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

It is currently 11 Dec 2018, 01:10

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.

The first three terms of an infinite sequence are 2, 7, and 22. After

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

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51096
The first three terms of an infinite sequence are 2, 7, and 22. After  [#permalink]

Show Tags

New post 21 Jul 2015, 02:08
1
7
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

63% (02:50) correct 37% (03:19) wrong based on 142 sessions

HideShow timer Statistics

The first three terms of an infinite sequence are 2, 7, and 22. After the first term, each consecutive term can be obtained by multiplying the previous term by 3 and then adding 1. What is the sum of the tens digit and the units digit of the thirty-fifth term in the sequence?

A. 2
B. 4
C. 7
D. 9
E. 13


Kudos for a correct solution.

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

CEO
CEO
User avatar
P
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2710
Location: India
GMAT: INSIGHT
WE: Education (Education)
Reviews Badge
The first three terms of an infinite sequence are 2, 7, and 22. After  [#permalink]

Show Tags

New post Updated on: 21 Jul 2015, 03:07
1
3
Bunuel wrote:
The first three terms of an infinite sequence are 2, 7, and 22. After the first term, each consecutive term can be obtained by multiplying the previous term by 3 and then adding 1. What is the sum of the tens digit and the units digit of the thirty-fifth term in the sequence?

A. 2
B. 4
C. 7
D. 9
E. 13


Kudos for a correct solution.


Following the rule of Infinite sequence we obtain the terms of the sequence as mentioned below

02, 07, 22, 67, 202, 607, 1822, 5467...

Observe the last two digits of the sequence which have the cyclicity of 4 and the last two digits repeat in the order {02, 07, 22, 67}

Also 35th Term = 4*8 + 3

i.e. 35th Terms will have same Last two digits as 3rd term of the sequence = 22

i.e. Sum of lat two digits of 35th Term = 2+2 = 4

Answer: Option B
_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION


Originally posted by GMATinsight on 21 Jul 2015, 02:57.
Last edited by GMATinsight on 21 Jul 2015, 03:07, edited 1 time in total.
CEO
CEO
avatar
S
Joined: 20 Mar 2014
Posts: 2633
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Premium Member Reviews Badge
Re: The first three terms of an infinite sequence are 2, 7, and 22. After  [#permalink]

Show Tags

New post 21 Jul 2015, 03:06
Bunuel wrote:
The first three terms of an infinite sequence are 2, 7, and 22. After the first term, each consecutive term can be obtained by multiplying the previous term by 3 and then adding 1. What is the sum of the tens digit and the units digit of the thirty-fifth term in the sequence?

A. 2
B. 4
C. 7
D. 9
E. 13


Kudos for a correct solution.


Writing the first few numbers in the sequence we get, 2, 7, 22, 67, 202, 607, 1822, 5467...

The repeated tens and unit digit seuqneces are 02,07,22,67. Thus the 35th term (8 sequences +3rd term ) will have 22 as its tens and unit's digit. Thus the sum = 2+2 = 4, B is the correct answer.
Current Student
avatar
Joined: 14 May 2014
Posts: 41
Schools: Broad '18 (WA)
GMAT 1: 700 Q44 V41
GPA: 3.11
GMAT ToolKit User Reviews Badge
Re: The first three terms of an infinite sequence are 2, 7, and 22. After  [#permalink]

Show Tags

New post 22 Jul 2015, 22:17
GMATinsight wrote:
Bunuel wrote:
The first three terms of an infinite sequence are 2, 7, and 22. After the first term, each consecutive term can be obtained by multiplying the previous term by 3 and then adding 1. What is the sum of the tens digit and the units digit of the thirty-fifth term in the sequence?

A. 2
B. 4
C. 7
D. 9
E. 13


Kudos for a correct solution.


Following the rule of Infinite sequence we obtain the terms of the sequence as mentioned below

02, 07, 22, 67, 202, 607, 1822, 5467...

Observe the last two digits of the sequence which have the cyclicity of 4 and the last two digits repeat in the order {02, 07, 22, 67}

Also 35th Term = 4*8 + 3

i.e. 35th Terms will have same Last two digits as 3rd term of the sequence = 22

i.e. Sum of lat two digits of 35th Term = 2+2 = 4

Answer: Option B


can this que be solved using formula of sequences in some way..?
CEO
CEO
User avatar
P
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2710
Location: India
GMAT: INSIGHT
WE: Education (Education)
Reviews Badge
The first three terms of an infinite sequence are 2, 7, and 22. After  [#permalink]

Show Tags

New post 22 Jul 2015, 22:24
1
riyazgilani wrote:
GMATinsight wrote:
Bunuel wrote:
The first three terms of an infinite sequence are 2, 7, and 22. After the first term, each consecutive term can be obtained by multiplying the previous term by 3 and then adding 1. What is the sum of the tens digit and the units digit of the thirty-fifth term in the sequence?

A. 2
B. 4
C. 7
D. 9
E. 13


Kudos for a correct solution.


Following the rule of Infinite sequence we obtain the terms of the sequence as mentioned below

02, 07, 22, 67, 202, 607, 1822, 5467...

