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• ### $450 Tuition Credit & Official CAT Packs FREE February 15, 2019 February 15, 2019 10:00 PM EST 11:00 PM PST EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) # If sequence S has 120 terms, what is the 105th term of S?  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Senior Manager Joined: 10 Mar 2013 Posts: 499 Location: Germany Concentration: Finance, Entrepreneurship GMAT 1: 580 Q46 V24 GPA: 3.88 WE: Information Technology (Consulting) If sequence S has 120 terms, what is the 105th term of S? [#permalink] ### Show Tags Updated on: 19 Sep 2015, 13:27 2 1 4 00:00 Difficulty: 5% (low) Question Stats: 93% (00:34) correct 7% (00:42) wrong based on 990 sessions ### HideShow timer Statistics If sequence S has 120 terms, what is the 105th term of S? (1) The first term of S is −8. (2) Each term of S after the first term is 10 more than the preceding term. Source: [OG 2016] _________________ When you’re up, your friends know who you are. When you’re down, you know who your friends are. Share some Kudos, if my posts help you. Thank you ! 800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50 GMAT PREP 670 MGMAT CAT 630 KAPLAN CAT 660 Originally posted by BrainLab on 19 Sep 2015, 12:01. Last edited by ENGRTOMBA2018 on 19 Sep 2015, 13:27, edited 1 time in total. Edited the question and renamed the topic CEO Joined: 20 Mar 2014 Posts: 2629 Concentration: Finance, Strategy Schools: Kellogg '18 (M) GMAT 1: 750 Q49 V44 GPA: 3.7 WE: Engineering (Aerospace and Defense) Re: If sequence S has 120 terms, what is the 105th term of S? [#permalink] ### Show Tags 19 Sep 2015, 13:35 1 2 BrainLab wrote: If sequence S has 120 terms, what is the 105th term of S? (1) The first term of S is −8. (2) Each term of S after the first term is 10 more than the preceding term. Source: [OG 2016] Follow the posting guidelines. If a question is from a particular source or year of official guide, mention it in the question and not in the topic title. Note that nowhere in the original question is it mentioned that the sequence S is some kind of a particular sequence (Arithmetic, Geometric etc). 105th term= $$S_{105}$$ Per statement 1, a=first term =-8. Still do not know what kind of a sequence is this. Per statement 2, Given that the sequence is an arithmetic progression (difference between 2 consecutive terms is constant) $$a_n$$=nth term in the sequence = $$a+(n-1)*d$$ where n=105 and d =10. Thus, 105th term = a+(105-1)*10 = a+1040. Still no information on 'a' or the first term. Not sufficient. Combining the 2 statements, a=-8 and thus, $$S_{105}$$ = $$a+(n-1)*d$$ = -108+1040=932. C is thus the correct answer. Director Status: Professional GMAT Tutor Affiliations: AB, cum laude, Harvard University (Class of '02) Joined: 10 Jul 2015 Posts: 674 Location: United States (CA) Age: 39 GMAT 1: 770 Q47 V48 GMAT 2: 730 Q44 V47 GMAT 3: 750 Q50 V42 GRE 1: Q168 V169 WE: Education (Education) Re: If sequence S has 120 terms, what is the 105th term of S? [#permalink] ### Show Tags 27 Mar 2016, 19:25 2 Here is a visual that should help. Attachments Screen Shot 2016-03-27 at 8.24.16 PM.png [ 316.93 KiB | Viewed 10613 times ] _________________ Harvard grad and 99% GMAT scorer, offering expert, private GMAT tutoring and coaching worldwide since 2002. One of the only known humans to have taken the GMAT 5 times and scored in the 700s every time (700, 710, 730, 750, 770), including verified section scores of Q50 / V47, as well as personal bests of 8/8 IR (2 times), 6/6 AWA (4 times), 50/51Q and 48/51V (1 question wrong). You can download my official test-taker score report (all scores within the last 5 years) directly from the Pearson Vue website: https://tinyurl.com/y7knw7bt Date of Birth: 09 December 1979. GMAT Action Plan and Free E-Book - McElroy Tutoring Contact: mcelroy@post.harvard.edu (I do not respond to PMs on GMAT Club.) ...or find me on Reddit: http://www.reddit.com/r/GMATpreparation CEO Joined: 11 Sep 2015 Posts: 3429 Location: Canada If sequence S has 120 terms, what is the 105th term of S? [#permalink] ### Show Tags 24 Jul 2017, 09:50 1 Top Contributor BrainLab wrote: If sequence S has 120 terms, what is the 105th term of S? (1) The first term of S is −8. (2) Each term of S after the first term is 10 more than the preceding term. Source: [OG 2016] Target question: What is the 105th term of S? Given: Sequence S has 120 terms Statement 1: The first term of S is −8. We have no information about the nature of the sequence. So, knowing the value of term 1 won't help is determine the value of term 105 Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT Statement 2: Each term of S after the first term is 10 more than the preceding term. This statement provides information about the nature of the sequence, but we don't know the first term. For example, the 105th term of the sequence {10, 20, 30, 40, ....} will be different from the 105th term of the sequence {3310, 3320, 3330, 3340, ....} Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT Statements 1 and 2 combined Statement 1 tells us that term 1 = -8 Statement 2 tells us that every term (after term 1) is 10 more than the preceding term So, the sequence is as follows: -8, 2, 12, 22, 32, 42, 52, 62, ..... At this point we COULD determine the value of the 105th term of the sequence . For example, we could keep listing every term until we get to the 105th term. However, we don't need to do that, since our sole objective is to determine whether we have sufficient information to answer the target question (which we DO) Since we can answer the target question with certainty, the combined statements are SUFFICIENT Answer: RELATED VIDEO _________________ Test confidently with gmatprepnow.com EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 13536 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If sequence S has 120 terms, what is the 105th term of S? [#permalink] ### Show Tags 16 Dec 2017, 14:13 1 Hi All, This question is another great example of a 'concept' question - if you understand the concept(s) involved, then you can get to the correct answer without doing much (if any) math. We're told that a sequence has 120 terms. We're asked for the 105th term in the sequence. 1) The first term of S is -8. While this Fact tells us the 1st term in the sequence, it does NOT tell us how the sequence progresses. The sequence might increase, decrease or 'oscillate', so there's no way to determine the 105th term. Fact 1 is INSUFFICIENT. 2) Each term of S after the first term is 10 more than the preceding term. Fact 2 tells us how the sequence progresses (each term is 10 greater than the term that precedes it), BUT we don't know any of the individual terms, so there's no way to determine the exact value of any of them. Fact 2 is INSUFFICIENT. Combined, we know: -The first term is -8 -Each term is 10 greater than the one that precedes it. Thus, we could figure out the 105th term (either algebraically or y just "adding 10s" until we get to that term). Either way, we CAN determine the value of the 105th term. Combined, SUFFICIENT. Final Answer: GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Joined: 09 Mar 2016
Posts: 1285
If sequence S has 120 terms, what is the 105th term of S?  [#permalink]

