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# The value of cube root of (-89) is:

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The value of cube root of (-89) is: [#permalink]

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03 Nov 2009, 18:23
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The value of cube root of (-89) is:

A. Between -9 and 10
B. Between -8 and -9
C. Between -4 and 5
D. Between -3 and 4
E. Undefined
[Reveal] Spoiler: OA

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Re: cube root of (-89) [#permalink]

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03 Nov 2009, 18:43
tejal777 wrote:
The value of cube root of (-89) is..?

Between -9 and 10
Between -8 and -9
Between -4 and 5
Between -3 and 4
Undefined

...................

[Reveal] Spoiler:
Is'nt the root of any negative number undefined?

not if it is - cube root(89)

you are getting the cube root of 89 and then multiplying that by (-)

that's my understanding
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Re: cube root of (-89) [#permalink]

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03 Nov 2009, 18:46
Expert's post
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tejal777 wrote:
The value of cube root of (-89) is..?

Between -9 and 10
Between -8 and -9
Between -4 and 5
Between -3 and 4
Undefined

...................

[Reveal] Spoiler:
Is'nt the root of any negative number undefined?

Even roots from negative number is undefined on the GMAT (as GMAT is dealing only with Real Numbers): $$\sqrt[{even}]{negative}=undefined$$, for example $$\sqrt{-25}=undefined$$.

Odd roots will have the same sign as the base of the root. For example, $$\sqrt[3]{125} =5$$ and $$\sqrt[3]{-64} =-4$$.

The above question is quite tricky:

$$\sqrt[3]{-89}$$ is more than -5 (as $$-5^3=-125$$) but less than -4 (as $$-4^3=-64$$) --> $$-5<x<-4$$, (actually it's $$\approx{-4.5}$$). So the the range would be between -5 and -4. The only answer choice to cover this range is A (-9, 10).

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Re: cube root of (-89) [#permalink]

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03 Nov 2009, 18:47
Bunuel wrote:
tejal777 wrote:
The value of cube root of (-89) is..?

Between -9 and 10
Between -8 and -9
Between -4 and 5
Between -3 and 4
Undefined

...................

[Reveal] Spoiler:
Is'nt the root of any negative number undefined?

The even root from negative power is undefined, for GMAT. For example: (negative number)^{1/2k} is undefined, (-8)^1/2 or (-3.5)^1/8 or (-1)^1/22. But the odd root can be found.

(-2)*(-2)*(-2)=-8 so (-8)^1/3=-2 or (-4)*(-4)*(-4)=-64 so (-64)^1/3=-4.

The question you posted is quite tricky:

(-89)^1/3 is more than -5 (-5^3=-125) but less than -4 (-4^3=-64) --> -5<x<-4, (actually it's ~-4.5). So the the range would be between -5 and -4. The only answer choice to cover this range is A (-9, 10).

forgot to answer the question...just curious if you typed the answers correctly...
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Re: cube root of (-89) [#permalink]

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03 Nov 2009, 18:51
lagomez wrote:
forgot to answer the question...just curious if you typed the answers correctly...

What you mean? What part are you referring to?
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Re: cube root of (-89) [#permalink]

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03 Nov 2009, 18:58
Bunuel wrote:
lagomez wrote:
forgot to answer the question...just curious if you typed the answers correctly...

What you mean? What part are you referring to?

sorry, meant the message for the original poster not you

I see many questions like this on gmat review and always see the same signs for the answers, i.e., -9 to -10 not -9 to 10

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Re: cube root of (-89) [#permalink]

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03 Nov 2009, 22:13
Yeah, quite tricky question, if not bunuel, would hardly understoon it.
Thanks.
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Re: cube root of (-89) [#permalink]

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03 Nov 2009, 22:22
i thought this was pretty simple by taking the answer options. E was out of question as the Bunual rightly mentioned.

only by looking at the lower limits of the ranges, we can discard option C and D.