Observe the last two digits of the sequence which have the cyclicity of 4 and the last two digits repeat in the order {02, 07, 22, 67}

Also 35th Term = 4*8 + 3

i.e. 35th Terms will have same Last two digits as 3rd term of the sequence = 22

i.e. Sum of lat two digits of 35th Term = 2+2 = 4

Answer: Option B


can this que be solved using formula of sequences in some way..?


The question is "What is the sum of the tens digit and the units digit of the thirty-fifth term in the sequence?"

The concept of Unit and Ten's digit is bases on CYCLICITY Principle so the apt principle to use here is Cyclicity Principle.

However, You may consider that the given sequence is a blend of AP and GP and is called AGP but calculating 35th Term would be too scary as the Common Ratio is 3 which is too big and would finally make the 35th Term as multiple of \(3^{34}\). Hence we, in any case, will never try to calculate 35th Term for this question and will strictly focus our calculations on the last two digits of 35th Term which is already calculated by the method mentioned above.

I hope it helps!
_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51096
Re: The first three terms of an infinite sequence are 2, 7, and 22. After  [#permalink]

Show Tags

New post 26 Jul 2015, 11:06
Bunuel wrote:
The first three terms of an infinite sequence are 2, 7, and 22. After the first term, each consecutive term can be obtained by multiplying the previous term by 3 and then adding 1. What is the sum of the tens digit and the units digit of the thirty-fifth term in the sequence?

A. 2
B. 4
C. 7
D. 9
E. 13


Kudos for a correct solution.


800score Official Solution:

(To understand units and tens, in 75 7 is tens and 5 is units.) We cannot reasonably be expected to write the sequence to the thirty-fifth term. We should therefore expect a repeating pattern within the tens and units digits of the sequence.

Let’s write out the first 8 terms and see what the pattern is:
2, 7, 22, 67, 202, 607, 1822, 5467.
Examining the tens and units digits, we see that the following four-term pattern repeats in those digits:
02, 07, 22, 67, etc.

To find what the tens and units digits of the thirty-fifth term will be, we must first divide the term number (35) by the number of terms in the repeating sequence (4):
35/4 = 8 remainder 3.
This means the four-term sequence fully repeats 8 times, and the remainder tells us how many terms into the repeating sequence the term in question will be.
Three terms into the repeating sequence, the tens and units digits are both 2. The sum of these digits is the answer to the question:
2 + 2 = 4.

The correct answer is choice (B).
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
avatar
Joined: 08 May 2015
Posts: 97
GMAT 1: 630 Q39 V38
GMAT 2: 670 Q44 V38
GMAT 3: 750 Q49 V44
The first three terms of a sequence are 2, 7, and 22. After the first  [#permalink]

Show Tags

New post 15 Aug 2015, 06:59
The first three terms of a sequence are 2, 7, and 22. After the first term, each consecutive term can be obtained by multiplying the previous term by 3 and then adding 1. If the sequence continues to be expanded, what will be the sum of the tens digit and the units digit of the thirty-fifth term in the sequence?

A. 2
B. 4
C. 7
D. 9
E. 13
CEO
CEO
avatar
S
Joined: 20 Mar 2014
Posts: 2633
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Premium Member Reviews Badge
Re: The first three terms of an infinite sequence are 2, 7, and 22. After  [#permalink]

Show Tags

New post 15 Aug 2015, 08:45
Mascarfi wrote:
The first three terms of a sequence are 2, 7, and 22. After the first term, each consecutive term can be obtained by multiplying the previous term by 3 and then adding 1. If the sequence continues to be expanded, what will be the sum of the tens digit and the units digit of the thirty-fifth term in the sequence?

A. 2
B. 4
C. 7
D. 9
E. 13


Please search for question before posting.
Manager
Manager
User avatar
Joined: 04 May 2015
Posts: 71
Concentration: Strategy, Operations
WE: Operations (Military & Defense)
Premium Member
The first three terms of an infinite sequence are 2, 7, and 22. After  [#permalink]

Show Tags

New post 15 Aug 2015, 19:20
Bunuel wrote:
The first three terms of an infinite sequence are 2, 7, and 22. After the first term, each consecutive term can be obtained by multiplying the previous term by 3 and then adding 1. What is the sum of the tens digit and the units digit of the thirty-fifth term in the sequence?

A. 2
B. 4
C. 7
D. 9
E. 13


Kudos for a correct solution.


I did in a similar but slightly different way:

1:0002
2:0007
3:0022
4:0067
5:0202
6:0607
7:1822


At this point I noticed that on the even terms the units digit was 7 and the odd terms the units digit was 2. I now knew on the 35th term the units digit was 2
I then also noticed that the tens digit followed the pattern 0, 0, 2,6, so knew that on the 36th term the tens digit was 6 therefore the 35th terms tens digit was also 2. 2 + 2 = 4

Hope this slightly different methodology helps someone as much as it does for me to write it out. haha :)
_________________

If you found my post useful, please consider throwing me a Kudos... Every bit helps :)

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 9103
Premium Member
Re: The first three terms of an infinite sequence are 2, 7, and 22. After  [#permalink]

Show Tags

New post 14 Jul 2018, 22:55
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: The first three terms of an infinite sequence are 2, 7, and 22. After &nbs [#permalink] 14 Jul 2018, 22:55
Display posts from previous: Sort by

The first three terms of an infinite sequence are 2, 7, and 22. After

  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®.