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Director  Joined: 28 Jun 2011
Posts: 815
Re: cube root of (-89)  [#permalink]

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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

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

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, $$\sqrt{125} =5$$ and $$\sqrt{-64} =-4$$.

The above question is quite tricky:

$$\sqrt{-89}$$ 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).

Concept was easy, messed up with the options..

-5 and -4 wll be only covered in option A
Manager  Joined: 30 Mar 2013
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Re: The value of cube root of (-89) is:  [#permalink]

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jcurry wrote:
$$\sqrt{-89}$$ 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 $$\sqrt{-81}= -3$$ and $$\sqrt{-64}= -4$$

Should be C. I'd take the -ve outside, and since $$\(-4)^3$$ = -64 and $$\(-5)^3$$ = -125, the answer just lies somewhere between these two, therefore C. Please note that this is a slightly different question than the first question asked in this thread.
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The value of cube root of (-89) is:  [#permalink]

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$$(-4)^3 = -64$$

$$(-5)^3 = -125$$

If a number line is drawn, the cube root would lie between -4 & -5

-10...... -9.......... -8.......... -7............ -6..... -5........................ -4 ...... -3...... -2... -1.......... 0..... 1..... 2..... 3...... 4....... 5....... 6........ 7....... 8....... 9.......... 10

Its very clear looking at the number line, answer = A
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The value of cube root of (-89) is:  [#permalink]

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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

The answer to this question is tricky...have to be careful while finding the answer...ans lies between -4 and -5 and option A is the only option that includes this range.
Thanks for the question.
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Re: The value of cube root of (-89) is:  [#permalink]

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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

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

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, $$\sqrt{125} =5$$ and $$\sqrt{-64} =-4$$.

The above question is quite tricky:

$$\sqrt{-89}$$ 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).

Hi! Can you explain this: So the the range would be between -5 and -4. The only answer choice to cover this range is A (-9, 10). ? I don't understand it. Thank you.
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Joined: 02 Sep 2009
Posts: 56277
Re: The value of cube root of (-89) is:  [#permalink]

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1
lpetroski 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

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

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, $$\sqrt{125} =5$$ and $$\sqrt{-64} =-4$$.

The above question is quite tricky:

$$\sqrt{-89}$$ 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).

Hi! Can you explain this: So the the range would be between -5 and -4. The only answer choice to cover this range is A (-9, 10). ? I don't understand it. Thank you.

The question asks about the range the cube root of (-89) is. We found that it's between -5 and -4, approximately -4.5. Now, can you tell me in which range from the options given is -4.5?
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GMAT 1: 630 Q44 V32 GMAT 2: 680 Q47 V35 Re: The value of cube root of (-89) is:  [#permalink]

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BTW, i noticed that the range given in option A -9 to +10, is the widest of all and covers all other ranges in the options. So, whatever falls in other ranges, will fall in this range. And this is an official question.
So, on the real test, why cant i just mark option A blindly and move on?

also, since no two options can be correct, option A has to win.
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Re: The value of cube root of (-89) is:  [#permalink]

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arhumsid wrote:
BTW, i noticed that the range given in option A -9 to +10, is the widest of all and covers all other ranges in the options. So, whatever falls in other ranges, will fall in this range. And this is an official question.
So, on the real test, why cant i just mark option A blindly and move on?

also, since no two options can be correct, option A has to win.

Yes, if it is defined, it will certainly lie in the range -9 and 10 since it covers all other ranges. So answer would be (A).
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GRE 1: Q169 V154 Re: The value of cube root of (-89) is:  [#permalink]

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Excellent Official Question.
Here is what I did on this one ->
Let m= (-84)^1/3

m^3 = -84

Hence m => (-5,-4)

Only bound that satisfies is A.
NOTE -> C is a BIG trap as within the time constraint we might end up choosing C.
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Re: The value of cube root of (-89) is:  [#permalink]

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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

Main idea: The cube root should be within the range even though the range may be large

Details: Cube root of -89 is between -4 and -5.

This is only in the range given in choice A .
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Re: The value of cube root of (-89) is:  [#permalink]

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This is a question that tests if you know the the basics well:

There are 2 parts to this:

1) Is it a Negative or Positive Integer?
A negative cube root integer will result in a negative integer. Similarly, a cubed negative integer will result in a another negative integer.
i.e. $$-3^3 = -9$$ and vice-versa

For this question, the answer must be in the negative region

2) What is the absolute value of the answer
$$4^3 = 64$$ & $$5^3 = 125$$

For this question, the answer must somehow involve $$4^3$$ & $$5^3$$

Putting (1) & (2) together,

The answer is between -4 & -5. Hence (A)
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Re: The value of cube root of (-89) is:  [#permalink]

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_________________ Re: The value of cube root of (-89) is:   [#permalink] 13 Mar 2019, 07:57

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