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

It is currently 19 Oct 2018, 17:03

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

In the sequence above, each term after the first term is equal to the

  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: 50002
In the sequence above, each term after the first term is equal to the  [#permalink]

Show Tags

New post 13 May 2015, 04:47
1
2
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

77% (02:34) correct 23% (03:14) wrong based on 187 sessions

HideShow timer Statistics

\(t_1\), \(t_2\), \(t_3\), ..., \(t_n\), ...
In the sequence above, each term after the first term is equal to the preceding term plus the constant k. If \(t_1+t_3+t_5+t_7=32\), what is the value of \(t_2+t_4+t_6\) ?

A. 8
B. 12
C. 24
D. 32
E. 72

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

Senior Manager
Senior Manager
User avatar
B
Joined: 28 Feb 2014
Posts: 294
Location: United States
Concentration: Strategy, General Management
Reviews Badge
Re: In the sequence above, each term after the first term is equal to the  [#permalink]

Show Tags

New post 13 May 2015, 07:03
2
1
x+x+2k+x+4k+x+6k=32
4x+12k=32
x+3k=8

We are looking for the value of:
x+k+x+3k+x+5k=?
3x+9k=?

3(x+3k=8)
3x+9k=24

Answer: C
Intern
Intern
avatar
Joined: 22 Mar 2015
Posts: 3
Re: In the sequence above, each term after the first term is equal to the  [#permalink]

Show Tags

New post 13 May 2015, 20:11
1
t1 + t3 +t5 +t7 = t1 + t1 +2k +t1 +4k +t1 +6k= 4t + 12k = 32
t = 2 ==> k =2 ==> t2+t4 +t6 = 4 +8 +12 = 24
=> C
Senior Manager
Senior Manager
User avatar
S
Joined: 21 Jan 2015
Posts: 346
Location: India
Concentration: Strategy, Marketing
GMAT 1: 620 Q48 V28
GMAT 2: 690 Q49 V35
WE: Sales (Consumer Products)
GMAT ToolKit User CAT Tests
Re: In the sequence above, each term after the first term is equal to the  [#permalink]

Show Tags

New post 13 May 2015, 21:59
1
1
Bunuel wrote:
\(t_1\), \(t_2\), \(t_3\), ..., \(t_n\), ...
In the sequence above, each term after the first term is equal to the preceding term plus the constant k. If \(t_1+t_3+t_5+t_7=32\), what is the value of \(t_2+t_4+t_6\) ?

A. 8
B. 12
C. 24
D. 32
E. 72


Ans: C
Solution: according to given condition
t2=t1+k
t3=t2+k = t1+2k
same way t4=t1+3k
t5=t1+4k
t6=t1+5k
t7=t1+6k

now by putting the values in given equation
t1+t3+t5+t7=32
t1+3k=8

required value
t2+t4+t6 = 3(t1+3k)= 3*8= 24

Ans: C
_________________

--------------------------------------------------------------------
The Mind is Everything, What we Think we Become.
Kudos will encourage many others, like me.
Please Give Kudos Image !!
Thanks :-)

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50002
In the sequence above, each term after the first term is equal to the  [#permalink]

Show Tags

New post 18 May 2015, 06:29
Bunuel wrote:
\(t_1\), \(t_2\), \(t_3\), ..., \(t_n\), ...
In the sequence above, each term after the first term is equal to the preceding term plus the constant k. If \(t_1+t_3+t_5+t_7=32\), what is the value of \(t_2+t_4+t_6\) ?

A. 8
B. 12
C. 24
D. 32
E. 72

Kudos for a correct solution.


OFFICIAL SOLUTION:

According to the stem:
\(t_2=t_1+k\);
\(t_3=t_2+k=t_1+2k\);
\(t_4=t_3+k=t_1+3k\);
...
\(t_n=t_1+(n-1)k\);

Since \(t_1+t_3+t_5+t_7=32\), then \(t_1+(t_1+2k)+(t_1+4k)+(t_1+6k)=32\). So, \(t_1+3k=8\)

We need to find the of \(t_2+t_4+t_6=(t_1+k)+(t_1+3k)+(t_1+5k)=3(t_1+3k)\). From above we know that \(t_1+3k=8\), thus \(3(t_1+3k)=3*8=24\).

Answer: C.
_________________

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

Intern
Intern
User avatar
Joined: 21 Feb 2016
Posts: 9
Location: United States (MA)
Re: In the sequence above, each term after the first term is equal to the  [#permalink]

Show Tags

New post 03 Jul 2016, 04:58
Bunuel wrote:
\(t_1\), \(t_2\), \(t_3\), ..., \(t_n\), ...
In the sequence above, each term after the first term is equal to the preceding term plus the constant k. If \(t_1+t_3+t_5+t_7=32\), what is the value of \(t_2+t_4+t_6\) ?

A. 8
B. 12
C. 24
D. 32
E. 72

Kudos for a correct solution.


