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# If n and y are positive integers and 450y=n^3

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Joined: 11 Jun 2011
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Re: If n and y are positive integers and 450y=n^3  [#permalink]

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29 Dec 2016, 12:10
abhi758 wrote:
If x and y are positive integers and 450y=x^3, which of the following must be an integer?

i) $$\frac{y}{{3*2^2*5}}$$
ii) $$\frac{y}{{3^2*2*5}}$$
iii) $$\frac{y}{{3*2*5^2}}$$

a. None
b. i only
c. ii only
d. iii only
e. i, ii and iii

$$450y=x^3$$

$$5^2*2*3^2*y = x^3$$

The minimum value of $$y =$$ $$2^2*5*3$$

Hence, among the given options, only (I) is possible...

So, correct answer must be (B)

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Thanks and Regards

Abhishek....

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Re: If n and y are positive integers and 450y=n^3  [#permalink]

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26 Jan 2017, 16:24
1) x is cubed, which means that its prime factors can be divided into three identical sets.
2) 450*y should have the same three sets of prime factors as x cubed, since the two expressions are equal
3) The prime factors of 450 are 2*5*5*3*3. This means that y has to consist of 2^2*5*3 at least, and it has to be divisible by this expression.

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Re: If n and y are positive integers and 450y=n^3  [#permalink]

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30 Jun 2017, 00:04
Cant we take higher values of N and Y so that it satisfies the equation,the all 3 possiblities are correct and answer is E
eg:
y= 5^4*3^4*2^5
N=5^2*3^2*2^2
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Posts: 49277
Re: If n and y are positive integers and 450y=n^3  [#permalink]

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30 Jun 2017, 00:18
jakexix wrote:
Cant we take higher values of N and Y so that it satisfies the equation,the all 3 possiblities are correct and answer is E
eg:
y= 5^4*3^4*2^5
N=5^2*3^2*2^2

The question asks which of the following MUST be an integer, not COULD be an integer. If y = 2^2*3*5, which is the least possible value of y, then only B is true. Please re-read the thread and follow the links to similar questions to understand the concept better.
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Re: If n and y are positive integers and 450y=n^3  [#permalink]

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09 Jul 2018, 05:13
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If n and y are positive integers and 450y=n^3 &nbs [#permalink] 09 Jul 2018, 05:13

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