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

 It is currently 19 Mar 2019, 20:14

### 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

# What is the value of a^3+b^3 ?

Author Message
TAGS:

### Hide Tags

GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 902
What is the value of a^3+b^3 ?  [#permalink]

### Show Tags

14 Feb 2019, 13:12
00:00

Difficulty:

55% (hard)

Question Stats:

57% (01:41) correct 43% (01:29) wrong based on 28 sessions

### HideShow timer Statistics

GMATH practice exercise (Quant Class 14)

What is the value of $${a^3} + {b^3}$$ ?

$$\left( 1 \right)\,\,a + b = 1$$
$$\left( 2 \right)\,\,{a^2} + {b^2} = 2$$

_________________

Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net

Senior Manager
Joined: 04 Aug 2010
Posts: 383
Schools: Dartmouth College
Re: What is the value of a^3+b^3 ?  [#permalink]

### Show Tags

14 Feb 2019, 14:58
1
fskilnik wrote:
GMATH practice exercise (Quant Class 14)

What is the value of $${a^3} + {b^3}$$ ?

$$\left( 1 \right)\,\,a + b = 1$$
$$\left( 2 \right)\,\,{a^2} + {b^2} = 2$$

Statement 1:
Case 1: a=0 and b=1, with the result that a+b = 0+1 = 1
In this case, a³+b³ = 0³ + 1³ = 1
Case 2: a=2 and b=-1, with the result that a+b = 2-1 = 1
In this case, a³+b³ = 2³ + (-1)³ = 7
Since a³+b³ can be different values, INSUFFICIENT.

Statement 2:
Case 3: a=1 and b=1, with the result that a²+b² = 1²+1² = 2
In this case, a³+b³ = 1³ + 1³ = 2
Case 4: a=-1 and b=-1, with the result that a²+b² = (-1)²+(-1)² = 2
In this case, a³+b³ = (-1)³ + (-1)³ = -2
Since a³+b³ can be different values, INSUFFICIENT.

Statements combined:
Squaring a+b = 1, we get:
a² + b² + 2ab = 1

Substituting a²+b²=2 into the red equation above, we get:
2 + 2ab = 1
2ab = -1
ab = -0.5

Multiplying a²+b²=2 by a+b=1, we get:
(a²+b²)(a+b) = 2*1
a³ + b³ + a²b + ab² = 2
a³ + b³ + ab(a+b) = 2

Substituting ab=-0.5 and a+b=1 into the blue equation above, we get:
a³ + b³ + (-0.5)(1) = 2
a³ + b³ = 2.5
SUFFICIENT.

_________________

GMAT and GRE Tutor
Over 1800 followers
GMATGuruNY@gmail.com
New York, NY
If you find one of my posts helpful, please take a moment to click on the "Kudos" icon.
Available for tutoring in NYC and long-distance.

GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 902
Re: What is the value of a^3+b^3 ?  [#permalink]

### Show Tags

14 Feb 2019, 18:35
fskilnik wrote:
GMATH practice exercise (Quant Class 14)

What is the value of $${a^3} + {b^3}$$ ?

$$\left( 1 \right)\,\,a + b = 1$$
$$\left( 2 \right)\,\,{a^2} + {b^2} = 2$$

$$? = {a^3} + {b^3}$$

$$\left( 1 \right)\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {a,b} \right) = \left( {1,0} \right)\,\,\,\, \Rightarrow \,\,\,? = 1 \hfill \cr \,{\rm{Take}}\,\left( {a,b} \right) = \left( {2, - 1} \right)\,\,\,\, \Rightarrow \,\,\,? \ne 1 \hfill \cr} \right.$$

$$\left( 2 \right)\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {a,b} \right) = \left( {1,1} \right)\,\,\,\, \Rightarrow \,\,\,? = 2 \hfill \cr \,{\rm{Take}}\,\left( {a,b} \right) = \left( {\sqrt 2 ,0} \right)\,\,\,\, \Rightarrow \,\,\,? \ne 2 \hfill \cr} \right.$$

$$\left( {1 + 2} \right)\,\,\,2 = \left( {a + b} \right)\left( {{a^2} + {b^2}} \right) = \underbrace {{a^3} + {b^3}}_{{\rm{focus}}} + ab\underbrace {\left( {a + b} \right)}_{ = \,1}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{?_{{\rm{temporary}}}} = ab$$

$$\left\{ \matrix{ \,{1^2} = {\left( {a + b} \right)^2} = {a^2} + 2ab + {b^2} \hfill \cr \,2 = {a^2} + {b^2} \hfill \cr} \right.\,\,\,\,\,\mathop \Rightarrow \limits^{\left( - \right)} \,\,\,2ab = - 1\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{?_{{\rm{temporary}}}}\,\,{\rm{unique}}\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}.$$

We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________

Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net

Re: What is the value of a^3+b^3 ?   [#permalink] 14 Feb 2019, 18:35
Display posts from previous: Sort by