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

 It is currently 19 Jul 2019, 05:41

### 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 is an integer, which of the following is a possible value of (x²

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 56302
If x is an integer, which of the following is a possible value of (x²  [#permalink]

### Show Tags

21 Aug 2015, 05:07
3
23
00:00

Difficulty:

65% (hard)

Question Stats:

62% (02:14) correct 38% (02:25) wrong based on 178 sessions

### HideShow timer Statistics

If x is an integer, which of the following is a possible value of (x^2 +2x – 7)/9?

A. -2.4
B. 0.268
C. 1.166 repeating
D. 4.555 repeating
E. 8.125

Kudos for a correct solution.

_________________
Senior Manager
Joined: 28 Feb 2014
Posts: 294
Location: United States
Concentration: Strategy, General Management
Re: If x is an integer, which of the following is a possible value of (x²  [#permalink]

### Show Tags

21 Aug 2015, 07:48
4
x is an integer, which of the following is a possible value of (x^2 +2x – 7)/9?
Used process of elimination
A. -2.4
when this is multiplied by 9, x is not an integer
B. 0.268
when this is multiplied by 9, x is not an integer
C. 1.166 repeating
when this is multiplied by 9, x is not an integer
D. 4.555 repeating
E. 8.125
when this is multiplied by 9, x is not an integer

Answer choice D seems to fit
Intern
Joined: 01 Jul 2015
Posts: 13
Re: If x is an integer, which of the following is a possible value of (x²  [#permalink]

### Show Tags

21 Aug 2015, 08:14
1
This question is actually testing the test taker's knowledge about property of number "9".
Any number, which is not divisible by 9, if divided by 9, the remainder repeats after decimal infinetely.
This property matches with option "D".
It is 41/9, which after multiplied with 9 leaves 41. Hence forming a quadratic equation X^2+2x-48=0, whose factors can be derived -> X=-8 or X=6
Intern
Joined: 01 Jul 2015
Posts: 5
Location: United States (IL)
Concentration: Technology, Finance
GMAT 1: 710 Q49 V38
GPA: 3.5
WE: Programming (Computer Software)
If x is an integer, which of the following is a possible value of (x²  [#permalink]

### Show Tags

21 Aug 2015, 08:19
2
Convert to fraction and multiply by 9, if you get an integer, then you've the solution.
As only one answer is correct, if I prove one to be correct, I have the solution.

For repeating decimals - I tried in order -
C)
a = 1.166
10a = 11.666 -- i
100a = 116.6666 -- ii

ii - i
90a = 105
a = 105/90
a*9 = 105/10 = 10.5 - not an answer

D)
x = 4.555
10x = 45.5555
9x = 41
x= 41/9
x*9 = 41 -- can be the answer

putting back in original equation we get x = 6,-8 as possible solutions. So this is the correct answer.

Rest of all can be tested simply by converting them into fractions.

Math Expert
Joined: 02 Sep 2009
Posts: 56302
Re: If x is an integer, which of the following is a possible value of (x²  [#permalink]

### Show Tags

23 Aug 2015, 12:11
Bunuel wrote:
If x is an integer, which of the following is a possible value of (x^2 +2x – 7)/9?

A. -2.4
B. 0.268
C. 1.166 repeating
D. 4.555 repeating
E. 8.125

Kudos for a correct solution.

GROCKIT OFFICIAL SOLUTION:

We don’t have to start plugging in. We know that when divided by 9, the remainder will be a number repeating to the right of the decimal place. Only choice (D) fits that description.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 56302
Re: If x is an integer, which of the following is a possible value of (x²  [#permalink]

### Show Tags

23 Aug 2015, 12:13
Bunuel wrote:
Bunuel wrote:
If x is an integer, which of the following is a possible value of (x^2 +2x – 7)/9?

A. -2.4
B. 0.268
C. 1.166 repeating
D. 4.555 repeating
E. 8.125

Kudos for a correct solution.

GROCKIT OFFICIAL SOLUTION:

We don’t have to start plugging in. We know that when divided by 9, the remainder will be a number repeating to the right of the decimal place. Only choice (D) fits that description.

As nominator is an integer and denominator equals to 9, their division will result either integer or the repeating decimal (A, B, E are out). Plus repeating decimal will be one digit long (eg 111... or 333... not 123123...) and right after the decimal point (C out).

To elaborate further: we have $$\frac{integer}{9}$$, don't get trapped by the expression x^2+2x-7. What is important here is that the numerator will be integer as x is an integer.

$$\frac{integer}{9}$$ can be either an integer 18/9=2, 27/9=3 ... or repeating decimal of the form k.aaaa..., where k is an integer >=0 and a is <9. Only D offers such number.
_________________
Manager
Joined: 31 Oct 2011
Posts: 50
Location: India
GMAT 1: 660 Q48 V32
GPA: 3.56
WE: Programming (Computer Software)
Re: If x is an integer, which of the following is a possible value of (x²  [#permalink]

### Show Tags

31 Aug 2015, 20:09
Solution : Let's try and see if we can get a pattern upon division of an integer by 9.

Trying 1/9 : 1/9 = 0.111111...

So, for any x by 9, the decimal part will be a multiple of 0.111111... That leaves us only with option D
Board of Directors
Joined: 17 Jul 2014
Posts: 2539
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
If x is an integer, which of the following is a possible value of (x²  [#permalink]

### Show Tags

25 Oct 2015, 10:21
1
a more rapid approach is understanding that x/9 will yield 0.xxxxxx repeating. Only D has this pattern, so D is the answer choice.
if to try, we can pick up x=6, 36+12-7 = 41/9 and this is equal to 4.55555 repeating.

we can as well notice that in C, the repeating decimal is 1666666.., this is clearly 1/6, but from the given fraction, we cannot get to smth/6.
_________________
Manager
Joined: 21 Jun 2017
Posts: 83
Re: If x is an integer, which of the following is a possible value of (x²  [#permalink]

### Show Tags

15 Oct 2017, 09:07
Bunuel wrote:
If x is an integer, which of the following is a possible value of (x^2 +2x – 7)/9?

A. -2.4
B. 0.268
C. 1.166 repeating
D. 4.555 repeating
E. 8.125

Kudos for a correct solution.

Short cut to this is the know number properties from the arithmetic section. Number not-nine is divided by nine, its digits repeat infinitely. Knowing this, focus on options c, d.

For option c, let x = 4. 16 + 8 - 7 /9 = 17/9 = 1 8/9 = 1.888; therefore, eliminate option d

let x = 6; 41/9 = 4 5/9 = 4.555
Thus, the answer is D) 4.555
Non-Human User
Joined: 09 Sep 2013
Posts: 11703
Re: If x is an integer, which of the following is a possible value of (x²  [#permalink]

### Show Tags

03 Jun 2019, 03:14
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, which of the following is a possible value of (x²   [#permalink] 03 Jun 2019, 03:14
Display posts from previous: Sort by