Author 
Message 
Retired Moderator
Joined: 26 Nov 2012
Posts: 597

If y = x2 + x  x+2 where x is an integer, then y can take how
[#permalink]
Show Tags
14 May 2017, 09:26
Question Stats:
82% (02:48) correct 18% (05:01) wrong based on 50 sessions
HideShow timer Statistics
If y = x2 + x  x+2 where x is an integer, then y can take how many nonzero integral values between 10 and 10, exclusive? A.10 B.11 C.12 D.13 E.14 == Message from the GMAT Club Team == THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION. This discussion does not meet community quality standards. It has been retired. If you would like to discuss this question please repost it in the respective forum. Thank you! To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative  Verbal Please note  we may remove posts that do not follow our posting guidelines. Thank you.
Official Answer and Stats are available only to registered users. Register/ Login.



Manager
Joined: 22 Mar 2014
Posts: 141
Location: United States
Concentration: Finance, Operations
GPA: 3.91
WE: Information Technology (Computer Software)

Re: If y = x2 + x  x+2 where x is an integer, then y can take how
[#permalink]
Show Tags
15 May 2017, 00:45
I am not sure about how to do this... Can anybody please suggest a process?



SVP
Joined: 08 Jul 2010
Posts: 2334
Location: India
GMAT: INSIGHT
WE: Education (Education)

If y = x2 + x  x+2 where x is an integer, then y can take how
[#permalink]
Show Tags
15 May 2017, 02:51
msk0657 wrote: If y = x2 + x  x+2 where x is an integer, then y can take how many nonzero integral values between 10 and 10, exclusive?
A.10 B.11 C.12 D.13 E.14 Start substituting values for the simplest approach to this question. y = x2 + x  x+2 @x = 0, y = 0 @x = 1, y = 1 @x = 2, y = 2 @x = 3, y = 1 @x = 4, y = 0 @x = 5, y = 1 @x = 6, y = 2 @x = 7, y = 3 @x = 8, y = 4 @x = 9, y = 5 and so on so all positive values till 10 so total Integer values of x = 12 {2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9} Answer: Option C
_________________
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html
22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



SVP
Joined: 12 Dec 2016
Posts: 1789
Location: United States
GPA: 3.64

If y = x2 + x  x+2 where x is an integer, then y can take how
[#permalink]
Show Tags
15 May 2017, 03:11
mine is A, only 10 values, after breaks the absolute sign, y can only takes range from 2 to 9, and except 0 => 10 values 2 0 2 x2  0 + x  0 + x+2  0 + /x+2/ x+2 x2
x >=2 y = x 4 => 10 values



SVP
Joined: 08 Jul 2010
Posts: 2334
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: If y = x2 + x  x+2 where x is an integer, then y can take how
[#permalink]
Show Tags
15 May 2017, 03:25
chesstitans wrote: mine is A, only 10 values, after breaks the absolute sign, y can only takes range from 2 to 9, and except 0 => 10 values 2 0 2 x2  0 + x  0 + x+2  0 + /x+2/ x+2 x2
x >=2 y = x 4 => 10 values I see two mistakes here 1) 2 to 9 there are 12 values 2) y may be 0 @x=0
_________________
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html
22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8288
Location: Pune, India

Re: If y = x2 + x  x+2 where x is an integer, then y can take how
[#permalink]
Show Tags
15 May 2017, 05:04
msk0657 wrote: If y = x2 + x  x+2 where x is an integer, then y can take how many nonzero integral values between 10 and 10, exclusive?
A.10 B.11 C.12 D.13 E.14 Use the number line to figure this out. ................. 5 ........ 4 ....... 3 ....... 2 ....... 1 ........ 0 ........ 1 ........ 2 ........ 3 ......... 4 ........ 5 .............. We need the sum of "distance from 0" + "distance from 2" and from that we need to subtract the "distance from 2". This will be y. A few things to note right away: At 0, distance from 2 = distance from 2 and hence y = 0 At the right of 0, distance from 2 and distance from 0 effectively will always add up to 2. We will just keep adding distance from 2 to this. At x = 1, this will give us y = 1. At x = 2, this will give us y = 2. At x = 3, this will give us y = 1. and now the distance from 2 will keep increasing so we will get all values from 0 to infinity. In our desired range, we get 0 to 9. At the left of 0, the distance from 2 will always get cancelled out by distance from 0 and hence y will always be positive. We have already got all positive values of y. So all values of y from 2 to 9 are possible i.e. 12 values. Answer (C)
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!



