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For positive integers x and y, x^y*8^3=2(10^8). What is the value of y

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For positive integers x and y, x^y*8^3=2(10^8). What is the value of y  [#permalink]

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08 Feb 2017, 09:17
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Question Stats:

51% (02:17) correct 49% (02:22) wrong based on 88 sessions

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For positive integers x and y, x^y*8^3=2(10^8). What is the value of y?

(1) x > y
(2) y is a prime number

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Re: For positive integers x and y, x^y*8^3=2(10^8). What is the value of y  [#permalink]

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08 Feb 2017, 10:37
B
Statement 1
x^y * 8^3 = 2^9 * 5^8(after simplyfying )
Now here x can b 5,25,625.

Statement 2
Now if we know that x is prime it's clear that x= 5 and y=8
So B

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Re: For positive integers x and y, x^y*8^3=2(10^8). What is the value of y  [#permalink]

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08 Feb 2017, 11:18
expanding the given equation

x^y . 2^9 = 2^9 . 5^8

x^y = 5^8

stat 1 : x>y,,we get two diff answers
stat 2 : only one possible answer,,, y = 2

hence ans B
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Re: For positive integers x and y, x^y*8^3=2(10^8). What is the value of y  [#permalink]

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13 Feb 2017, 08:44
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Bunuel wrote:
For positive integers x and y, x^y*8^3=2(10^8). What is the value of y?

(1) x > y
(2) y is a prime number

Let’s first simplify the given expression:

x^y(8^3) = 2(10^8)

x^y(2^9) = 2^1(2^8 x 5^8)

x^y(2^9) = 2^9 x 5^8

x^y = 5^8

We need to determine the value of y. At this point, it’s tempting to conclude that x = 5 and y = 8. However, this is not always the case; it can be one of the following 4 cases:

1) x = 5, y = 8
2) x = 5^2 = 25, y = 4
3) x = 5^4 = 625, y = 2
4) x = 5^8, y = 1

Statement One Alone:

x > y

Although x is greater than y, we still do not have enough information to determine the value of y. For example, we could have x = 25 and y = 4, or we could have x = 625 and y = 2.

Statement Two Alone:

y is a prime number.

Since y is a prime number, x must be 625 and y must be 2. Statement two alone is sufficient to answer the question.

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Re: For positive integers x and y, x^y*8^3=2(10^8). What is the value of y  [#permalink]

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18 Mar 2019, 07:21
For positive integers x and y, $$x^y*8^3=2(10^8)$$. What is the value of y?

(1) x > y
(2) y is a prime number

Solution: Simply the Question stem
$$x^y*8^3=2(10^8)$$
$$x^y*(2^3)^3=2(2^8*5^8)$$
$$x^y*(2^9)=(2^9*5^8)$$

$$x^y=(5^8)=(25^4)=625^2$$

(1) x > y
$$x^y=(5^8)=(25^4)=625^2$$

first case x could be 8 and y could be 5.
second case x could be 25 and y could be 4
Not sufficient.

(2) y is a prime number
x will be 8 and y will be 5

hence B
Re: For positive integers x and y, x^y*8^3=2(10^8). What is the value of y   [#permalink] 18 Mar 2019, 07:21
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