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Math Expert V
Joined: 02 Sep 2009
Posts: 55706
If x and y are positive integers, is x/y a terminating decimal?  [#permalink]

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Difficulty:   95% (hard)

Question Stats: 38% (01:59) correct 62% (01:52) wrong based on 159 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 V
Joined: 02 Aug 2009
Posts: 7754
Re: If x and y are positive integers, is x/y a terminating decimal?  [#permalink]

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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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Manager  B
Joined: 18 Jan 2018
Posts: 51
Re: If x and y are positive integers, is x/y a terminating decimal?  [#permalink]

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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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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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Math Expert V
Joined: 02 Sep 2009
Posts: 55706
Re: If x and y are positive integers, is x/y a terminating decimal?  [#permalink]

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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

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Intern  B
Joined: 24 Dec 2018
Posts: 40
Location: India
Re: If x and y are positive integers, is x/y a terminating decimal?  [#permalink]

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x/y will be a terminating decimal only if y is 1 or a multiple of 2 and/or 5. y cannot be a multiple of any other number other than 2 and/or 5.

With this principle in mind, let's look at the statements

Statement 1: y/x is even. So, this means either x=1 and y=even number or x is a factor of y such that the resulting fraction y/x is even
Let's take examples to understand this.

If x=3 and y=6, then y/x=6/3=2(=even number). But since y=6, x/y can't be terminating decimal

If x=5 and y=10, then y/x=10/5=2(=even number). Since y=10, x/y is a terminating decimal

Thus, this statement is insufficient

Statement 2: If the greatest common factor between two numbers is 1, this proves that any of the following cases can be true: 1) the two numbers are odd and even or 2) the two numbers are prime number or 3) that at least one of the two numbers is 1.

In any of the above cases, we cannot distinguish which one will y be, hence we cannot be sure if x/y will be terminating or not.

Thus, this statement is insufficient

Combining statements 1 & 2: we get that contrary to what we had deduced in statement 1, x cannot be a factor of y. Thus, x=1 and y is an even number.

Checking on the three cases:

1) x=1 and y= even doesn't prove whether x/y will necessarily be terminating. Eg: x=1 and y=10: results in x/y terminating vs x=1 and y=14, results in x/y non-terminating
Although this is enough to prove that statement 2 is insufficient, let's check the other two cases as well for our understanding.

2) This cannot hold true since x=1 which is neither prime nor composite

3) This is a repeat of case 1.

Thus, the statements when combined are also insufficient

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Re: If x and y are positive integers, is x/y a terminating decimal?  [#permalink]

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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

x/y will be terminating if y is in the form of 2^a * 5^b
now s1: y= 2*p*x
Now whether x/y will be terminating depends upon P. So not sufficient.
S2: Clearly not sufficient

S1+S2 x=1 but the rest depends upon P. So E
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If my post anyway helped you,please spare Kudos ! Re: If x and y are positive integers, is x/y a terminating decimal?   [#permalink] 28 Mar 2019, 04:15
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