|
Author |
Message |
|
TAGS:
|
|
|
Manager
Joined: 21 Jun 2010
Posts: 113
Schools: Tuck, Duke, Cambridge, Said
Followers: 3
Kudos [?]:
6
[0], given: 0
|
S is the infinite sequence S1=2, S2=22, S3=222 [#permalink]
 18 Jul 2010, 15:47
Question Stats:
46% (02:57) correct
53% (01:51) wrong based on 3 sessions
S is the infinite sequence S1 = 2, S2 = 22, S3 = 222,...Sk = Sk–1 + 2(10k–1). If p is the sum of the first 30 terms of S, what is the eleventh digit of p, counting right to left from the units digit? A) 1 B) 2 C) 4 D) 6 E) 9 Anyone knows what is the easiest and fastest method of solving this ?
|
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11507
Followers: 1791
Kudos [?]:
9530
[2] , given: 826
|
Re: Infinite seq of 2 [#permalink]
18 Jul 2010, 16:30
2
This post received
KUDOS
mn2010 wrote: S is the infinite sequence S1 = 2, S2 = 22, S3 = 222,...Sk = Sk–1 + 2(10k–1). If p is the sum of the first 30 terms of S, what is the eleventh digit of p, counting right to left from the units digit?
A) 1
B) 2
C) 4
D) 6
E) 9
Anyone knows what is the easiest and fastest method of solving this ? --------------------------------------------------2 -------------------------------------------------22 -----------------------------------------------222 ---------------------------------------------2,222 -------------------------------------------22,222 ... 222,222,222,222,222,222,222,222,222,222 Total 30 numbers. For the first digit (units place) we should add 30 2's --> 30*2=60, so 0 will be units digit and 6 will be carried over; For the second digit (tens place) we should add 29 2's --> 29*2=58+6=64, so 4 will be written for this digit and 6 will be carried over; ... For the 10th digit we should add 21 2's --> 21*2=42, so min value for the number carried over is 4. Max value is also 4, because even if the carry remained 6, as we had at the beginning, still --> 42+6=48, so still 4 will be carried over; For the 11th digit we should add 20 2's --> 20*2+4=44, so 11th digit will be 4. Answer: C. Just curios: is it GMAT question?
_________________
PLEASE READ AND FOLLOW: 11 Rules for Posting!!!
RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory
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. NEW!!!
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. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
Manager
Joined: 21 Jun 2010
Posts: 113
Schools: Tuck, Duke, Cambridge, Said
Followers: 3
Kudos [?]:
6
[0], given: 0
|
Re: Infinite seq of 2 [#permalink]
18 Jul 2010, 16:43
thanks bunuel .....
its in the MGMAT online practice question bank so I am assuming its a GMAT Q.
|
|
|
|
|
|
SVP
Joined: 17 Feb 2010
Posts: 1570
Followers: 12
Kudos [?]:
121
[0], given: 6
|
Re: Infinite seq of 2 [#permalink]
21 Jul 2010, 13:58
Hey Bunuel,
Is it possible to come up with a sequence formula for this question.
Because we have the value (2) of first term and with the sequnece formula we can get the value of the last term (30th term).
Once we have the first and last term values, we can take the average of the first and last values and multiply that by 30 to get the sum of 30 terms. That way we can get the eleventh digit of p.
Please share your thoughts on the same.
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11507
Followers: 1791
Kudos [?]:
9530
[0], given: 826
|
Re: Infinite seq of 2 [#permalink]
21 Jul 2010, 14:21
seekmba wrote: Hey Bunuel,
Is it possible to come up with a sequence formula for this question.
Because we have the value (2) of first term and with the sequnece formula we can get the value of the last term (30th term).
Once we have the first and last term values, we can take the average of the first and last values and multiply that by 30 to get the sum of 30 terms. That way we can get the eleventh digit of p.
Please share your thoughts on the same. Formula Sum = average of the first and last terms multiplied by # of terms can be used for evenly spaced set, but 2, 22, 222, ... is not such set, hence you can not use this formula here.
