Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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).

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).

Answer: A.

forgot to answer the question...just curious if you typed the answers correctly...

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.

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).

Answer: A.

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?
_________________

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).

Answer: A.

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.
_________________

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.
_________________

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

Show Tags

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!
_________________

If you found my post useful and/or interesting - you are welcome to give kudos!

gmatclubot

Re: The value of cube root of (-89) is:
[#permalink]
06 Jun 2013, 06:58

After days of waiting, sharing the tension with other applicants in forums, coming up with different theories about invites patterns, and, overall, refreshing my inbox every five minutes to...

I was totally freaking out. Apparently, most of the HBS invites were already sent and I didn’t get one. However, there are still some to come out on...

In early 2012, when I was working as a biomedical researcher at the National Institutes of Health , I decided that I wanted to get an MBA and make the...