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Bunuel
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If x is a positive integer, what is the smallest possible value of x 09 Oct 2020, 04:15
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D
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71% (01:52) correct 29% (02:10) wrong based on 165 sessions

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If x is a positive integer, what is the smallest possible value of x such that 1080000*x is a cube of an integer?​

A. 5

B. 10​

C. 15​

D. 25​

E. 130
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D
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If x is a positive integer, what is the smallest possible value of x 09 Oct 2020, 04:24
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Explanation:

Checking Options as no other way to solve problem.

Option D 25

1080000*25 = 27000000

27000000^1/3 = 300

IMO-D
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If x is a positive integer, what is the smallest possible value of x 09 Oct 2020, 06:16
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Concept: for the value to be a cube of an Integer, it must contain Prime Bases that ALL have the Power raised to a Multiple of 3

X will need to “add” the extra prime factors needed so that this becomes true.


1, 080, 000 =

108 * 10, 000 =

(4 * 27) * (100 * 100) =

4 * (3)^3 * 25 * 4 * 25 * 4=

(4)^3 * (3)^3 * (25)^2 = 1, 080, 000


The Minimum Value that X can be to have the Expression be a Cube of an Integer is:

25



When X = 25 —> the Cube Root of: 1, 080, 000 * X =

4 * 3 * 25 =

300

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If x is a positive integer, what is the smallest possible value of x 09 Oct 2020, 06:54
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To be a perfect cube all the prime factors should have the power of '3'.

1080000 * x = 108 * 1000 * x

=>1080000 * x = \((2^2 * 3^3) * (10^3 * 10) * x\)

=>1080000 * x = \((2^2) * (3^3) * (10^3) * (10) * x\)

=>1080000 * x = \((3^3) * (10^3) * (2^2) * (2 * 5) * x\)

=>1080000 * x = \((3^3) * (10^3) * (2^3) * (5) * x\)

We need 5^2 now to make the number as a perfect cube: x = \(5^2\) = 25

Answer D
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If x is a positive integer, what is the smallest possible value of x 09 Oct 2020, 08:04
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If x is a positive integer, what is the smallest possible value of x such that 1080000*x is a cube of an integer?​

A. 5

B. 10​

C. 15​

D. 25​

E. 130

Explanation:

1080000*x=108*10^4
=2^2*3^3*(2*5)^4*x
=2^6*3^3*5^4*x

for cube of an integer all the power must be multiple of 3
as we can see prime factors 2 & 3 have exponents which are multiple of 3 and prime factor 5 have exponents which is not a multiple of 3
Thus min value of X to make it cube of an integer will be 5^2=25

Hence D is the correct answer.
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If x is a positive integer, what is the smallest possible value of x 09 Aug 2022, 02:32
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To know cube all the prime factors should be 3
so 1080000 = 2*3 X 2*3 X 3*3 X 5*3 X 5*1

So we need 5*2 thus 1080000 X 5*2 will be a perfect cube
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If x is a positive integer, what is the smallest possible value of x 20 Nov 2023, 10:03
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