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# The value of (0.4)^4 – (0.4)^3

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The value of (0.4)^4 – (0.4)^3  [#permalink]

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Updated on: 22 Oct 2019, 23:16
00:00

Difficulty:

45% (medium)

Question Stats:

63% (01:36) correct 37% (01:31) wrong based on 65 sessions

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EMPOWERgmat PS Series:
Pack 3, Question 1

The value of (0.4)^4 – (0.4)^3 is between

A. -1 and -1/2
B. -1/2 and 0
C. 0 and 1/2
D. ½ and 1
E. 1 and 2

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Originally posted by EMPOWERgmatRichC on 11 Oct 2019, 18:16.
Last edited by EMPOWERgmatRichC on 22 Oct 2019, 23:16, edited 1 time in total.
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Re: The value of (0.4)^4 – (0.4)^3  [#permalink]

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11 Oct 2019, 18:41
EMPOWERgmatRichC wrote:
EMPOWERgmat PS Series:
Pack 3, Question 1

The value of (0.4)^4 – (0.4)^3 is between

A. -1 and -1/2
B. -1/2 and 0
C. 0 and 1/2
D. ½ and 1
E. 1 and 2

48 Hour Window To Win An $85 EMPOWERgmat Tuition Credit (1 Month Free!) Share your explanation! The GMAT Club member with the most verified Kudos in total on the 5 question PS Block 3 question pack will win an$85 EMPOWERgmat tuition credit, which will entitle the winner to a full month of complete access to the EMPOWERgmat system. Even if you're not sure about your answer or your rationale, share your explanation to help boost your learning and earn a chance to win.

To be eligible, your explanation must be submitted within the 48 hour window after this post was created and should explain your reasoning why the answer you chose is correct

The OA and official explanation will be held until the 48 hour window has lapsed.

.4^3(.4-1)= .064*(-.6)= -.0384

IMO B

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Re: The value of (0.4)^4 – (0.4)^3  [#permalink]

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11 Oct 2019, 19:18
EMPOWERgmatRichC wrote:

The value of (0.4)^4 – (0.4)^3 is between

A. -1 and -1/2
B. -1/2 and 0
C. 0 and 1/2
D. ½ and 1
E. 1 and 2

The better way would be to convert into fractions..
$$(0.4)^4 – (0.4)^3=(\frac{4}{10})^4-(\frac{4}{10})^3=(\frac{2}{5})^4-(\frac{2}{5})^3=(\frac{2}{5})^3((\frac{2}{5})-1)=\frac{8}{125}*\frac{-3}{5}=\frac{-24}{625}$$
So between 0 and -1/2

Also 4/10 <1/2 and it will keep reducing as we increase the power, so (0.4)^4 < (0.4)^3 and answer will be negative..
The value of both (0.4)^4 – and (0.4)^3 will be way lesser than 1/2 and when we subtract them, they will surely remain less than 1/2
So between 0 and -1/2
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Re: The value of (0.4)^4 – (0.4)^3  [#permalink]

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11 Oct 2019, 19:54
$${0.4}^4$$ - $${0.4}^3$$ ==> $${0.4}^3$$(0.4 - 1) ==> $${0.4}^3$$ (-0.6) ==> $${(\frac{2}{5})}^3$$(-$$\frac{3}{5}$$) ==> -$$\frac{24}{625}$$ ==> Answer is B

Extra:

$$\frac{24}{625}$$ < $$\frac{1}{2}$$ ==> -$$\frac{24}{625}$$ > -$$\frac{1}{2}$$
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Re: The value of (0.4)^4 – (0.4)^3  [#permalink]

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11 Oct 2019, 21:34
EMPOWERgmatRichC wrote:
EMPOWERgmat PS Series:
Pack 3, Question 1

The value of (0.4)^4 – (0.4)^3 is between

A. -1 and -1/2
B. -1/2 and 0
C. 0 and 1/2
D. ½ and 1
E. 1 and 2

(0.4)^4 – (0.4)^3 = (0.4)^3 [0.4 - 1] = (0.4)^3 (-0.6)

There is no need of actual calculation as we know the answer will be negative and very close of 0.
Options B is correct.
Re: The value of (0.4)^4 – (0.4)^3   [#permalink] 11 Oct 2019, 21:34
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