a + b| < 2  [#permalink]

### Show Tags

1
tinalongmao wrote:
Could I seperate the equation |(a+b)(a-b)|<10 as |a+b|*|a-b|<10?

Yes, you could.

Remember, Product and Division in absolute values could be separated.

I mean if we have |a/b|, we can write it as |a|/|b|

or |a*b|=|a|*|b|
_________________
My GMAT Story: From V21 to V40
My MBA Journey: My 10 years long MBA Dream
My Secret Hacks: Best way to use GMATClub | Importance of an Error Log!
Verbal Resources: All SC Resources at one place | All CR Resources at one place

GMAT Club Inbuilt Error Log Functionality - View More.
New Visa Forum - Ask all your Visa Related Questions - here.
New! Best Reply Functionality on GMAT Club!
Find a bug in the new email templates and get rewarded with 2 weeks of GMATClub Tests for free
Check our new About Us Page here.
SC Moderator P
Status: GMAT - Pulling Quant and Verbal together
Joined: 04 Sep 2017
Posts: 215
Location: United States (OH)
Concentration: Technology, Leadership
GPA: 3.6
WE: Sales (Computer Software)
Re: Is |a^2 - b^2| < 10? (1) |a - b| < 5 (2) |a + b| < 2  [#permalink]

### Show Tags

MathRevolution wrote:
Is |a^2-b^2|<10?
1) |a-b|<5
2) |a+b|<2

*An answer will be posted in 2 days.

I am struggling on this one. I understand that Statement 1 and Statement 2 are Not Sufficient. But I am not sure how to combine them algebraically and solve for statement 1 and statement 2 together. Can someone please show how to do this or an easier way to solve this?

Thanks,
_________________
Would I rather be feared or loved? Easy. Both. I want people to be afraid of how much they love me.

How to sort questions by Topic, Difficulty, and Source:
https://gmatclub.com/forum/search.php?view=search_tags
Math Expert V
Joined: 02 Sep 2009
Posts: 57025
Re: Is |a^2 - b^2| < 10? (1) |a - b| < 5 (2) |a + b| < 2  [#permalink]

### Show Tags

msurls wrote:
MathRevolution wrote:
Is |a^2-b^2|<10?
1) |a-b|<5
2) |a+b|<2

*An answer will be posted in 2 days.

I am struggling on this one. I understand that Statement 1 and Statement 2 are Not Sufficient. But I am not sure how to combine them algebraically and solve for statement 1 and statement 2 together. Can someone please show how to do this or an easier way to solve this?

Thanks,

Is |a^2 - b^2| < 10?

(1) |a - b| < 5.

If a = b = 0, then the answer to the question is YES.
If a = 4 and b = 0, then the answer to the question is NO.

Not sufficient.

(2) |a + b| < 2

If a = b = 0, then the answer to the question is YES.
If a = 10 and b = -9, then the answer to the question is NO.

Not sufficient.

(1)+(2) Notice that |xy| = |x|*|y|, so the question asks whether |a^2 - b^2| = |(a - b)(a + b)| = |a - b|*|a + b| is less than 10. From (1) we have that 0 <= |a - b| < 5 and From (2) we have that 0 <= |a + b| < 2. Their product will be less than 10: 0 <= |a - b|*|a + b| < 10. Sufficient.

Answer: C.

Hope it's clear.
_________________
Intern  B
Joined: 11 Feb 2018
Posts: 34
Is |a^2 - b^2| < 10? (1) |a - b| < 5 (2) |a + b| < 2  [#permalink]

### Show Tags

Bunuel wrote:
msurls wrote:
MathRevolution wrote:
Is |a^2-b^2|<10?
1) |a-b|<5
2) |a+b|<2

*An answer will be posted in 2 days.

I am struggling on this one. I understand that Statement 1 and Statement 2 are Not Sufficient. But I am not sure how to combine them algebraically and solve for statement 1 and statement 2 together. Can someone please show how to do this or an easier way to solve this?

Thanks,

Is |a^2 - b^2| < 10?

(1) |a - b| < 5.

If a = b = 0, then the answer to the question is YES.
If a = 4 and b = 0, then the answer to the question is NO.

Not sufficient.

(2) |a + b| < 2

If a = b = 0, then the answer to the question is YES.
If a = 10 and b = -9, then the answer to the question is NO.

Not sufficient.

(1)+(2) Notice that |xy| = |x|*|y|, so the question asks whether |a^2 - b^2| = |(a - b)(a + b)| = |a - b|*|a + b| is less than 10. From (1) we have that 0 <= |a - b| < 5 and From (2) we have that 0 <= |a + b| < 2. Their product will be less than 10: 0 <= |a - b|*|a + b| < 10. Sufficient.

Answer: C.

Hope it's clear.

Can we write |xy| = |x|*|y|, isn't it fundamentally wrong
Board of Directors V
Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3605
Re: Is |a^2 - b^2| < 10? (1) |a - b| < 5 (2) |a + b| < 2  [#permalink]

### Show Tags

cruiseav wrote:
We cannot write |xy| = |x|*|y|, it is fundamentally wrong

We can always do so. It is absolutely correct.

Check my comments here: https://gmatclub.com/forum/is-a-2-b-2-1 ... l#p1711648
_________________
My GMAT Story: From V21 to V40
My MBA Journey: My 10 years long MBA Dream
My Secret Hacks: Best way to use GMATClub | Importance of an Error Log!
Verbal Resources: All SC Resources at one place | All CR Resources at one place

GMAT Club Inbuilt Error Log Functionality - View More.
New Visa Forum - Ask all your Visa Related Questions - here.
New! Best Reply Functionality on GMAT Club!
Find a bug in the new email templates and get rewarded with 2 weeks of GMATClub Tests for free
Check our new About Us Page here.
Math Expert V
Joined: 02 Sep 2009
Posts: 57025
Re: Is |a^2 - b^2| < 10? (1) |a - b| < 5 (2) |a + b| < 2  [#permalink]

### Show Tags

cruiseav wrote:
Bunuel wrote:
msurls wrote:
I am struggling on this one. I understand that Statement 1 and Statement 2 are Not Sufficient. But I am not sure how to combine them algebraically and solve for statement 1 and statement 2 together. Can someone please show how to do this or an easier way to solve this?

Thanks,

Is |a^2 - b^2| < 10?

(1) |a - b| < 5.

If a = b = 0, then the answer to the question is YES.
If a = 4 and b = 0, then the answer to the question is NO.

Not sufficient.

(2) |a + b| < 2

If a = b = 0, then the answer to the question is YES.
If a = 10 and b = -9, then the answer to the question is NO.

Not sufficient.

(1)+(2) Notice that |xy| = |x|*|y|, so the question asks whether |a^2 - b^2| = |(a - b)(a + b)| = |a - b|*|a + b| is less than 10. From (1) we have that 0 <= |a - b| < 5 and From (2) we have that 0 <= |a + b| < 2. Their product will be less than 10: 0 <= |a - b|*|a + b| < 10. Sufficient.

Answer: C.

Hope it's clear.

Can we write |xy| = |x|*|y|, isn't it fundamentally wrong

Yes, we can. Why do you say that? In mathematics it's called multiplicativity: |xy| = |x|*|y| is true for all numbers x and y.
_________________
Intern  B
Joined: 31 Oct 2018
Posts: 16
WE: Research (Hospitality and Tourism)
Re: Is |a^2 - b^2| < 10? (1) |a - b| < 5 (2) |a + b| < 2  [#permalink]

### Show Tags

Bunuel wrote:
msurls wrote:
MathRevolution wrote:
Is |a^2-b^2|<10?
1) |a-b|<5
2) |a+b|<2

*An answer will be posted in 2 days.

I am struggling on this one. I understand that Statement 1 and Statement 2 are Not Sufficient. But I am not sure how to combine them algebraically and solve for statement 1 and statement 2 together. Can someone please show how to do this or an easier way to solve this?

Thanks,

Is |a^2 - b^2| < 10?

(1) |a - b| < 5.

If a = b = 0, then the answer to the question is YES.
If a = 4 and b = 0, then the answer to the question is NO.

Not sufficient.

(2) |a + b| < 2

If a = b = 0, then the answer to the question is YES.
If a = 10 and b = -9, then the answer to the question is NO.

Not sufficient.

(1)+(2) Notice that |xy| = |x|*|y|, so the question asks whether |a^2 - b^2| = |(a - b)(a + b)| = |a - b|*|a + b| is less than 10. From (1) we have that 0 <= |a - b| < 5 and From (2) we have that 0 <= |a + b| < 2. Their product will be less than 10: 0 <= |a - b|*|a + b| < 10. Sufficient.

Answer: C.

Hope it's clear.

Bunuel

1) |a-b|<5
2) |a+b|<2

Can you multiply 1 and 2 and retain the inequality because LHS and RHS are both positive so no question of sign change?
if yes then |a-b| |a+b| < 10---> |a2-b2| < 10..Is this true? Re: Is |a^2 - b^2| < 10? (1) |a - b| < 5 (2) |a + b| < 2   [#permalink] 08 Aug 2019, 13:12
Display posts from previous: Sort by

# Is |a^2 - b^2| < 10? (1) |a - b| < 5 (2) |a + b| < 2

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

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

#### MBA Resources  