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∛(328 - 800 - 48)

by Brent@GMATPrepNow » Fri Nov 04, 2016 6:45 am
∛(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

There are a few different ways to solve this one.

OA: E
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by [email protected] » Fri Nov 04, 2016 9:51 am
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]

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by melguy » Fri Nov 04, 2016 11:28 pm
∛(328 - 800 - 48)

Rephrase ∛(-520)

-7 x -7 x -7 = -343
-8 x -8 x -8 = -512
-9 x -9 x -9 = -729

The value is lesser than (-8)³ so answer should be E
Last edited by melguy on Sat Nov 05, 2016 8:49 pm, edited 1 time in total.
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by Brent@GMATPrepNow » Sat Nov 05, 2016 4:45 am
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

RELATED VIDEO
- Properties of roots: https://www.gmatprepnow.com/module/gmat ... video/1037
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by Jeff@TargetTestPrep » Mon Nov 07, 2016 4:22 pm
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
We can start by combining the values in the parenthesis:

∛(328 - 800 - 48) = ∛-520

Since 8^3 = 512 and 9^3 = 729, (-8)^3 = -512 and (-9)^3 = -729. Since -520 is between -729 and -512, ∛-520 is between -9 and -8, and thus ∛-520 is less than -8.

Answer: E

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by Matt@VeritasPrep » Fri Nov 11, 2016 3:31 pm
This is ∛-520, so we should look for a cube in the vicinity of 520.

8 * 8 * 8 = 512, so in the positive world, the cube root is slightly greater than 8.

We're in the negative world, so our answer is slightly less than -8, or E.
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by Matt@VeritasPrep » Fri Nov 11, 2016 3:33 pm
Factoring out also seems like a good plan:

∛(-8*(41 - 100 - 6))

∛(-8) * ∛(-41 + 100 + 6)

∛(-8) * ∛65

which is slightly less than -2 * ∛64, or -2 * 4.
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