_________________
PLEASE READ AND FOLLOW: 11 Rules for Posting!!!
RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory
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. NEW!!!
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. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
SVP
Joined: 17 Feb 2010
Posts: 1570
Followers: 12
Kudos [?]:
121
[0], given: 6
|
Re: Infinite seq of 2 [#permalink]
22 Jul 2010, 07:43
Thanks Bunuel. Makes sense. I forgot about the evenly spaced set and hence mixed it up.
|
|
|
|
|
|
Director
Status: Preparing for the 4th time -:(
Joined: 25 Jun 2011
Posts: 558
Location: United Kingdom
Concentration: International Business, Strategy
GMAT Date: 06-22-2012
GPA: 2.9
WE: Information Technology (Consulting)
Followers: 8
Kudos [?]:
61
[0], given: 212
|
S is the infinite sequence S1 = 2, S2 = 22, S3 = 222,...Sk = Sk–1 + 2(10^k–1). If p is the sum of the first 30 terms of S, what is the eleventh digit of p, counting right to left from the units digit? 1 2 4 6 9 For me the answer is 2. Any thoughts anyone if you think I am wrong please?
_________________
Best Regards,
E.
MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610 
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11507
Followers: 1791
Kudos [?]:
9530
[0], given: 826
|
|
|
|
|
|
|
Manager
Joined: 23 Oct 2011
Posts: 85
Followers: 0
Kudos [?]:
11
[0], given: 34
|
Re: Infinite seq of 2 [#permalink]
13 Jan 2012, 16:55
Bunuel wrote: mn2010 wrote: S is the infinite sequence S1 = 2, S2 = 22, S3 = 222,...Sk = Sk–1 + 2(10k–1). If p is the sum of the first 30 terms of S, what is the eleventh digit of p, counting right to left from the units digit?
A) 1
B) 2
C) 4
D) 6
E) 9
Anyone knows what is the easiest and fastest method of solving this ? --------------------------------------------------2 -------------------------------------------------22 -----------------------------------------------222 ---------------------------------------------2,222 -------------------------------------------22,222 ... 222,222,222,222,222,222,222,222,222,222 Total 30 numbers. For the first digit (units place) we should add 30 2's --> 30*2=60, so 0 will be units digit and 6 will be carried over; For the second digit (tens place) we should add 29 2's --> 29*2=58+6=64, so 4 will be written for this digit and 6 will be carried over; ... For the 10th digit we should add 21 2's --> 21*2=42, so min value for the number carried over is 4. Max value is also 4, because even if the carry remained 6, as we had at the beginning, still --> 42+6=48, so still 4 will be carried over; For the 11th digit we should add 20 2's --> 20*2+4=44, so 11th digit will be 4. Answer: C. Just curios: is it GMAT question? Another more risky solution would be to try and find a pattern.. 1st digit ---> 30*2=60 ---> 0 and 6 will be carried over 2nd digit ---> 29*2+6=64 ---> 4 and 6 will be carried over 3rd digit ---> 28*2+6=62 ----> 2 and 6 will be carried over 4th digit --->27*2+6=60 ----> 0 and 6 will be carried over we could assume that this pattern will go on, therefore 11/3 gives as a remainder of 2 therefore the 11th digit will be the same wit the 2nd ---> C is my reasoning correct bunuel?
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11507
Followers: 1791
Kudos [?]:
9530
[1] , given: 826
|
Re: Infinite seq of 2 [#permalink]
13 Jan 2012, 17:18
1
This post received
KUDOS
SonyGmat wrote: Bunuel wrote: mn2010 wrote: S is the infinite sequence S1 = 2, S2 = 22, S3 = 222,...Sk = Sk–1 + 2(10k–1). If p is the sum of the first 30 terms of S, what is the eleventh digit of p, counting right to left from the units digit?
