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705-805 (Hard)|   Arithmetic|      
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If x =-100^1/3*100^3 , then the value of 1/x is 14 Jan 2013, 06:51
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59% (02:33) correct 41% (02:22) wrong based on 700 sessions

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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
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B
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Bunuel
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If x =-100^1/3*100^3 , then the value of 1/x is 14 Jan 2013, 07:19
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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
Show more

\(-\sqrt[3]{100}\) 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.
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If x =-100^1/3*100^3 , then the value of 1/x is 03 Oct 2015, 05:56
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daviesj
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
Show more

Can this be solved in the following way? POE which is faster....

Solve for x = -10 ^ 20/3 which is ~ -10 ^ 6.66

Therefore, 1/x = - 1/10 ^ -6.66

Of the options, only one range is both -ve in sign and power of 10 .... Hence, B
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If x =-100^1/3*100^3 , then the value of 1/x is 20 Oct 2015, 12:41
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Bunuel
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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.
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Do we need to know the approx. value of 3rd root of 100 for the actual gmat??
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If x =-100^1/3*100^3 , then the value of 1/x is 21 Oct 2015, 04:01
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LaxAvenger
Bunuel
daviesj
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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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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If x =-100^1/3*100^3 , then the value of 1/x is 21 Oct 2015, 04:14
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Thanks, but my question was more aiming on whether we are actually expecting to see such a question on the real exam ?

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Lax
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If x =-100^1/3*100^3 , then the value of 1/x is 21 Oct 2015, 04:50
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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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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 29 Oct 2015, 05:10
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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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If x =-100^1/3*100^3 , then the value of 1/x is 02 Feb 2025, 23:49
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daviesj
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
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x = - 100^(1/3) * 100^3

First of all, the answer must be a negative number. So it cannot be D or E
Since the base is 100 for both, the exponents would get added, not multiplied. So it cannot be C.

100^(1/3) i.e. cube root of 100 is between 4 and 5 (since 5^3 is 125 and 4^3 is 64)
So, the value of x is between -5*100^3 and -4*100^3

100^3 = (10^2)^3 = 10^6
So, the value of x is between -5*10^6 and -4*10^6 (i.e. x is entirely negative) - Observe that this matches with A, so 1/x cannot be the same value. At this point, you can mark B and move on.

So, 1/x will lie between 1/[-4*10^6] and 1/[-5*10^6]
i.e. between -0.25*10^(-6) and -0.2*10^(-6)
i.e. between -2.5*10^(-7) and -2*10^(-7)

Option B
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If x =-100^1/3*100^3 , then the value of 1/x is 23 Feb 2025, 06:52
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Confused about how it went from -0.5 to -0.25 and -0.4 to -0.20

Bunuel
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If x =-100^1/3*100^3 , then the value of 1/x is 23 Feb 2025, 07:44
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saynchalk
Confused about how it went from -0.5 to -0.25 and -0.4 to -0.20

Bunuel
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\(\frac{1}{-0.4*10^7}<\frac{1}{x}<\frac{1}{-0.5*10^7}\) -->

\(\frac{-1}{0.4}*\frac{1}{10^7}<\frac{1}{x}<\frac{-1}{0.5}*\frac{1}{10^7}\) -->

\(\frac{-10}{4}*\frac{1}{10^7}<\frac{1}{x}<\frac{-10}{5}*\frac{1}{10^7}\) -->

\(-2.5*10^{-7}<\frac{1}{x}<-2*10^{-7}\)
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