integers

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integers

by vaibhav101 » Wed Aug 01, 2018 9:42 am

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if x , y and z are integers and 2^x*5^y*z=0.00064, what is the value of xy?

1) z=20
2) x=-1

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by Jay@ManhattanReview » Thu Aug 02, 2018 12:20 am

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vaibhav101 wrote:if x , y and z are integers and 2^x*5^y*z=0.00064, what is the value of xy?

1) z=20
2) x=-1
Given: 2^x*5^y*z = 0.00064

=> 2^x*5^y*z = 64/10^5 = 2^6/10^5 = 2^6/(2^5*5^5) = 2*5^(-5)

=> 2^x*5^y*z = 2*5^(-5)

Let's take each statement one by one.

1) z = 20

We have 2^x*5^y*z = 2*5^(-5)
2^x*5^y*20 = 2*5^(-5)
2^x*5^y*(2^2*5) = 2*5^(-5)
2^(x+2)*5^(y+1) = 2*5^(-5)

=> x + 2 = 1 => x = -1 and y +1 = -5 => y = -6

=> xy = -1*-6 = 6. Sufficient.

2) x = -1

We do not have any information about z. Insufficient.

The correct answer: A

Hope this helps!

-Jay
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