∛(328 - 800 - 48)

Hi All,

For anyone looking for a hint as to how to solve this quickly...

[spoiler]The GMAT will never expect you to do a super-complex calculation to get to the correct answer, so you should look at how the entire prompt is designed - there will almost certainly be a way to avoid that complex calculation. Here, it's the answer choices. Notice how they're all RANGES - you can use that to your advantage. Can you calculate (-4)^3 and (-5)^3? Then you have the range for Answer A. Does the prompt fit in that range? If not, then you have to keep working until you find the range that it does fit into. And you don't necessarily have to define all of the ranges to get the correct answer...[/spoiler]

GMAT assassins aren't born, they're made,
Rich

Brent@GMATPrepNow wrote:∛(328 - 800 - 48) is

A) Between -4 and -5
B) Between -5 and -6
C) Between -6 and -7
D) Between -7 and -8
E) Less than -8

OA: E

Another approach is to use a nice rule that says ∛(ab) = (∛a)(∛b)
We'll also recognize that we can factor out an 8 (and we happens to know that ∛8 = 2)


We get: ∛(328 - 800 - 48) = ∛[8(41 - 100 - 6)
= ∛[(8)(-65)]
= (∛8)(∛-65) [once we apply the above rule]
= (2)(∛-65)

Hmmm, what about (∛-65)?

Well we know that (∛-64) = -4
And we know that (∛-125) = -5
Since -65 lies BETWEEN -64 and -125, we know that (∛-65) lies between -4 and -5
So, let's say that (∛-65) = -4.something

This means that (2)(∛-65) = (2)(-4.something) = some number that's LESS THAN -8

Answer: E

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