A) 1
B) 2
C) 4
D) 6
E) 9
Anyone knows what is the easiest and fastest method of solving this ? --------------------------------------------------2 -------------------------------------------------22 -----------------------------------------------222 ---------------------------------------------2,222 -------------------------------------------22,222 ... 222,222,222,222,222,222,222,222,222,222 Total 30 numbers. For the first digit (units place) we should add 30 2's --> 30*2=60, so 0 will be units digit and 6 will be carried over; For the second digit (tens place) we should add 29 2's --> 29*2=58+6=64, so 4 will be written for this digit and 6 will be carried over; ... For the 10th digit we should add 21 2's --> 21*2=42, so min value for the number carried over is 4. Max value is also 4, because even if the carry remained 6, as we had at the beginning, still --> 42+6=48, so still 4 will be carried over; For the 11th digit we should add 20 2's --> 20*2+4=44, so 11th digit will be 4. Answer: C. Just curios: is it GMAT question? Another more risky solution would be to try and find a pattern.. 1st digit ---> 30*2=60 ---> 0 and 6 will be carried over 2nd digit ---> 29*2+6=64 ---> 4 and 6 will be carried over 3rd digit ---> 28*2+6=62 ----> 2 and 6 will be carried over 4th digit --->27*2+6=60 ----> 0 and 6 will be carried over we could assume that this pattern will go on, therefore 11/3 gives as a remainder of 2 therefore the 11th digit will be the same wit the 2nd ---> C is my reasoning correct bunuel? Unfortunately not. If you continue you'll see that there is no pattern of 3: 5th digit ---> 26*2+6=58 ---> 8 and 5 will be carried over; 6th digit ---> 25*2+5=55 ---> 5 and 5 will be carried over; 7th digit ---> 24*2+5=53 ---> 3 and 5 will be carried over; 8th digit ---> 23*2+5=51 ---> 1 and 5 will be carried over; 9th digit ---> 22*2+5=49 ---> 9 and 4 will be carried over; 10th digit ---> 21*2+4=46 ---> 6 and 4 will be carried over; 11th digit ---> 20*2+4=44 ---> 4.
_________________
PLEASE READ AND FOLLOW: 11 Rules for Posting!!!
RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory
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. NEW!!!
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. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
Director
Status: Preparing for the 4th time -:(
Joined: 25 Jun 2011
Posts: 558
Location: United Kingdom
Concentration: International Business, Strategy
GMAT Date: 06-22-2012
GPA: 2.9
WE: Information Technology (Consulting)
Followers: 8
Kudos [?]:
61
[0], given: 212
|
Re: S is the infinite sequence S1=2, S2=22, S3=222 [#permalink]
13 Jan 2012, 23:12
Thanks Bunuel for a great and thorough explanation.
_________________
Best Regards,
E.
MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
|
|
|
|
|
|
Manager
Status: MBA Aspirant
Joined: 12 Jun 2010
Posts: 190
Location: India
Concentration: Finance, International Business
WE: Information Technology (Investment Banking)
Followers: 3
Kudos [?]:
14
[0], given: 1
|
Re: S is the infinite sequence S1=2, S2=22, S3=222 [#permalink]
14 Jan 2012, 03:17
Bunuel thanks for the explanation 
|
|
|
|
|
|
Senior Manager
Joined: 13 Aug 2012
Posts: 468
Followers: 12
Kudos [?]:
74
[0], given: 11
|
Re: S is the infinite sequence S1=2, S2=22, S3=222 [#permalink]
21 Dec 2012, 08:06
1st digit: 2*30 = 60, carry over 6
2nd digit: 2*29 = 58 + 6 = 64, carry over 6
3rd: 2*28 = 56 + 6 = 62, carry over 6
4th: 2*27 = 54 + 6 = 60, carry over 6
5th: 2*26 = 52 + 6 = 58, carry over 5
6th: 2*25 = 50 + 5 = 55, carry over 5
7th: 2*24 = 48 + 5 = 53, carry over 5
8th: 2*23 = 46 + 5 = 51, carry over 5
9th: 2*22= 44 + 5 = 49, carry over 4
10th: 2*21 = 42 + 4 = 46, carry over 4
11th: 2*20 = 40 + 4 = 44
Answer: 4
|
|
|
|
|
|
Manager
Joined: 26 Jul 2011
Posts: 119
Location: India
WE: Marketing (Manufacturing)
Followers: 1
Kudos [?]:
13
[0], given: 14
|
Re: S is the infinite sequence S1=2, S2=22, S3=222 [#permalink]
21 Dec 2012, 08:35
bunuel
can you please explain this part " so min value for the number carried over is 4. Max value is also 4, because even if the carry remained 6, as we had at the beginning, still --> 42+6=48, so still 4 will be carried over"
|
|
|
|
|
|
Intern
Joined: 17 Dec 2012
Posts: 3
Followers: 0
Kudos [?]:
0
[0], given: 0
|
Re: S is the infinite sequence S1=2, S2=22, S3=222 [#permalink]
21 Dec 2012, 17:28
Can someone please clarify what use is the "Sk = Sk–1 + 2(10k–1)" in the stem? is it used to throw you off? I'm not clear as to the reason it was provided nor do I see how it's used to provide the answer, 4.