Option B was a short ranged between -8 to -9 and the squares of these numbers are near 89. cube must be very high. without actually solving it, we can ignore it. Remaining option has to be the right one i.e. A.
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22 Aug 2010, 14:31
$$\sqrt[3]{-89}$$ is:

A) Between -9 and -10
B) Between -8 and -9
C) Between -4 and -5
D) Between -3 and -4
E) Undefined

My guess (D) was incorrect because I guess I did $$\sqrt[4]{-81}= -3$$ and $$\sqrt[3]{-64}= -4$$

Last edited by jcurry on 22 Aug 2010, 15:15, edited 1 time in total.
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22 Aug 2010, 14:38
Merging similar topics. Note that answer choices are different and thus OA for 1st question is A and for the 2nd C.
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Re: cube root of (-89) [#permalink]

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22 Aug 2010, 15:03
Thanks I searched google and the forum but the math notation made it difficult to find.
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Re: cube root of (-89) [#permalink]

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22 Aug 2010, 20:31
Wow pretty similar questions. BTW will they ask such questions (like the first question where the answer choice is not very clear) on the GMAT?
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Re: cube root of (-89) [#permalink]

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06 Sep 2010, 08:23
Bunuel wrote:
tejal777 wrote:
The value of cube root of (-89) is..?

Between -9 and 10
Between -8 and -9
Between -4 and 5
Between -3 and 4
Undefined

...................

[Reveal] Spoiler:
Is'nt the root of any negative number undefined?

Even roots from negative number is undefined on the GMAT (as GMAT is dealing only with Real Numbers): $$\sqrt[{even}]{negative}=undefined$$, for example $$\sqrt{-25}=undefined$$.

Odd roots will have the same sign as the base of the root. For example, $$\sqrt[3]{125} =5$$ and $$\sqrt[3]{-64} =-4$$.

The above question is quite tricky:

$$\sqrt[3]{-89}$$ is more than -5 (as $$-5^3=-125$$) but less than -4 (as $$-4^3=-64$$) --> $$-5<x<-4$$, (actually it's $$\approx{-4.5}$$). So the the range would be between -5 and -4. The only answer choice to cover this range is A (-9, 10).

Hey bunuel

i did this quesiton wrong cuz remember your words that $$\sqrt{-25}=undefined$$.

cube root means that it has to be a negative number after you took out. Then it should be something \sqrt{negative X} therefore should be undefined? where am i missing?
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Re: cube root of (-89) [#permalink]

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06 Sep 2010, 08:35
fatihaysu wrote:
Bunuel wrote:
tejal777 wrote:
The value of cube root of (-89) is..?

Between -9 and 10
Between -8 and -9
Between -4 and 5
Between -3 and 4
Undefined

...................

[Reveal] Spoiler:
Is'nt the root of any negative number undefined?

Even roots from negative number is undefined on the GMAT (as GMAT is dealing only with Real Numbers): $$\sqrt[{even}]{negative}=undefined$$, for example $$\sqrt{-25}=undefined$$.

Odd roots will have the same sign as the base of the root. For example, $$\sqrt[3]{125} =5$$ and $$\sqrt[3]{-64} =-4$$.

The above question is quite tricky:

$$\sqrt[3]{-89}$$ is more than -5 (as $$-5^3=-125$$) but less than -4 (as $$-4^3=-64$$) --> $$-5<x<-4$$, (actually it's $$\approx{-4.5}$$). So the the range would be between -5 and -4. The only answer choice to cover this range is A (-9, 10).

Hey bunuel

i did this quesiton wrong cuz remember your words that $$\sqrt{-25}=undefined$$.

cube root means that it has to be a negative number after you took out. Then it should be something \sqrt{negative X} therefore should be undefined? where am i missing?

Not sure that understand your question. But again:

Even roots from negative number is undefined on the GMAT (as GMAT is dealing only with Real Numbers): $$\sqrt[{even}]{negative}=undefined$$, for example $$\sqrt{-25}=undefined$$.

Odd roots will have the same sign as the base of the root. For example, $$\sqrt[3]{125} =5$$ and $$\sqrt[3]{-64} =-4$$.