According to the question, t2=t1+k, t3=t2+k=t1+k+k So, t3=t1+2k, t4=t1+3k, t5=t1+4k.. That's the pattern.
So, t1+t3+t5+t7
=t1+t1+2k+t1+4k+t1+6k
=4t+12k which is 32 given
At this point, u can take any value of t and k that satisfies the equation 4t+12k=32. (The (t,k) pairs could be (2,2) or (5,1).
Now, we are asked to find t2+t4+t6, which can be written as 3t+k+3k+5k, which in turn is equal to 3t+9k.
Taking either pair of values of (t,k), we get 3t+9k=6+18=24.
So answer is B

Alternatively, you could see that as t1+t3+t5+t7=32, and as 1+3+5+7=16, so the total, to be 32, each term has to be double, i.e. 2+6+10+14=32. Now these terms are not consecutive meaning there is one term between any two consecutive of these terms. So, t2+t4+t6 would be 4+8+12, which is 24.
Hope it helps.
VP
VP
avatar
P
Joined: 07 Dec 2014
Posts: 1104
In the sequence above, each term after the first term is equal to the  [#permalink]

Show Tags

New post Updated on: 07 Jul 2018, 20:58
t1t1, t2t2, t3t3, ..., tntn, ...
In the sequence above, each term after the first term is equal to the preceding term plus the constant k. If t1+t3+t5+t7=32t1+t3+t5+t7=32, what is the value of t2+t4+t6t2+t4+t6 ?

A. 8
B. 12
C. 24
D. 32
E. 72


t1+t3+t5+t7=32
➡4*t1+12k=32
➡t1+3k=8
t1=2
k=2
t2+t4+t6=4+8+12=24
C

Originally posted by gracie on 03 Jul 2016, 19:58.
Last edited by gracie on 07 Jul 2018, 20:58, edited 1 time in total.
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8397
Location: Pune, India
Re: In the sequence above, each term after the first term is equal to the  [#permalink]

Show Tags

New post 03 Jul 2016, 20:27
Bunuel wrote:
\(t_1\), \(t_2\), \(t_3\), ..., \(t_n\), ...
In the sequence above, each term after the first term is equal to the preceding term plus the constant k. If \(t_1+t_3+t_5+t_7=32\), what is the value of \(t_2+t_4+t_6\) ?

A. 8
B. 12
C. 24
D. 32
E. 72

Kudos for a correct solution.



Another method is to note that the average of the two sequences would be the same.

The average of \(t_1\), \(t_3\), \(t_5\) and \(t_7\) will be the middle of \(t_3\) and \(t_5\) which is \(t_4\). (All terms in an AP are equidistant from the term before it and the term after it.)
The average of \(t_2\), \(t_4\), \(t_6\) is obviously \(t_4\).

\(t_1+t_3+t_5+t_7=4 * t_4 = 32\)

\(t_4 = 8\)

Then \(t_2+t_4+t_6 = 3 * t_4 = 24\)

Answer (C)
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Intern
Intern
avatar
B
Joined: 26 Jul 2017
Posts: 6
Re: In the sequence above, each term after the first term is equal to the  [#permalink]

Show Tags

New post 06 Jul 2018, 22:54
1
Bunuel wrote:
Bunuel wrote:
\(t_1\), \(t_2\), \(t_3\), ..., \(t_n\), ...
In the sequence above, each term after the first term is equal to the preceding term plus the constant k. If \(t_1+t_3+t_5+t_7=32\), what is the value of \(t_2+t_4+t_6\) ?

A. 8
B. 12
C. 24
D. 32
E. 72

Kudos for a correct solution.


OFFICIAL SOLUTION:

According to the stem:
\(t_2=t_1+k\);
\(t_3=t_2+k=t_1+2k\);
\(t_4=t_3+k=t_1+3k\);
...
\(t_n=t_1+(n-1)k\);

Since \(t_1+t_3+t_5+t_7=32\), then \(t_1+(t_1+2k)+(t_1+4k)+(t_1+6k)=32\). So, \(t_1+3k=8\)

We need to find the of \(t_2+t_4+t_6=(t_1+k)+(t_1+3k)+(t_1+5k)=3(t_1+3k)\). From above we know that \(t_1+3k=8\), thus \(3(t_1+3k)=3*8=24\).

Answer: C.



What about the box symbol that is in front of t3, t5 and t4? How are we saying that t3 = box t3?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50002
Re: In the sequence above, each term after the first term is equal to the  [#permalink]

Show Tags

New post 07 Jul 2018, 00:29
sk1007 wrote:
Bunuel wrote:
Bunuel wrote:
\(t_1\), \(t_2\), \(t_3\), ..., \(t_n\), ...
In the sequence above, each term after the first term is equal to the preceding term plus the constant k. If \(t_1+t_3+t_5+t_7=32\), what is the value of \(t_2+t_4+t_6\) ?

A. 8
B. 12
C. 24
D. 32
E. 72

Kudos for a correct solution.


OFFICIAL SOLUTION:

According to the stem:
\(t_2=t_1+k\);
\(t_3=t_2+k=t_1+2k\);
\(t_4=t_3+k=t_1+3k\);
...
\(t_n=t_1+(n-1)k\);

Since \(t_1+t_3+t_5+t_7=32\), then \(t_1+(t_1+2k)+(t_1+4k)+(t_1+6k)=32\). So, \(t_1+3k=8\)

We need to find the of \(t_2+t_4+t_6=(t_1+k)+(t_1+3k)+(t_1+5k)=3(t_1+3k)\). From above we know that \(t_1+3k=8\), thus \(3(t_1+3k)=3*8=24\).

Answer: C.



What about the box symbol that is in front of t3, t5 and t4? How are we saying that t3 = box t3?


That was some bug. Edited. Thank you.
_________________

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

GMAT Club Bot
Re: In the sequence above, each term after the first term is equal to the &nbs [#permalink] 07 Jul 2018, 00:29
Display posts from previous: Sort by

In the sequence above, each term after the first term is equal to the

  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®.