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Re: If x =-100^1/3*100^3 , then the value of 1/x is [#permalink]
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Bunuel wrote:
daviesj wrote:
If x =\(-100^{1/3}*100^3\) , then the value of 1/x is


A. between −5×10^6 and −4×10^6

B. between −2.5×10^−7 and −2×10^−7

C. equal to −100

D. between 2×10^−7 and 2.5×10^−7

E. between 4×10^6 and 5×10^6


\(-\sqrt[3]{100}\) a bit more than -5 and is a bit less than -4 (-5^3=-125 and -4^3=-64). Actually \(-\sqrt[3]{100}\approx{-4.6}\)

So, \(-5*100^3<x<-4*100^3\) --> \(-5*10^6<x<-4*10^6\) --> \(\frac{1}{-4*10^6}<\frac{1}{x}<\frac{1}{-5*10^6}\) --> \(\frac{1}{-0.4*10^7}<\frac{1}{x}<\frac{1}{-0.5*10^7}\) --> \(-2.5*10^{-7}<\frac{1}{x}<-2*10^{-7}\).

Answer: B.

Hope it's clear.


Do we need to know the approx. value of 3rd root of 100 for the actual gmat??
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Re: If x =-100^1/3*100^3 , then the value of 1/x is [#permalink]
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LaxAvenger wrote:
Bunuel wrote:
daviesj wrote:
If x =\(-100^{1/3}*100^3\) , then the value of 1/x is


A. between −5×10^6 and −4×10^6

B. between −2.5×10^−7 and −2×10^−7

C. equal to −100

D. between 2×10^−7 and 2.5×10^−7

E. between 4×10^6 and 5×10^6


\(-\sqrt[3]{100}\) a bit more than -5 and is a bit less than -4 (-5^3=-125 and -4^3=-64). Actually \(-\sqrt[3]{100}\approx{-4.6}\)

So, \(-5*100^3<x<-4*100^3\) --> \(-5*10^6<x<-4*10^6\) --> \(\frac{1}{-4*10^6}<\frac{1}{x}<\frac{1}{-5*10^6}\) --> \(\frac{1}{-0.4*10^7}<\frac{1}{x}<\frac{1}{-0.5*10^7}\) --> \(-2.5*10^{-7}<\frac{1}{x}<-2*10^{-7}\).

Answer: B.

Hope it's clear.


Do we need to know the approx. value of 3rd root of 100 for the actual gmat??


Not necessarily. You can always approximate the value.
The cube of 4 is 64 and the cube of 5 is 125.
Hence the value will lie somewhere between 4 and 5.

If you see closely, the value will be north of 4.5 as 100 is closer to 125 than to 64.

Does this help?
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Re: If x =-100^1/3*100^3 , then the value of 1/x is [#permalink]
Thanks, but my question was more aiming on whether we are actually expecting to see such a question on the real exam ?

Best regards,
Lax
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Re: If x =-100^1/3*100^3 , then the value of 1/x is [#permalink]
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LaxAvenger wrote:
Thanks, but my question was more aiming on whether we are actually expecting to see such a question on the real exam ?

Best regards,
Lax


No ... the questions on the GMAT would not require you to solve for cube root of 100.
Knowing the square roots should suffice.
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If x =-100^1/3*100^3 , then the value of 1/x is [#permalink]
I solved this question by simply removing the obviously wrong answers:
\(\frac{1}{x} = -100^{\frac{-1}{3}}*100^{-3} = 10^{-7}*\sqrt[3]{10}\)
Now what we got:
C D and E are out coz number is negaitve
power of A is just to low so its an easy B w/o thinking really coz \(\sqrt[3]{10}\) isn't big enough to change power.
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Re: If x =-100^1/3*100^3 , then the value of 1/x is [#permalink]
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Re: If x =-100^1/3*100^3 , then the value of 1/x is [#permalink]
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