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# If x and y are positive integers, is x/y a terminating decimal?

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Math Expert
Joined: 02 Sep 2009
Posts: 50009
If x and y are positive integers, is x/y a terminating decimal?  [#permalink]

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30 Jan 2018, 07:19
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Difficulty:

85% (hard)

Question Stats:

37% (01:51) correct 63% (02:00) wrong based on 79 sessions

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If x and y are positive integers, is x/y a terminating decimal?

(1) y/x is even
(2) The greatest common factor of x and y is 1

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Math Expert
Joined: 02 Aug 2009
Posts: 6975
Re: If x and y are positive integers, is x/y a terminating decimal?  [#permalink]

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30 Jan 2018, 09:24
5
2
Bunuel wrote:
If x and y are positive integers, is x/y a terminating decimal?

(1) y/x is even
(2) The greatest common factor of x and y is 1

For $$x/y$$ to be a terminating decimal, y should be multiple of 2 or 5 only..

Let's see the statements..

1) y/x is even...
Just confirms that y is MULTIPLE of 2 and also of y..
But y can be 2, x/y will be terminating decimal
If y is 18 and X is 3, x/y will be 1/6, a non terminating decimal.
Insufficient

2) GCF of x and y is 1.
x as 3 and y as 2 will give x/y is terminating decimal.
x as 3 and y as 7 will give x/y as non-terminating decimal.
Insufficient

Combined
X and y are co-prime and y/x as even means x is 1 and y is MULTIPLE of 2..
If x is 1 and y is 10, x/y is terminating..
If x is 1 and y is 30, x/y is not terminating..
Insufficient

E
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##### General Discussion
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Joined: 18 Jan 2018
Posts: 50
Re: If x and y are positive integers, is x/y a terminating decimal?  [#permalink]

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05 Feb 2018, 12:53
Bunuel wrote:
If x and y are positive integers, is x/y a terminating decimal?

(1) y/x is even
(2) The greatest common factor of x and y is 1

Statement 1, y/x is even i.e 2 * (num), therefore x/y = 1/ (2*num). If this num is 5, x/y is terminating, if num is 7 x/y is not terminating. Not sufficient.

Statement 2, since GCF of x & y is 1, values of x & y could be 10 & 5 or 10 & 7. This statement is not sufficient since the x/y could be terminating or not terminating.

Together, the statements would not confirm whether the value of y is 5 or 7 or anything else.

Hence the answer is E. Correct me if I am wrong.
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If x and y are positive integers, is x/y a terminating decimal?  [#permalink]

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25 Feb 2018, 05:06
Bunuel wrote:
If x and y are positive integers, is x/y a terminating decimal?

(1) y/x is even
(2) The greatest common factor of x and y is 1

We can do it by taking $$x = 1, y =6$$ and $$x = 1, y = 4.$$ It will stand for both the equations.
Hence, E
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If x and y are positive integers, is x/y a terminating decimal? &nbs [#permalink] 25 Feb 2018, 05:06
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