February 17, 2019 February 17, 2019 07:00 AM PST 09:00 AM PST Attend this Free Algebra Webinar and learn how to master Inequalities and Absolute Value problems on GMAT. February 18, 2019 February 18, 2019 10:00 PM PST 11:00 PM PST We don’t care what your relationship status this year  we love you just the way you are. AND we want you to crush the GMAT!
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 25 Mar 2013
Posts: 240
Location: United States
Concentration: Entrepreneurship, Marketing
GPA: 3.5

Re: If a is a positive integer, and if the units digit of a^2 is
[#permalink]
Show Tags
26 Jan 2017, 08:27
a = Positive Integer a^2 = _9 Here , 2 cases a = 3 or a = 7 Since, Units digit of (a+1)^2 = 6 4 ; a should be 7 (a+2)^2 = (7+2)^2 = 9^2 = 8 1 A
_________________
I welcome analysis on my posts and kudo +1 if helpful. It helps me to improve my craft.Thank you



Director
Joined: 02 Sep 2016
Posts: 670

Re: If a is a positive integer, and if the units digit of a^2 is
[#permalink]
Show Tags
03 Apr 2017, 09:27
a^2 ends in 9 Possible cases: 3^2= 97^2=4 9(a+1)^2 ends in 4 Possible cases: (7+1)^2= 8^2=6 47 is the value of a because there is no need to consider any other value for a as from the first condition a^2, we know that a can either be 3 or 7. Information in second case confirms that the value of a is 7. Thus (a+2)^2 will end in 1.
_________________
Help me make my explanation better by providing a logical feedback.
If you liked the post, HIT KUDOS !!
Don't quit.............Do it.



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2827

Re: If a is a positive integer, and if the units digit of a^2 is
[#permalink]
Show Tags
06 Apr 2017, 09:05
ChenggongMAS wrote: If a is a positive integer, and if the units digit of a^2 is 9 and the units digit of (a+1)^2 is 4, what is the units digit of (a+2)^2?
A. 1 B. 3 C. 5 D. 6 C. 14 Since the units digit of a^2 is 9, the units digit of a is either 3 or 7. However, since the units digit of (a+1)^2 is 4, we see that the units digit of a must equal 7, since then the units digit of a + 1 is 8 and 8^2 = 64 (had the units digit of a been 3, then the units digit of a + 1 would have been 4, but 4^2 = 16). Thus, the units digit of a + 2 is 9, and since 9^2 = 81, the units digit of (a + 2)^2 is 1. Answer: A
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4383
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)

Re: If a is a positive integer, and if the units digit of a^2 is
[#permalink]
Show Tags
06 Apr 2017, 10:06
ChenggongMAS wrote: If a is a positive integer, and if the units digit of a^2 is 9 and the units digit of (a+1)^2 is 4, what is the units digit of (a+2)^2?
A. 1 B. 3 C. 5 D. 6 C. 14
I guess I am just not reading this properly. I don't understand what they mean by units digit... Since, units digit of \(a^2\) is \(9\) : a can be 3 or 7Since, units digit of \((a+1)^2\) is \(4\) : a must be 7Thus, \((a+2)^2 = (7+2)^2 = 81\) , so units digit is 1 Answer must be (A) 1
_________________
Thanks and Regards
Abhishek....
PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS
How to use Search Function in GMAT Club  Rules for Posting in QA forum  Writing Mathematical Formulas Rules for Posting in VA forum  Request Expert's Reply ( VA Forum Only )



Manager
Joined: 24 Jun 2017
Posts: 122

Re: If a is a positive integer, and if the units digit of a^2 is
[#permalink]
Show Tags
02 Jul 2017, 17:05
Another possible solution without the substitution based on a logical equation: a^2= x9 (where x  other place values, tenths, hundredths and so on) (a + 1)^2 = a^2 + 2a + 1 = x4 ,so x9 + 1 + 2a = x0 + 2a = x4 (a + 2)^2 = a^2 + 4a + 4 = x9 +4 + 4а = x3 + 8 = x1 (result of logical equation compared to the above one, with 2а)



NonHuman User
Joined: 09 Sep 2013
Posts: 9837

Re: If a is a positive integer, and if the units digit of a^2 is
[#permalink]
Show Tags
06 Sep 2018, 09:35
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.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: If a is a positive integer, and if the units digit of a^2 is
[#permalink]
06 Sep 2018, 09:35



Go to page
Previous
1 2
[ 26 posts ]



