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by GMATGuruNY » Fri Sep 04, 2015 4:55 am
oquiella wrote:If the sum of the cubes of a and b is 8 and a6 - b6 = 14, what is the value of a3?


7/4

23/6

39/8

6

22/3
a� - b� = (a³ + b³)(a³ - b³).

Since a� - b� = 14 and a³ + b³ = 8, we get:
14 = 8(a³ - b³)
14/8 = a³ - b³.
7/4 = a³ - b³

Adding together a³ - b³ = 7/4 and a³ + b³ = 8, we get:
(a³ - b³) + (a³ + b³) = 7/4 + 8
2a³ = 39/4
a³ = 39/8.

The correct answer is C.
Last edited by GMATGuruNY on Fri Sep 04, 2015 9:53 am, edited 1 time in total.
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by oquiella » Fri Sep 04, 2015 9:18 am
GMATGuruNY wrote:
oquiella wrote:If the sum of the cubes of a and b is 8 and a6 - b6 = 14, what is the value of a3?


7/4

23/6

39/8

6

22/3
a� - b� = (a³ + b³)(a³ - b³).

Since a� - b� = 14 and a³ - b³ = 8, we get:
14 = (a³ + b³)(8)
14/8 = a³ + b³.
7/4 = a³ + b³

Adding together a³ + b³ = 7/4 and a³ - b³ = 8, we get:
(a³ + b³) + (a³ - b³) = 7/4 + 8
2a³ = 39/4
a³ = 39/8.

The correct answer is C.


How did you get a³ - b³ = 8 if the question states "the sum of the cubes of a and b is 8"?
Im a little confused
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by GMATGuruNY » Fri Sep 04, 2015 10:03 am
oquiella wrote: How did you get a³ - b³ = 8 if the question states "the sum of the cubes of a and b is 8"?
Im a little confused
Good catch. My post above had some typos, which have since been corrected.
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by Matt@VeritasPrep » Fri Sep 04, 2015 5:32 pm
Another way of breaking this down:

(a³ + b³) = 8
a� - b� = (a³ + b³)(a³ - b³) = 14

so (a³ - b³) = (14/8) = 7/4

Now we have two equations


(a³ + b³) = 8
(a³ - b³) = 7/4

Adding them together, we have

2a³ = 8 + (7/4), or
a³ = 4 + (7/8), or
a³ = 39/8
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