Or:
$$\sqrt[{even}]{positive}=positive$$: $$\sqrt{25}=5$$. Even roots have only a non-negative value on the GMAT.

$$\sqrt[{even}]{negative}=undefined$$: $$\sqrt{-25}=undefined$$. Even roots from negative number is undefined on the GMAT (as GMAT is dealing only with Real Numbers).

$$\sqrt[{odd}]{positive}=positive$$ and $$\sqrt[{odd}]{negative}=negative$$: $$\sqrt[3]{125} =5$$ and $$\sqrt[3]{-64} =-4$$. Odd roots will have the same sign as the base of the root.
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Re: cube root of (-89) [#permalink]

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21 Sep 2010, 04:20
Hi Bunuel,

Is there any specific reason why GMAT want to confuse us with the Range that we calculate and actual range provided in the answer?
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Re: cube root of (-89) [#permalink]

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21 Sep 2010, 04:46
prashantbacchewar wrote:
Hi Bunuel,

Is there any specific reason why GMAT want to confuse us with the Range that we calculate and actual range provided in the answer?

Don't think there is other reason than to make question trickier.
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06 Nov 2011, 13:44
jcurry wrote:
$$\sqrt[3]{-89}$$ is:

A) Between -9 and -10
B) Between -8 and -9
C) Between -4 and -5
D) Between -3 and -4
E) Undefined

My guess (D) was incorrect because I guess I did $$\sqrt[4]{-81}= -3$$ and $$\sqrt[3]{-64}= -4$$

Are these 2 different questions ? Bunnels post says merging similar topics and they have different OA's ...I am not sure what the difference is ?

The value of cube root of (-89) is..?

Between -9 and 10
Between -8 and -9
Between -4 and 5
Between -3 and 4
Undefined

AND

$$\sqrt[3]{-89}$$ is:

A) Between -9 and -10
B) Between -8 and -9
C) Between -4 and -5
D) Between -3 and -4
E) Undefined
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06 Nov 2011, 23:47
siddhans wrote:
jcurry wrote:
$$\sqrt[3]{-89}$$ is:

A) Between -9 and -10
B) Between -8 and -9
C) Between -4 and -5
D) Between -3 and -4
E) Undefined

My guess (D) was incorrect because I guess I did $$\sqrt[4]{-81}= -3$$ and $$\sqrt[3]{-64}= -4$$

Are these 2 different questions ? Bunnels post says merging similar topics and they have different OA's ...I am not sure what the difference is ?

The value of cube root of (-89) is..?

Between -9 and 10
Between -8 and -9
Between -4 and 5
Between -3 and 4
Undefined

AND

$$\sqrt[3]{-89}$$ is:

A) Between -9 and -10
B) Between -8 and -9
C) Between -4 and -5
D) Between -3 and -4
E) Undefined

The questions are the same but as Bunuel mentioned while merging, the answer options are different "Between -4 and 5" and "Between -4 and -5"
The answer lies between -4 and -5 but not between -4 and 5 so the range which covers '-4 to -5' is '-9 to 10' in the first question.
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Re: The value of cube root of (-89) is: [#permalink]

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05 Jun 2013, 04:27
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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Tough and tricky exponents and roots questions (PS): new-tough-and-tricky-exponents-and-roots-questions-125956.html

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Re: The value of cube root of (-89) is: [#permalink]

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06 Jun 2013, 06:58
tejal777 wrote:
The value of cube root of (-89) is:

A. Between -9 and 10
B. Between -8 and -9
C. Between -4 and 5
D. Between -3 and 4
E. Undefined

Very tricky question.

Questions seeks to find out for a range of numbers that include a number after multiplying it by itself gives -89.
First thing we know is that it is a negative number. We can easily check few numbers, take -3*-3*-3=-27 too low, -4*-4*-4=-64 still low, -5*-5*-5=-125 too big. So basically it should be a number between -4 and -5. Do we have such range? Trick here is that it is tmpting automatically go to choice C. But this is wrong choice because it does not cover the range required. The only range that includes number between -4 and -5 is A. Although it is very broad and covers many other values, but we have never been restricted. So the choice the A is the best!
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Re: The value of cube root of (-89) is:   [#permalink] 06 Jun 2013, 06:58

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