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

It is currently 11 Nov 2019, 22:19

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

If the 3rd term of sequence A is 15, what is the 2nd term?

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

Hide Tags

Find Similar Topics 
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15430
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
If the 3rd term of sequence A is 15, what is the 2nd term?  [#permalink]

Show Tags

New post Updated on: 04 Oct 2019, 16:40
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

60% (01:18) correct 40% (01:18) wrong based on 57 sessions

HideShow timer Statistics

EMPOWERgmat DS Series:
Pack 2, Question 1

If the 3rd term of sequence A is 15 and all of the terms in the sequence are positive, then what is the 2nd term?

1) The 1st term of A is 5.
2) Each term of A after the 1st term is y times the preceding term.


48 Hour Window To Win An $85 EMPOWERgmat Tuition Credit (1 Month Free!)
Share your explanation! The GMAT Club member with the most verified Kudos in total on the 5 question DS Block 2 question pack will win an $85 EMPOWERgmat tuition credit, which will entitle the winner to a full month of complete access to the EMPOWERgmat system. Even if you're not sure about your answer or your rationale, share your explanation to help boost your learning and earn a chance to win.

To be eligible, your explanation must be submitted within the 48 hour window after this post was created and should explain your reasoning why the answer you chose is correct

The OA and official explanation will be held until the 48 hour window has lapsed.

_________________
Contact Rich at: Rich.C@empowergmat.com
Image


The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★

Originally posted by EMPOWERgmatRichC on 01 Oct 2019, 21:06.
Last edited by EMPOWERgmatRichC on 04 Oct 2019, 16:40, edited 1 time in total.
Manager
Manager
avatar
S
Status: Student
Joined: 14 Jul 2019
Posts: 68
Location: United States
Concentration: Accounting, Finance
GPA: 3.9
WE: Education (Accounting)
Re: If the 3rd term of sequence A is 15, what is the 2nd term?  [#permalink]

Show Tags

New post 03 Oct 2019, 16:13
2
From Statement 1, we get the 1st term of the sequence, 5. But, from this we cannot infer about the 2nd term. It can be of any value. NOT SUFFICIENT.
Statement 2 tells us each term of the sequence is y times the preceding term. But it doesn't specify the value of y, without which we cannot get the value of any other term. NOT SUFFICIENT.

Together, 1st term, A= 5
2nd term, A*y=5y
3rd term, A* y^2 = 5y^2 =15 , or y^2= 10,

So y will be the positive root of 10 as 3rd term is greater than 1st term. From this we will get the 2nd term. SUFFICIENT.

Answer is C.
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15430
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
If the 3rd term of sequence A is 15, what is the 2nd term?  [#permalink]

Show Tags

New post Updated on: 07 Oct 2019, 19:31
OFFICIAL EXPLANATION

Hi All,

We're told that all of the terms in a sequence are positive and the 3rd term of sequence A is 15. We're asked for the 2nd term of the sequence.

1) The 1st term of A is 5.

Knowing 2 terms of the sequence is not enough to define how the sequence 'works' - or any of the other terms in the sequence. It's certainly possible that the sequence is Arithmetic and 'increases by 5' from term to term... meaning that the first three terms would be 5, 10 and 15.... and the answer to the question would be 10.

However, it's also possible that the sequence is Geometric and each term increases by some constant product (such as √3)... meaning that the first three terms would be 5, 5√3 and 15... and the answer to the question would be 5√3.
Fact 1 is INSUFFICIENT

2) Each term of A after the 1st term is y times the preceding term.

Fact 2 tells us how the sequence works, but without the first term in the sequence, we cannot determine the second term in the sequence.
Fact 2 is INSUFFICIENT

Combined, we know...
-The 1st term of A is 5.
-Each term of A after the 1st term is y times the preceding term.

With the information in both Facts, we know that the first term is 5, the third term is 15 and each term increases by some constant product. The only way for that sequence to exist is if y = √3... meaning that the first three terms are 5, 5√3 and 15... and the answer to the question is 5√3.

