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# If the sum of the cubes of a and b is 8 and a^6 – b^6 = 14, what is th

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Math Expert
Joined: 02 Sep 2009
Posts: 45225
If the sum of the cubes of a and b is 8 and a^6 – b^6 = 14, what is th [#permalink]

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05 Nov 2014, 08:16
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Difficulty:

5% (low)

Question Stats:

86% (01:00) correct 14% (01:31) wrong based on 94 sessions

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Tough and Tricky questions: Word Problems.

If the sum of the cubes of a and b is 8 and a^6 – b^6 = 14, what is the value of a^3 – b^3?

A. 1/4
B. 1/2
C. 5/4
D. 7/4
E. 2

Kudos for a correct solution.

_________________
Senior Manager
Joined: 13 Jun 2013
Posts: 277
Re: If the sum of the cubes of a and b is 8 and a^6 – b^6 = 14, what is th [#permalink]

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06 Nov 2014, 02:06
1
KUDOS
Bunuel wrote:

Tough and Tricky questions: Word Problems.

If the sum of the cubes of a and b is 8 and a^6 – b^6 = 14, what is the value of a^3 – b^3?

A. 1/4
B. 1/2
C. 5/4
D. 7/4
E. 2

Kudos for a correct solution.

a^3 + b^3 =8 ---------------1)

(a^3)^2-(b^3)^2=14

we know that a^2-b^2 = (a-b)(a+b)
thus
(a^3+b^3)(a^3-b^3) =14
using 1, we have

a^3 - b^3 = 14/8
=7/4
Intern
Joined: 10 Jul 2014
Posts: 42
Concentration: Technology, Strategy
Re: If the sum of the cubes of a and b is 8 and a^6 – b^6 = 14, what is th [#permalink]

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06 Nov 2014, 15:19
1
KUDOS
Bunuel wrote:

Tough and Tricky questions: Word Problems.

If the sum of the cubes of a and b is 8 and a^6 – b^6 = 14, what is the value of a^3 – b^3?

A. 1/4
B. 1/2
C. 5/4
D. 7/4
E. 2

Kudos for a correct solution.

Give that $$a^3 + b^3 = 8$$
and
$$a^6 - b^6 = 14$$

Solve left hand side:
$$(a^3)^2 - (b^3)^2 = 14$$

This is in form $$a^2-b^2$$. Hence: $$(a^3+b^3) (a^3-b^3) = 14$$

$$8 (a^3-b^3) = 14$$

$$(a^3-b^3)=$$ 14/8 = 7/4

Manager
Status: I am not a product of my circumstances. I am a product of my decisions
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Posts: 128
Location: India
Concentration: Operations, General Management
GPA: 3.92
WE: Operations (Energy and Utilities)
Re: If the sum of the cubes of a and b is 8 and a^6 – b^6 = 14, what is th [#permalink]

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06 Nov 2014, 20:41
2
KUDOS
Bunuel wrote:

Tough and Tricky questions: Word Problems.

If the sum of the cubes of a and b is 8 and a^6 – b^6 = 14, what is the value of a^3 – b^3?

A. 1/4
B. 1/2
C. 5/4
D. 7/4
E. 2

Kudos for a correct solution.

Given :
$$a^3 + b^3 = 8$$ and $$a^6 - b^6 = 14$$

$$a^6 - b^6 = (a^3)^2 - (b^3)^2$$
$$a^6 - b^6 = (a^3 - b^3) (a^3 + b^3)$$

$$14 = (a^3 - b^3) 8$$

$$(a^3 - b^3) = 7/4$$

Director
Joined: 12 Nov 2016
Posts: 778
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: 315 Q157 V158
GPA: 2.66
Re: If the sum of the cubes of a and b is 8 and a^6 – b^6 = 14, what is th [#permalink]

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31 Aug 2017, 17:46
Bunuel wrote:

Tough and Tricky questions: Word Problems.

If the sum of the cubes of a and b is 8 and a^6 – b^6 = 14, what is the value of a^3 – b^3?

A. 1/4
B. 1/2
C. 5/4
D. 7/4
E. 2

Kudos for a correct solution.

this is just another a sub b question-

(a-b)(a+b) = a^2-b^2

(a^3+b^3)(a^3-b^3)= a^6-b^6= 14

8(a^3-b^3)= 14

(a^3-b^3) = 14/8

d
Re: If the sum of the cubes of a and b is 8 and a^6 – b^6 = 14, what is th   [#permalink] 31 Aug 2017, 17:46
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