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

 It is currently 16 Oct 2018, 22:34

### 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 a^6-b^6=0 what is the value of a^3+b^3?

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

### Hide Tags

Manager
Joined: 04 Oct 2013
Posts: 172
GMAT 1: 590 Q40 V30
GMAT 2: 730 Q49 V40
WE: Project Management (Entertainment and Sports)
If a^6-b^6=0 what is the value of a^3+b^3?  [#permalink]

### Show Tags

29 Dec 2013, 07:29
2
6
00:00

Difficulty:

85% (hard)

Question Stats:

46% (01:59) correct 54% (01:49) wrong based on 133 sessions

### HideShow timer Statistics

If $$a^6-b^6=0$$ what is the value of $$a^3+b^3$$?

(1) $$a^3-b^3=-2$$
(2) $$ab<0$$

_________________

learn the rules of the game, then play better than anyone else.

Math Expert
Joined: 02 Sep 2009
Posts: 49916
Re: If a^6-b^6=0 what is the value of a^3+b^3?  [#permalink]

### Show Tags

30 Dec 2013, 01:47
4
2
mrwells2 wrote:
When reverse factoring a^6 - b^6 to (a^3 - b^3) (a^3 + b^3) how do you come to the conclusion that a^3 must equal either b^3 or -b^3 ? Is this a rule that can be applied when factoring any equation? Or just applicable because the equation is = 0 ?

Does Statement #2 verify the assumption that a^3 = -b^3 ?

Additionally, how can you be certain on statement 2 alone? Is it because (a^3 - b^3) = positive number assuming a = -b^3 and a is positive. then (a^3 + b^3) = zero, assuming a = -b^3 and a is positive ?

[EDIT]

Based on statement two you can infer that a is positive and that b is negative.

Therefore (a^3 -(-b)^3) = positive number or 2(a)^3.

And that (a^3 + (-b)^3) = 0 ?

If $$a^6-b^6=0$$ what is the value of $$a^3+b^3$$?

$$a^6-b^6=0$$ --> apply $$x^2-y^2=(x-y)(x+y)$$: $$(a^3-b^3)(a^3+b^3)=0$$ --> the product of two multiples is 0, which implies that at least one of them must be 0: $$a^3-b^3=0$$ ($$a^3=b^3$$ --> $$a=b$$) or $$a^3+b^3=0$$.

(1) $$a^3-b^3=-2$$. Since $$a^3-b^3\neq{0}$$, then $$a^3+b^3=0$$. Sufficient.

(2) $$ab<0$$. This implies that a and b have opposite signs, thus $$a\neq{b}$$ ($$a^3-b^3\neq{0}$$). Therefore $$a^3+b^3=0$$. Sufficient.

Hope it's clear.
_________________
##### General Discussion
Manager
Joined: 04 Oct 2013
Posts: 172
GMAT 1: 590 Q40 V30
GMAT 2: 730 Q49 V40
WE: Project Management (Entertainment and Sports)
Re: If a^6-b^6=0 what is the value of a^3+b^3?  [#permalink]

### Show Tags

29 Dec 2013, 07:29
let's rephrase $$a^6-b^6=0$$ is equal to $$(a^3-b^3)(a^3+b^3)=0$$ and thus either $$a^3=b^3$$ or $$a^3=-b^3$$ or both.

1. $$a^3-b^3=-2$$ thus for $$(a^3-b^3)(a^3+b^3)=0$$ to be zero $$(a^3+b^3)=0$$
Sufficient.

2. ab<0 a and b have opposite sign thus $$a^3-b^3=0$$
Sufficient.

D
_________________

learn the rules of the game, then play better than anyone else.

Manager
Joined: 26 May 2013
Posts: 95
Re: If a^6-b^6=0 what is the value of a^3+b^3?  [#permalink]

### Show Tags

29 Dec 2013, 14:19
1
When reverse factoring a^6 - b^6 to (a^3 - b^3) (a^3 + b^3) how do you come to the conclusion that a^3 must equal either b^3 or -b^3 ? Is this a rule that can be applied when factoring any equation? Or just applicable because the equation is = 0 ?

Does Statement #2 verify the assumption that a^3 = -b^3 ?

Additionally, how can you be certain on statement 2 alone? Is it because (a^3 - b^3) = positive number assuming a = -b^3 and a is positive. then (a^3 + b^3) = zero, assuming a = -b^3 and a is positive ?

[EDIT]

Based on statement two you can infer that a is positive and that b is negative.