Combined, SUFFICIENT

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com
Image


The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★

Originally posted by EMPOWERgmatRichC on 04 Oct 2019, 16:39.
Last edited by EMPOWERgmatRichC on 07 Oct 2019, 19:31, edited 1 time in total.
Intern
Intern
avatar
B
Joined: 05 Mar 2018
Posts: 22
Re: If the 3rd term of sequence A is 15, what is the 2nd term?  [#permalink]

Show Tags

New post 04 Oct 2019, 23:02
1
minustark wrote:
From Statement 1, we get the 1st term of the sequence, 5. But, from this we cannot infer about the 2nd term. It can be of any value. NOT SUFFICIENT.
Statement 2 tells us each term of the sequence is y times the preceding term. But it doesn't specify the value of y, without which we cannot get the value of any other term. NOT SUFFICIENT.

Together, 1st term, A= 5
2nd term, A*y=5y
3rd term, A* y^2 = 5y^2 =15 , or y^2= 10,

So y will be the positive root of 10 as 3rd term is greater than 1st term. From this we will get the 2nd term. SUFFICIENT.

Answer is C.


Good logic, but Y^2 should be 3 not 10, y is the square root of 3
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15430
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If the 3rd term of sequence A is 15, what is the 2nd term?  [#permalink]

Show Tags

New post 07 Oct 2019, 19:32
Hi colinlin1,

Thanks for catching that typo; I've corrected it in my explanation.

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com
Image


The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Intern
Intern
avatar
B
Joined: 18 Jul 2019
Posts: 15
Re: If the 3rd term of sequence A is 15, what is the 2nd term?  [#permalink]

Show Tags

New post 14 Oct 2019, 12:17
1
EMPOWERgmatRichC wrote:
OFFICIAL EXPLANATION

Hi All,

We're told that all of the terms in a sequence are positive and the 3rd term of sequence A is 15. We're asked for the 2nd term of the sequence.

1) The 1st term of A is 5.

Knowing 2 terms of the sequence is not enough to define how the sequence 'works' - or any of the other terms in the sequence. It's certainly possible that the sequence is Arithmetic and 'increases by 5' from term to term... meaning that the first three terms would be 5, 10 and 15.... and the answer to the question would be 10.

However, it's also possible that the sequence is Geometric and each term increases by some constant product (such as √3)... meaning that the first three terms would be 5, 5√3 and 15... and the answer to the question would be 5√3.
Fact 1 is INSUFFICIENT



2) Each term of A after the 1st term is y times the preceding term.

Fact 2 tells us how the sequence works, but without the first term in the sequence, we cannot determine the second term in the sequence.
Fact 2 is INSUFFICIENT

Combined, we know...
-The 1st term of A is 5.
-Each term of A after the 1st term is y times the preceding term.

With the information in both Facts, we know that the first term is 5, the third term is 15 and each term increases by some constant product. The only way for that sequence to exist is if y = √3... meaning that the first three terms are 5, 5√3 and 15... and the answer to the question is 5√3.

Combined, SUFFICIENT

Final Answer:

GMAT assassins aren't born, they're made,
Rich



Hi, from both, Y^2 =3==> Y= +/- √3, shouldn't the answer still be E?? or should I ignore the -ve sign because its an AP.?
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15430
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If the 3rd term of sequence A is 15, what is the 2nd term?  [#permalink]

Show Tags

New post 14 Oct 2019, 16:37
Hi ankitprad,

You pose an important question - and under certain situations, you would have to consider negative values. However, the prompt tells us that all of the terms in the sequence are POSITIVE... and if you multiplied the first, positive term by a negative number, then the second term would be NEGATIVE. That does not fit the 'restrictions' given by the prompt, so it's not a possibility.

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com
Image


The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
GMAT Club Bot
Re: If the 3rd term of sequence A is 15, what is the 2nd term?   [#permalink] 14 Oct 2019, 16:37
Display posts from previous: Sort by

If the 3rd term of sequence A is 15, what is the 2nd term?

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





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne