GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 22 Sep 2018, 21:42

### 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 a is a positive integer, and if the units digit of a^2 is

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 25 Mar 2013
Posts: 256
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, 09:27
a = Positive Integer
a^2 = _9
Here , 2 cases
a = 3 or a = 7
Since, Units digit of (a+1)^2 = 64 ; a should be 7
(a+2)^2 = (7+2)^2 = 9^2 = 81
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: 720
Re: If a is a positive integer, and if the units digit of a^2 is  [#permalink]

### Show Tags

03 Apr 2017, 10:27
a^2 ends in 9
Possible cases:
3^2= 9
7^2=49

(a+1)^2 ends in 4
Possible cases:
(7+1)^2= 8^2=64

7 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: 2835
Re: If a is a positive integer, and if the units digit of a^2 is  [#permalink]

### Show Tags

06 Apr 2017, 10:05
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.

_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4033
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, 11:06
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 7

Since, units digit of $$(a+1)^2$$ is $$4$$ : a must be 7

Thus, $$(a+2)^2 = (7+2)^2 = 81$$ , 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, 18:05
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)
Non-Human User
Joined: 09 Sep 2013
Posts: 8150
Re: If a is a positive integer, and if the units digit of a^2 is  [#permalink]

### Show Tags

06 Sep 2018, 10:35
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.
_________________
Re: If a is a positive integer, and if the units digit of a^2 is &nbs [#permalink] 06 Sep 2018, 10:35

Go to page   Previous    1   2   [ 26 posts ]

Display posts from previous: Sort by

# If a is a positive integer, and if the units digit of a^2 is

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

## Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.