Therefore (a^3 -(-b)^3) = positive number or 2(a)^3.

And that (a^3 + (-b)^3) = 0 ?
Manager
Joined: 04 Oct 2013
Posts: 172
GMAT 1: 590 Q40 V30
GMAT 2: 730 Q49 V40
WE: Project Management (Entertainment and Sports)
Re: If a^6-b^6=0 what is the value of a^3+b^3?  [#permalink]

### Show Tags

30 Dec 2013, 01:55
1
mrwells2 wrote:
When reverse factoring a^6 - b^6 to (a^3 - b^3) (a^3 + b^3) how do you come to the conclusion that a^3 must equal either b^3 or -b^3 ? Is this a rule that can be applied when factoring any equation? Or just applicable because the equation is = 0 ?

the equation equals to zero whenever that happen... it's like having (x-3)(x+2)=0 the equation yields zero when x=3 [(3-3)(3+2)=0] or when x=-2 (plug in) here we are doing the same thing but with letters. In particular whenever $$a^3=|b^3|$$ then our equation will hold true because the result will be zero.

mrwells2 wrote:
Does Statement #2 verify the assumption that a^3 = -b^3 ?

statement two says that a and b have opposit sign, refer back to our two solutions and check what happens whenever a and b have opposite sign (odd exponents don't hide the sign).
If $$a^3=-b^3 ------> a^3+b^3=0 ------> (a^3-b^3)(0)=0$$ the equation is valid.

mrwells2 wrote:
Based on statement two you can infer that a is positive and that b is negative.

Therefore (a^3 -(-b)^3) = positive number or 2(a)^3.

And that (a^3 + (-b)^3) = 0 ?

it doesn't necessarely have to be b the negative one. ab<0 case1: a=-ve b=+ve case2: a=+ve b=-ve (and viceversa)
ab<0 tells us that the variables have opposite sign and that they are different from zero.

Hope it shoves some haze away. Let me know.
_________________

learn the rules of the game, then play better than anyone else.

Manager
Joined: 04 Oct 2013
Posts: 154
Location: India
GMAT Date: 05-23-2015
GPA: 3.45
Re: If a^6-b^6=0 what is the value of a^3+b^3?  [#permalink]

### Show Tags

31 Dec 2013, 10:00
If a^6-b^6=0 what is the value of a^3+b^3?

(1) a^3-b^3=-2
(2) ab<0

Given, $$a^6 - b^6 = 0$$

Statement I:

$$a^6 - b^6 = 0$$

Or, $$(a ^ 3 - b^3) (a ^ 3 + b^3) = 0$$

As per statement (1), $$a^3-b^3=-2$$ , hence $$(a ^ 3 + b^3) = 0$$ to make $$a^6 - b^6 = 0$$

Hence, statement (1) sufficient.

Statement 2:

$$a^6 - b^6 = 0$$

Or, $$a ^ 6 = b ^ 6$$

Or, $$(a^3) (a ^3) = (b^3)(b^3)$$ ....(A)

As per statement 2, $$ab<0$$
Or, a and b are of opposite sign
Or, a ^3 and b ^3 are of opposite sign ...(B)

From (A) & (B) above, $$(a^3) = - (b^3)$$
Or, $$a^3 + b^3 = 0$$

Hence, statement (2) sufficient.

Intern
Joined: 11 Nov 2017
Posts: 12
Re: If a^6-b^6=0 what is the value of a^3+b^3?  [#permalink]

### Show Tags

21 Nov 2017, 13:49
gmat6nplus1 wrote:
let's rephrase $$a^6-b^6=0$$ is equal to $$(a^3-b^3)(a^3+b^3)=0$$ and thus either $$a^3=b^3$$ or $$a^3=-b^3$$ or both.

1. $$a^3-b^3=-2$$ thus for $$(a^3-b^3)(a^3+b^3)=0$$ to be zero $$(a^3+b^3)=0$$
Sufficient.

2. ab<0 a and b have opposite sign thus $$a^3-b^3=0$$
Sufficient.

D

For the second statement, if ab<0 then a^3+b^3=0 not the other factor.

Cheers,
_________________

Cheers.

Never gonna give up!!!!

Re: If a^6-b^6=0 what is the value of a^3+b^3? &nbs [#permalink] 21 Nov 2017, 13:49
Display posts from previous: Sort by

# If a^6-b^6=0 what is the value of a^3+b^3?

 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®.