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If x^3*y^4 = 5000, what is the value of y ? (1) x and y are integers

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Bunuel
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If x^3*y^4 = 5000, what is the value of y ? (1) x and y are integers [#permalink] New post   11 Nov 2022, 06:20
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A
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If x^3*y^4 = 5000, what is the value of y ?

(1) x and y are integers
(2) y is a positive number
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C
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divyadna
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Re: If x^3*y^4 = 5000, what is the value of y ? (1) x and y are integers [#permalink] New post   11 Nov 2022, 06:31
5000= 5^4*2^3
Statement I: x and y are integers
x is 2 but y can be either 5 or -5
Since 5^4=(-5)^4
Statement I alone is not sufficient.

Statement II:y is a positive integer.
This essentially means that y is 5.
So, statement II alone is sufficient.

Answer is option B IMO

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Re: If x^3*y^4 = 5000, what is the value of y ? (1) x and y are integers [#permalink] New post   13 Nov 2022, 12:44
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How is the answer C here ? Why do we need statement A? Please provide some explanation.
Statement two confirms y is 5 and not -5 ... Isn't that enough?

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Re: If x^3*y^4 = 5000, what is the value of y ? (1) x and y are integers [#permalink] New post   13 Nov 2022, 13:11
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GabriellaKhingg wrote:
How is the answer C here ? Why do we need statement A? Please provide some explanation.
Statement two confirms y is 5 and not -5 ... Isn't that enough?

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No.

If x^3*y^4 = 5000, what is the value of y ?

Let's start by factoring 5000:

    \(5000=2^3*5^4\)

(1) x and y are integers.

    Since y is in even power, then y can be 5 or -5.

Not sufficient.

(2) y is a positive number.

For ANY positive (integer or non-integer) value of y, there exists some x satisfying x^3y^4 = 5,000. For example:

    \(y=\frac{1}{2}\) --> \(x = 20*\sqrt[3]{10}\)
    \(y=1\) --> \(x=\sqrt[3]{5,000}\);
    \(y=2\) --> \(x=\sqrt[3]{\frac{5,000}{16}}\);
    \(y=3\) --> \(x=\sqrt[3]{\frac{5,000}{81}}\);
    ...
    \(y=5\) --> \(x=2\);
    ...
    \(y=10\) --> \(x=\sqrt[3]{\frac{5,000}{10,000}}\);
    ...


Not sufficient.

(1)+(2) Since both x and y are integers, and y > 0, then then from \(x^3y^4 = 2^35^4\), it follows that \(y=5\). Sufficient.

Answer: C.

Hope it's clear.
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Re: If x^3*y^4 = 5000, what is the value of y ? (1) x and y are integers [#permalink] New post   13 Nov 2022, 13:16
That helped ... Thank you :)

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Re: If x^3*y^4 = 5000, what is the value of y ? (1) x and y are integers [#permalink]
13 Nov 2022, 13:16
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