Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 17 Jul 2019, 08:30 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If x is an integer and x ≠ 31, is (31 - x)/x an integer?

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Aug 2009
Posts: 7764
If x is an integer and x ≠ 31, is (31 - x)/x an integer?  [#permalink]

### Show Tags 00:00

Difficulty:   55% (hard)

Question Stats: 57% (01:39) correct 43% (01:08) wrong based on 75 sessions

### HideShow timer Statistics If x is an integer and $$x\neq{31}$$, is $$\frac{31-x}{x}$$ an integer?

(1) x > 1.
(2) x is an even number.

_________________
Retired Moderator D
Joined: 25 Feb 2013
Posts: 1197
Location: India
GPA: 3.82
Re: If x is an integer and x ≠ 31, is (31 - x)/x an integer?  [#permalink]

### Show Tags

2
2
chetan2u wrote:
If x is an integer and $$x\neq{31}$$, is $$\frac{31-x}{x}$$ an integer?

(1) x > 1.
(2) x is an even number.

self made - on seeing a Bunuel Q

$$\frac{31-x}{x}=\frac{31}{x}-\frac{x}{x}=\frac{31}{x}-1$$

as $$x\neq{31}$$ and $$31$$ is a prime number, so the only way the above equation can be an integer is if $$x=1$$, $$-1$$ or $$-31$$

Statement 1: as $$x>1$$ so the equation is not integer. Sufficient

Statement 2: Again as $$x\neq31, 1, -1$$ or $$-31$$, so the equation will not be an integer. Sufficient

Option D

Originally posted by niks18 on 10 Dec 2017, 09:56.
Last edited by niks18 on 11 Dec 2017, 06:33, edited 2 times in total.
Retired Moderator P
Joined: 22 Aug 2013
Posts: 1435
Location: India
Re: If x is an integer and x ≠ 31, is (31 - x)/x an integer?  [#permalink]

### Show Tags

chetan2u wrote:
If x is an integer and $$x\neq{31}$$, is $$\frac{31-x}{x}$$ an integer?

(1) x > 1.
(2) x is an even number.

self made - on seeing a Bunuel Q

(31-x)/x can be written as 31/x - 1. Here -1 is already an integer, so 31/x - 1 will be an integer only when 31/x is an integer. This will be true only if x takes the following values: 1, 31, -1, -31 (its easy to see which values will satisfy because 31 is a prime number and thus has only 2 factors - 1 and 31. But the negative values of these will also result in integer). But we are already given that x is NOT equal to 31. So the only possible integer values of x which will result in 31/x being an integer are: 1, -1, -31.

(1) x > 1
This means there is simply no value x can take which will make 31/x an integer (because 1, -1, -31 are not possible here given that x > 1). So this can never be an integer. This gives us an answer as NO to the question. Sufficient.

(2) x is an even number.
Since 31 is odd, it can never be divisible by any even number. So 31/x cannot be an integer. This gives us an answer as NO to the question. Sufficient.

Manager  B
Joined: 09 Nov 2013
Posts: 63
Re: If x is an integer and x ≠ 31, is (31 - x)/x an integer?  [#permalink]

### Show Tags

1
no so much calculation required; it's simple but tricky question

(31-x)/x =>

for all x > 1 and even : (31-x) = odd so (31-x)/x [odd/even] can not be integer.
for all x > 1 and odd : (31-x) = even so (31-x)/x[even/odd] can not be integer.
Retired Moderator D
Joined: 25 Feb 2013
Posts: 1197
Location: India
GPA: 3.82
If x is an integer and x ≠ 31, is (31 - x)/x an integer?  [#permalink]

### Show Tags

Sidhrt wrote:
no so much calculation required; it's simple but tricky question

(31-x)/x =>

for all x > 1 and even : (31-x) = odd so (31-x)/x [odd/even] can not be integer.
for all x > 1 and odd : (31-x) = even so (31-x)/x[even/odd] can not be integer.

Well I don't think calculation is at all required in this question even if we use any other method. the answer is visually and logically quite evident.
Nonetheless you have brought in an excellent approach.
Kudos given to you Intern  B
Joined: 04 Sep 2017
Posts: 12
Re: If x is an integer and x ≠ 31, is (31 - x)/x an integer?  [#permalink]

### Show Tags

Sidhrt wrote:
no so much calculation required; it's simple but tricky question

(31-x)/x =>

for all x > 1 and even : (31-x) = odd so (31-x)/x [odd/even] can not be integer.
for all x > 1 and odd : (31-x) = even so (31-x)/x[even/odd] can not be integer.

Did you mean that even/odd can not be an integer? I know the numbers for this question will be such that it will never be an integer, but it's not true in every case.
6/3, 28/7, etc are even/odd and they are integers.
Non-Human User Joined: 09 Sep 2013
Posts: 11668
Re: If x is an integer and x ≠ 31, is (31 - x)/x an integer?  [#permalink]

### Show Tags

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________ Re: If x is an integer and x ≠ 31, is (31 - x)/x an integer?   [#permalink] 25 Jun 2019, 01:10
Display posts from previous: Sort by

# If x is an integer and x ≠ 31, is (31 - x)/x an integer?  