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 Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

So thE units digit is the digit to the left of the decimal point or in integer it's the rightmost digit. For example: the units digit of 1.2 is 1 and the units digit of 13 is 3.

Back to the original question. 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?

The units digit of a^2 is 9 --> the units digit of a itself is either 3 or 7 (3^2=9 and 7^2=49); The units digit of (a+1)^2 is 4 --> the units digit of a+1 is either 2 or 8 (2^2=4 and 8^2=64), so the the units digit of a itself is either 2-1=1 or 8-1=7;

To satisfy both conditions the units digit of a must be 7. Now, a+2 will have the units digit equal to 7+2=9, thus the units digit of (a+2)^2, will be 1 (9^2=81).

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

Show Tags

19 Apr 2012, 05:40

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...

Substitution Method was followed to get the Answer A: 1

guess values: 3 satisfies 2nd condition, but not 3rd condition... but 7 satisfied both conditions and hence the answer 1 was obatined due the sq of 9 _________________

Regards, Harsha

Note: Give me kudos if my approach is right , else help me understand where i am missing.. I want to bell the GMAT Cat

So th units digit is the digit to the left of the decimal point or in integer it's the rightmost digit. For example: the units digit of 1.2 is 1 and the units digit of 13 is 3.

Back to the original question. 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?

The units digit of a^2 is 9 --> the units digit of a itself is either 3 or 7 (3^2=9 and 7^2=49); The units digit of (a+1)^2 is 4 --> the units digit of a+1 is either 2 or 8 (2^2=4 and 8^2=64), so the the units digit of a itself is either 2-1=1 or 8-1=7;

To satisfy both conditions the units digit of a must be 7. Now, a+2 will have the units digit equal to 7+2=9, thus the units digit of (a+2)^2, will be 1 (9^2=81).

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

Show Tags

08 Feb 2013, 09:40

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...

For unit digit of a^2 to be 9...unit digit of a has to be 3 or 7... Now for unit digit of (a+1)^2 to be 4..unit digit of a has to be 1 or 7.... From the above two conditions, unit value of a has to be 7, which will satisfy both the conditions... Now id unit digit of a is 7, unit digit of (a+2)^2 hast to be 1..

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

Show Tags

12 May 2014, 03:02

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 [#permalink]

Show Tags

12 May 2014, 03:14

1

This post received KUDOS

Expert's post

MensaNumber wrote:

Hi Bunuel, This one too is tagged as 'hard' in GMATPrep. While it is marked as sub 600 here. Thanks!

You are right but the difficulty level here is based on percentage of users who answered the question correctly/incorrectly: 89% of the users answered this question correctly. Hence the tag.

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

Show Tags

12 May 2014, 03:33

Bunuel, Thanks for your reply. Yup, it does!

However, I have not seen this logic hold true in every case. What are the percentage ranges for sub600, 600-700, +700 etc? This will help me point out incorrect tags if any so as to improve this forum.

And quite frankly I didnt find this question that easy. But cannot argue against the statistics unless those 101 users somehow were not representative of an average test taker. Moreover, I have heard GMAC also categorizes questions based on how many test takers got it right/wrong. With hundreds of thousands taking the gmat each year they are likely to have bigger data.

I am just trying to understand tagging here. Thanks for your understanding. _________________

Please contact me for super inexpensive quality private tutoring

My journey V46 and 750 -> http://gmatclub.com/forum/my-journey-to-46-on-verbal-750overall-171722.html#p1367876

Last edited by NoHalfMeasures on 03 Jun 2014, 19:23, edited 1 time in total.

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

Show Tags

12 May 2014, 03:40

Expert's post

MensaNumber wrote:

Bunuel, Thanks for your reply. Yup, it does!

However, I have not seen this logic hold true in every case. What are the percentage ranges for sub600, 600-700, +700 etc? This will help me point out incorrect tags if any so as to improve this forum.

And quite frankly I didnt find this question that easy. But cannot argue against the statistics unless those 101 users somehow were not representative of an average test taker. Moreover, I have hard GMAC also categorizes questions based on how many test takers got it right/wrong. With hundreds of thousands taking the gmat each year they are likely to have bigger data.

I am just trying to understand tagging here. Thanks for your understanding.

Well, you can judge the difficulty level of a question based on the statistics and not on the tags. I agree that GMAC has larger data and their stats might be more representative. Having said that I must add that still the difficulty level is quite subjective issue. _________________

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

Show Tags

12 May 2014, 03:49

Yes difficulty is a subjective matter. Hence I think defining percentage ranges corresponding to sub600, 600-700 and +700 is a great way to bring in objectivity? Or do we have these ranges already? Thanks! _________________

Please contact me for super inexpensive quality private tutoring

My journey V46 and 750 -> http://gmatclub.com/forum/my-journey-to-46-on-verbal-750overall-171722.html#p1367876

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

Show Tags

13 May 2014, 01:20

1

This post received KUDOS

Expert's post

MensaNumber wrote:

Yes difficulty is a subjective matter. Hence I think defining percentage ranges corresponding to sub600, 600-700 and +700 is a great way to bring in objectivity? Or do we have these ranges already? Thanks!

% of incorrect answers - Difficulty 0 - 29 = low (sub-600) 30 - 69 = medium (600-700) 70 - 99 = hard (700+) _________________

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

Show Tags

23 Jun 2015, 11:53

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. _________________

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

Show Tags

14 Jul 2016, 09:55

Gentlemen,

Good afternoon. It´s my first time in the Forum - I am glad to see such a nice resource!

Question: How can I be sure that if the units digit of (a^2 ) = 9 , for sure the units digit of "a" must be 3 or 7 ?

I have followed the answer by expanding the equations and adding the units digits, which I did too, but took quite a longer time.

My first thought when I saw the quation was this " units digit of "a" must e 7 or 9 " approach, however it just sounded in my mind like good a guess - how can I be sure that no other number squared from 0 to infinite will result in a number with 9 ,( or x, or y) in the units digit ? What theory am I missing, guys?

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

Show Tags

14 Jul 2016, 10:15

Expert's post

itabra wrote:

Gentlemen,

Good afternoon. It´s my first time in the Forum - I am glad to see such a nice resource!

Question: How can I be sure that if the units digit of (a^2 ) = 9 , for sure the units digit of "a" must be 3 or 7 ?

I have followed the answer by expanding the equations and adding the units digits, which I did too, but took quite a longer time.

My first thought when I saw the quation was this " units digit of "a" must e 7 or 9 " approach, however it just sounded in my mind like good a guess - how can I be sure that no other number squared from 0 to infinite will result in a number with 9 ,( or x, or y) in the units digit ? What theory am I missing, guys?

Thank you and luck to all!

If x is an integer to get the units digit of x^2 the only thing we need to know is the units digit of x itself. There are ten digits, so we can have only the following cases:

Excellent posts dLo saw your blog too..!! Man .. you have got some writing skills. And Just to make an argument = You had such an amazing resume ; i am glad...

So Much $$$ Business school costs a lot. This is obvious, whether you are a full-ride scholarship student or are paying fully out-of-pocket. Aside from the (constantly rising)...

I barely remember taking decent rest in the last 60 hours. It’s been relentless with submissions, birthday celebration, exams, vacating the flat, meeting people before leaving and of...

Rishabh from Gyan one services, India had a one to one interview with me where I shared my experience at IMD till now. http://www.gyanone.com/blog/life-at-imd-interview-with-imd-mba/ ...