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

It is currently 11 Dec 2018, 21:36

Close

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
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.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • Free GMAT Prep Hour

     December 11, 2018

     December 11, 2018

     09:00 PM EST

     10:00 PM EST

    Strategies and techniques for approaching featured GMAT topics. December 11 at 9 PM EST.
  • The winning strategy for 700+ on the GMAT

     December 13, 2018

     December 13, 2018

     08:00 AM PST

     09:00 AM PST

    What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.

X1=1, for all positive integers, Xn=1+7Xn-1 , what is the units digit

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

Hide Tags

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6621
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
X1=1, for all positive integers, Xn=1+7Xn-1 , what is the units digit  [#permalink]

Show Tags

New post 08 Feb 2016, 17:45
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

84% (02:10) correct 16% (02:05) wrong based on 106 sessions

HideShow timer Statistics

X1=1, for all positive integers, Xn=1+7Xn-1 , what is the units digit of X102?

A. 3
B. 5
C. 8
D. 11
E. 15

Attachment:
X1=1.jpg
X1=1.jpg [ 7.25 KiB | Viewed 1460 times ]

* A solution will be posted in two days.

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Intern
Intern
avatar
Joined: 11 Sep 2010
Posts: 10
Location: India
GMAT 1: 620 Q49 V25
Re: X1=1, for all positive integers, Xn=1+7Xn-1 , what is the units digit  [#permalink]

Show Tags

New post 08 Feb 2016, 19:30
MathRevolution wrote:
X1=1, for all positive integers, Xn=1+7Xn-1 , what is the units digit of X102?

A. 3
B. 5
C. 8
D. 11
E. 15

Attachment:
X1=1.jpg

* A solution will be posted in two days.


X1 = 1
x2 = 1+7*1 = 8
X3 = 1+7*8 = 57
X4 = 1+7*57 = 400

From this we can see for all even X the unit digit is even and for Odd it is Odd.
From the answer choices only C is even hence that is the correct choice.
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7102
Re: X1=1, for all positive integers, Xn=1+7Xn-1 , what is the units digit  [#permalink]

Show Tags

New post 08 Feb 2016, 20:04
ankushjain wrote:
MathRevolution wrote:
X1=1, for all positive integers, Xn=1+7Xn-1 , what is the units digit of X102?

A. 3
B. 5
C. 8
D. 11
E. 15

Attachment:
X1=1.jpg

* A solution will be posted in two days.


X1 = 1
x2 = 1+7*1 = 8
X3 = 1+7*8 = 57
X4 = 1+7*57 = 400

From this we can see for all even X the unit digit is even and for Odd it is Odd.
From the answer choices only C is even hence that is the correct choice.


hi ankush,
if there was a choice as 0 or 4 also, then what would you have done..
you have to look for patterns in these Qs..
if you check for x5 it will be 1, since x4 had a 0 in units digit..
and thereafter ti will keep following the pattern..
1,8,7,0,1,8,7,0..
repetition is after every 4th number..
102= 4*25 + 2..
so it will have the same units digit as the second number, which is 8..
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6621
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Re: X1=1, for all positive integers, Xn=1+7Xn-1 , what is the units digit  [#permalink]

Show Tags

New post 10 Feb 2016, 20:55
X1=1, for all positive integers, Xn=1+7Xn-1 , what is the units digit of X102?

A. 3
B. 5
C. 8
D. 11
E. 15

--> When substituting, it becomes X1=1, X2=~8, X3=~7. X4=~0, X5=~1. That is, 1 -> 8 -> 7 -> 0 -> 1.. are repeated every 4 cycle.
Thus, X102=X4*25+2 -> X2=~8 and the answer is C.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Manager
Manager
avatar
Joined: 19 Jan 2016
Posts: 72
Location: India
Concentration: Strategy
Premium Member
Re: X1=1, for all positive integers, Xn=1+7Xn-1 , what is the units digit  [#permalink]

Show Tags

New post 16 Feb 2016, 02:04
1
Xn=1+7Xn-1

So when n=1, X1 = 1 + 7X(1-1) = 1 (which is true per question) therefore X0=0.
when n=2, X2 = 1 + 7X(2-1) = 1 + 7X1 = 1 + 7(1) = 8 (here we know X1 = 1 from the previous step).

Whatever value N may be, the value of X(n-1) is less than 1.

If N =102, then X(n-1) = 101.

Substituting in the equation,
X102 = 1 + 7(101) = 1 + 707 = 708.
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 9121
Premium Member
Re: X1=1, for all positive integers, Xn=1+7Xn-1 , what is the units digit  [#permalink]

Show Tags

New post 01 Aug 2018, 08:41
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

GMAT Club Bot
Re: X1=1, for all positive integers, Xn=1+7Xn-1 , what is the units digit &nbs [#permalink] 01 Aug 2018, 08:41
Display posts from previous: Sort by

X1=1, for all positive integers, Xn=1+7Xn-1 , what is the units digit

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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®.