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∛(328 - 800 - 48) is

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BrentGMATPrepNow
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∛(328 - 800 - 48) is [#permalink] New post   04 Nov 2016, 07:44
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E

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45% (medium)

Question Stats:

64% (01:52) correct 36% (01:52) wrong based on 326 sessions
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∛(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.
*Kudos for all correct solutions
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E
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∛(328 - 800 - 48) is [#permalink] New post   04 Nov 2016, 08:07
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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

There are a few different ways to solve this one.
*Kudos for all correct solutions



\(∛(328 - 800 - 48) = ∛(-520)\)

Now, \(-8^3 = -512\)

Think of a number line -520 will lie to the left of -512...

Hence, Answer will be (E)..
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Re: ∛(328 - 800 - 48) is [#permalink] New post   04 Nov 2016, 08:11
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Here is a detailed answer,

Please don't hesitate if you have any question.

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BrentGMATPrepNow
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∛(328 - 800 - 48) is [#permalink] New post   Updated on: 21 Sep 2021, 17:56
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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


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

Originally posted by BrentGMATPrepNow on 04 Nov 2016, 11:06.
Last edited by BrentGMATPrepNow on 21 Sep 2021, 17:56, edited 1 time in total.
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Re: ∛(328 - 800 - 48) is [#permalink] New post   04 Nov 2016, 11:11
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\sqrt{(328 - 800 - 48} = \sqrt{-520}

since -8^3 = -512

\sqrt{-520} is less than \sqrt{- 8}

hence E
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Re: ∛(328 - 800 - 48) is [#permalink] New post   05 Nov 2016, 11:53
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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

There are a few different ways to solve this one.
*Kudos for all correct solutions


\(∛(328 - 800 - 48)\)= ∛(-520)

the prime factorization of 520 is \(2^4*5*7\)

therefore the expression is equal to \(-2*∛(2*5*7)= -2*∛70\)

as 70 is very close to 64 which is 4^3 the value of ∛70 is a little bit higher than 4

therefore \(∛(328 - 800 - 48)>-2*4\)\(=-8\)

ANSWER E
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Re: ∛(328 - 800 - 48) is [#permalink] New post   07 Nov 2016, 17:23
Expert Reply
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



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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Re: (328 - 800 - 48) is [#permalink] New post   12 Jun 2023, 00:02
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Re: (328 - 800 - 48) is [#permalink]
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