Math Expert
Joined: 02 Aug 2009
Posts: 6800

Re: If y = x2 + x  x+2 where x is an integer, then y can take how
[#permalink]
Show Tags
15 May 2017, 05:54
Hi, As explained above, the values y can take is from 2 to 9... When x is 0, y=0... At all values of x above 2, an increase of 1 in value of x, increase in x2 and x will also be 1 each and x+2 will increase by 1.. Thus effect will be 1+11=1.. At x as 2, y=22+22+2=2.. so y can take all values of 2 and above it.. So 12 values.. But be careful, inspite of doing everything correct, you will land up with wrong answer as we are looking for nonzero.. There are 12 values including 0.. Ans=121=11
B
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
GMAT online Tutor



Senior CR Moderator
Status: Long way to go!
Joined: 10 Oct 2016
Posts: 1387
Location: Viet Nam

Re: If y = x2 + x  x+2 where x is an integer, then y can take how
[#permalink]
Show Tags
15 May 2017, 08:11
msk0657 wrote: If y = x2 + x  x+2 where x is an integer, then y can take how many nonzero integral values between 10 and 10, exclusive?
A.10 B.11 C.12 D.13 E.14 If \(x<2\) then \(y=(2x)x+(x+2)=4x\)\(x=3 \implies y=7\) \(x=4 \implies y=8\) If \(x\) decreases then \(y\) increases. If \(2 \leq x < 0\) then \(y=(2x)x(x+2)=3x\)\(x=2 \implies y=6\) \(x=1 \implies y=3\) If \(0 \leq x < 2\) then \(y=(2x)+x(x+2)=x\)\(x=0 \implies y=0\) \(x=1 \implies y=1\) If \(x \geq 2\) then \(y=(x2)+x(x+2)=x4\)\(x=2 \implies y=2\) \(x=3 \implies y=1\) \(x=4 \implies y=0\) ... \(x=13 \implies y=9\) \(x=14 \implies y=10\) If \(x\) increases then \(y\) increases. Based on cases above, we see that \(y\) could receive value from \(2\) to positive infinitive. Hence, y could receive 13 values between 10 and 10 (from 10 to 10). However, the question asks for nonzero integral values, hence we need to exclude 0 and 10. Hence the answer will be 11. 2, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9 The answer is B
_________________
Actual LSAT CR bank by Broall
How to solve quadratic equations  Factor quadratic equations Factor table with sign: The useful tool to solve polynomial inequalities Applying AMGM inequality into finding extreme/absolute value
New Error Log with Timer



SVP
Joined: 26 Mar 2013
Posts: 1808

Re: If y = x2 + x  x+2 where x is an integer, then y can take how
[#permalink]
Show Tags
16 May 2017, 04:52
GMATinsight wrote: msk0657 wrote: If y = x2 + x  x+2 where x is an integer, then y can take how manynonzero integral values between 10 and 10, exclusive?
A.10 B.11 C.12 D.13 E.14 Start substituting values for the simplest approach to this question. y = x2 + x  x+2 @x = 0, y = 0@x = 1, y = 1 @x = 2, y = 2 @x = 3, y = 1 @x = 4, y = 0 @x = 5, y = 1 @x = 6, y = 2 @x = 7, y = 3 @x = 8, y = 4 @x = 9, y = 5 and so on so all positive values till 10 so total Integer values of x = 12 {2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9} Answer: Option C The question asks fro Nonzero integer values.



Manager
Joined: 12 Feb 2015
Posts: 125
Location: India
Concentration: Technology, Operations
GPA: 3.9
WE: Information Technology (Computer Software)

Re: If y = x2 + x  x+2 where x is an integer, then y can take how
[#permalink]
Show Tags
17 May 2017, 10:55
Bunuel plz can u explain this qn... i m not very confident on how the sign changes for range related values as above soln does. == Message from the GMAT Club Team == THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION. This discussion does not meet community quality standards. It has been retired. If you would like to discuss this question please repost it in the respective forum. Thank you! To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative  Verbal Please note  we may remove posts that do not follow our posting guidelines. Thank you.




Re: If y = x2 + x  x+2 where x is an integer, then y can take how &nbs
[#permalink]
17 May 2017, 10:55