I understand why the answer is 4, just not why or what that expression is provided for.
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11507
Followers: 1791
Kudos [?]:
9530
[0], given: 826
|
Re: S is the infinite sequence S1=2, S2=22, S3=222 [#permalink]
23 Dec 2012, 07:15
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11507
Followers: 1791
Kudos [?]:
9530
[0], given: 826
|
Re: S is the infinite sequence S1=2, S2=22, S3=222 [#permalink]
23 Dec 2012, 07:18
|
|
|
|
|
|
Manager
Joined: 11 Aug 2012
Posts: 78
Followers: 0
Kudos [?]:
4
[0], given: 11
|
Re: S is the infinite sequence S1=2, S2=22, S3=222 [#permalink]
24 Dec 2012, 12:02
+1 C
But it seems to be too long. It seems not a GMAT question.
|
|
|
|
|
|
Intern
Joined: 21 Jun 2012
Posts: 4
Followers: 0
Kudos [?]:
1
[0], given: 1
|
Re: S is the infinite sequence S1=2, S2=22, S3=222 [#permalink]
24 Dec 2012, 22:25
mn2010 wrote: S is the infinite sequence S1 = 2, S2 = 22, S3 = 222,...Sk = Sk–1 + 2(10k–1). If p is the sum of the first 30 terms of S, what is the eleventh digit of p, counting right to left from the units digit?
A) 1
B) 2
C) 4
D) 6
E) 9
Anyone knows what is the easiest and fastest method of solving this ? The answer is C i.e. 4. The 11th place from left has twenty 2's. Sum of which is 40, note there is a carry of 4 from the 10th digit from left and thus the total sum is 44. Thus the 11th digit from left is 4. I have used the long conventional way to figure this out. It took a good 3 mins. Can anyone share a way where you can find trends in the data. Thanks
|
|
|
|
|
|
|
Re: S is the infinite sequence S1=2, S2=22, S3=222
[#permalink]
24 Dec 2012, 22:25
|
|
|
|
|
|
|
|
|
Similar topics |
Author |
Replies |
Last post |
|
Similar
Topics:
|
 |
|
|
In a certain infinite sequence
|
AJB77 |
3 |
02 Jul 2005, 22:56 |
|
|
|
|
Infinite Sequence The infinite sequence a1, a2, , an, is
|
rbcola |
7 |
21 Jun 2006, 17:12 |
|
|
|
|
If S is an infinite sequence of positive integers, is S an
|
GMATT73 |
1 |
04 Sep 2006, 08:15 |
|
|
1
|
 |
Infinite sequence
|
ITC |
5 |
21 Apr 2010, 06:49 |
|
|
3
|
|
S is an infinite sequence, in which the value of a
|
gmatprep2011 |
4 |
23 Sep 2011, 23:23 |
|
|
|
|
|
|
close
