Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 44295

If x is an integer, which of the following is a possible value of (x² [#permalink]
Show Tags
21 Aug 2015, 05:07
1
This post received KUDOS
Expert's post
16
This post was BOOKMARKED
Question Stats:
62% (01:51) correct 38% (01:59) wrong based on 194 sessions
HideShow timer Statistics



Senior Manager
Joined: 28 Feb 2014
Posts: 296
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
2
This post received KUDOS
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: 17

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 post received KUDOS
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+2x48=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
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
This post received KUDOS
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.
So correct answer is (D).



Math Expert
Joined: 02 Sep 2009
Posts: 44295

Re: If x is an integer, which of the following is a possible value of (x² [#permalink]
Show Tags
23 Aug 2015, 12:11



Math Expert
Joined: 02 Sep 2009
Posts: 44295

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). Answer: D. To elaborate further: we have \(\frac{integer}{9}\), don't get trapped by the expression x^2+2x7. 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.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Current Student
Joined: 31 Oct 2011
Posts: 52
Location: India
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: 2752
Location: United States (IL)
Concentration: Finance, Economics
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
This post received KUDOS
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+127 = 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: 78

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 notnine 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




Re: If x is an integer, which of the following is a possible value of (x²
[#permalink]
15 Oct 2017, 09:07






