GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 Jun 2019, 16:03

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

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

### Show Tags

30 Jan 2018, 07:19
1
11
00:00

Difficulty:

95% (hard)

Question Stats:

38% (01:59) correct 62% (01:52) wrong based on 159 sessions

### HideShow timer Statistics

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

_________________
Math Expert
Joined: 02 Aug 2009
Posts: 7754
Re: If x and y are positive integers, is x/y a terminating decimal?  [#permalink]

### Show Tags

30 Jan 2018, 09:24
7
3
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
_________________
##### General Discussion
Manager
Joined: 18 Jan 2018
Posts: 51
Re: If x and y are positive integers, is x/y a terminating decimal?  [#permalink]

### Show Tags

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.
Director
Joined: 31 Jul 2017
Posts: 516
Location: Malaysia
GMAT 1: 700 Q50 V33
GPA: 3.95
WE: Consulting (Energy and Utilities)
If x and y are positive integers, is x/y a terminating decimal?  [#permalink]

### Show Tags

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
_________________
If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !!
Math Expert
Joined: 02 Sep 2009
Posts: 55706
Re: If x and y are positive integers, is x/y a terminating decimal?  [#permalink]

### Show Tags

24 Dec 2018, 02:46
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

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

### Show Tags

02 Jan 2019, 05:41
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

_________________
Hit Kudos if you like my answer!
Manager
Joined: 23 Nov 2016
Posts: 138
Re: If x and y are positive integers, is x/y a terminating decimal?  [#permalink]

### Show Tags

28 Mar 2019, 04:15
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
_________________
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
Display posts from previous: Sort by