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25 Apr 2018, 12:46
ENGRTOMBA2018 wrote:
BrainLab wrote:
If sequence S has 120 terms, what is the 105th term of S?

(1) The first term of S is −8.
(2) Each term of S after the first term is 10 more than the preceding term.

Source: [OG 2016]

Follow the posting guidelines. If a question is from a particular source or year of official guide, mention it in the question and not in the topic title.

Note that nowhere in the original question is it mentioned that the sequence S is some kind of a particular sequence (Arithmetic, Geometric etc). 105th term= $$S_{105}$$

Per statement 1, a=first term =-8. Still do not know what kind of a sequence is this.

Per statement 2, Given that the sequence is an arithmetic progression (difference between 2 consecutive terms is constant) $$a_n$$=nth term in the sequence = $$a+(n-1)*d$$ where n=105 and d =10. Thus, 105th term = a+(105-1)*10 = a+1040. Still no information on 'a' or the first term. Not sufficient.

Combining the 2 statements, a=-8 and thus, $$S_{105}$$ = $$a+(n-1)*d$$ = -108+1040=932. C is thus the correct answer.

hello pushpitkc, can you please point out my mistake

$$S_{105}$$ = $$-8+(105-1)*10$$ ----> -8+1050-40 = 1032

even if I do so $$-8+(n-1)*10$$ I get 10n-18 ---> plug in 105 I get the same result 1032
DS Forum Moderator
Joined: 21 Aug 2013
Posts: 1431
Location: India
Re: If sequence S has 120 terms, what is the 105th term of S?  [#permalink]

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25 Apr 2018, 21:05
1
dave13 wrote:
ENGRTOMBA2018 wrote:
BrainLab wrote:
If sequence S has 120 terms, what is the 105th term of S?

(1) The first term of S is −8.
(2) Each term of S after the first term is 10 more than the preceding term.

Source: [OG 2016]

Follow the posting guidelines. If a question is from a particular source or year of official guide, mention it in the question and not in the topic title.

