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If x and y are positive integers such that x/y=5.4, which of the

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If x and y are positive integers such that x/y=5.4, which of the  [#permalink]

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New post 22 Mar 2019, 11:49
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A
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D
E

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Question Stats:

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If x and y are positive integers such that x/y=5.4, which of the following could be the value of y?

A. 12
B. 13
C. 14
D. 15
E. 16
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Re: If x and y are positive integers such that x/y=5.4, which of the  [#permalink]

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New post 22 Mar 2019, 12:37
If you rewrite 5.4 as 27/5, and cross multiply, you get:

5x = 27y

Now x and y are integers, and 5x is the exact same number as 27y. So the divisors of 5x must be identical to the divisors of 27y. In particular, since 5 is clearly a divisor of 5x, it must also be a divisor of 27y. And since 5 is not a divisor of 27, 5 must be a divisor of y, and the only answer choice that has 5 as a divisor is 15.

Of course once you get to this equation:

x/y = 27/5

you might just be able to see that if we multiply by 3/3 on the right side to get 81/15, it might be that x=81 and y=15. But if you understand the more theoretical solution above, that's more useful, since you can apply it to other kinds of questions.
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Re: If x and y are positive integers such that x/y=5.4, which of the  [#permalink]

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New post 22 Mar 2019, 16:30
kiran120680 wrote:
If x and y are positive integers such that x/y=5.4, which of the following could be the value of y?

A. 12
B. 13
C. 14
D. 15
E. 16



Note: Both x and y have to be integers.

x/y = 5.4

Back solve the question.

Option D.
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Re: If x and y are positive integers such that x/y=5.4, which of the  [#permalink]

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New post 22 Mar 2019, 18:50
2
x/y = 5.4
= 54/10
= 27/5

so y can be 5 or multiple of 5

here we see only 15 satisy this condition


award kudos if helpful

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Re: If x and y are positive integers such that x/y=5.4, which of the  [#permalink]

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New post 23 Mar 2019, 01:57
x/y = 5,4

x = 5,4*y --> x needs to be a positive integer

The only answer choice that creates a positive integer for x is y = 15
(Hint: You can check if the last digit of the respective answer choices multiplied with 0,4 results in an integer with no remainder)

Answer: D
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Re: If x and y are positive integers such that x/y=5.4, which of the  [#permalink]

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New post 23 Mar 2019, 03:56
x/y = 54/10. it means it is 27/5. to have x as an integer, y should be 5 or multiple of 5
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Re: If x and y are positive integers such that x/y=5.4, which of the   [#permalink] 23 Mar 2019, 03:56
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