Note that nowhere in the original question is it mentioned that the sequence S is some kind of a particular sequence (Arithmetic, Geometric etc). 105th term= $$S_{105}$$

Per statement 1, a=first term =-8. Still do not know what kind of a sequence is this.

Per statement 2, Given that the sequence is an arithmetic progression (difference between 2 consecutive terms is constant) $$a_n$$=nth term in the sequence = $$a+(n-1)*d$$ where n=105 and d =10. Thus, 105th term = a+(105-1)*10 = a+1040. Still no information on 'a' or the first term. Not sufficient.

Combining the 2 statements, a=-8 and thus, $$S_{105}$$ = $$a+(n-1)*d$$ = -108+1040=932. C is thus the correct answer.

hello pushpitkc, can you please point out my mistake

$$S_{105}$$ = $$-8+(105-1)*10$$ ----> -8+1050-40 = 1032

even if I do so $$-8+(n-1)*10$$ I get 10n-18 ---> plug in 105 I get the same result 1032

Hello

There is no mistake, the 105th term will be 1032 only.
Intern
Joined: 26 Jul 2018
Posts: 13
Re: If sequence S has 120 terms, what is the 105th term of S?  [#permalink]

### Show Tags

07 Sep 2018, 17:26
ENGRTOMBA2018 wrote:
BrainLab wrote:
If sequence S has 120 terms, what is the 105th term of S?

(1) The first term of S is −8.
(2) Each term of S after the first term is 10 more than the preceding term.

Source: [OG 2016]

Follow the posting guidelines. If a question is from a particular source or year of official guide, mention it in the question and not in the topic title.

Note that nowhere in the original question is it mentioned that the sequence S is some kind of a particular sequence (Arithmetic, Geometric etc). 105th term= $$S_{105}$$

Per statement 1, a=first term =-8. Still do not know what kind of a sequence is this.

Per statement 2, Given that the sequence is an arithmetic progression (difference between 2 consecutive terms is constant) $$a_n$$=nth term in the sequence = $$a+(n-1)*d$$ where n=105 and d =10. Thus, 105th term = a+(105-1)*10 = a+1040. Still no information on 'a' or the first term. Not sufficient.

Combining the 2 statements, a=-8 and thus, $$S_{105}$$ = $$a+(n-1)*d$$ = -108+1040=932. C is thus the correct answer.

= -8+1040= 1032. C is thus the correct answer
Manager
Joined: 14 Jan 2017
Posts: 55
Location: India
Concentration: Strategy, General Management
Re: If sequence S has 120 terms, what is the 105th term of S?  [#permalink]

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10 Oct 2018, 12:41
1
dave13 wrote:
ENGRTOMBA2018 wrote:
BrainLab wrote:
If sequence S has 120 terms, what is the 105th term of S?

(1) The first term of S is −8.
(2) Each term of S after the first term is 10 more than the preceding term.

Source: [OG 2016]

Follow the posting guidelines. If a question is from a particular source or year of official guide, mention it in the question and not in the topic title.

Note that nowhere in the original question is it mentioned that the sequence S is some kind of a particular sequence (Arithmetic, Geometric etc). 105th term= $$S_{105}$$

Per statement 1, a=first term =-8. Still do not know what kind of a sequence is this.

Per statement 2, Given that the sequence is an arithmetic progression (difference between 2 consecutive terms is constant) $$a_n$$=nth term in the sequence = $$a+(n-1)*d$$ where n=105 and d =10. Thus, 105th term = a+(105-1)*10 = a+1040. Still no information on 'a' or the first term. Not sufficient.

Combining the 2 statements, a=-8 and thus, $$S_{105}$$ = $$a+(n-1)*d$$ = -108+1040=932. C is thus the correct answer.

hello pushpitkc, can you please point out my mistake

$$S_{105}$$ = $$-8+(105-1)*10$$ ----> -8+1050-40 = 1032

even if I do so $$-8+(n-1)*10$$ I get 10n-18 ---> plug in 105 I get the same result 1032

Hey dave13,
The problem lies in here;
Quote:
$$S_{105}$$ = $$-8+(105-1)*10$$ ----> -8+1050-40 = 1032

When you open the brackets it will be = -8 + 1050 - 10 = 1032. According to the calculation in RED, it should have been 1002.

Well, in both the cases you mentioned, the solution is correct and it will be 1032 anyway.
Intern
Joined: 20 Oct 2016
Posts: 36
Re: If sequence S has 120 terms, what is the 105th term of S?  [#permalink]

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12 Feb 2019, 03:19
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Re: If sequence S has 120 terms, what is the 105th term of S?   [#permalink] 12 Feb 2019, 03:19
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