Sum of all terms in the set {S13, S14, ..., S28}?

Question

Hello,

Can you please tell me what is the best approach to solve this problem:

If S is the infinite sequence S1 = 6, S2 = 12, ..., Sn = Sn-1 + 6,..., what is the sum of all terms in the set {S13, S14, ..., S28}?

1,800
1,845
1,890
1,968
2,016

OA: 1,968

My approach:

S13 = 78
S28 = 168

Number of terms, n = ( 28 - 13 ) + 1 = 16

Average = Sum/n

=> (78 + 168)/2 = Sum/16
=> 246/2 = Sum/16
=> 123 = Sum/16
=> Sum = 123 x 16

Since only D has a unit's digit ending in 8, answer is D

I was just wondering if there is a quicker approach to solving this problem? Thanks a lot.

Regards,
Sri

Rich.C@EMPOWERgmat.com · Answer

Hi Sri,

You've used a standard, algebraic approach to this question, which is fine. Another way to answer this question is to use "bunching"….

Since we're dealing with the 13th through 28th terms, we're dealing with 16 terms….

The sum of the 1st and 16th term = 78 + 168 = 246
The sum of the 2nd and 15th term = 84 + 162 = 246
etc.

So, we have 8 "sets" of 2 terms that all sum to 246

8(246) = 1968

The "shortcut" that you mentioned about the unit's digit still applies here.

Final Answer: D

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

Contact Rich at [email protected]

sanju09 · Answer

gmattesttaker2 wrote:Hello,

Can you please tell me what is the best approach to solve this problem:

If S is the infinite sequence S1 = 6, S2 = 12, ..., Sn = Sn-1 + 6,..., what is the sum of all terms in the set {S13, S14, ..., S28}?

1,800
1,845
1,890
1,968
2,016

OA: 1,968

My approach:

S13 = 78
S28 = 168

Number of terms, n = ( 28 - 13 ) + 1 = 16

Average = Sum/n

=> (78 + 168)/2 = Sum/16
=> 246/2 = Sum/16
=> 123 = Sum/16
=> Sum = 123 x 16

Since only D has a unit's digit ending in 8, answer is D

I was just wondering if there is a quicker approach to solving this problem? Thanks a lot.

Regards,
Sri

Shortcut maybe the fact that the average (arithmetic mean) of evenly spaced numbers is equal to the average of first and last numbers in the list, which is a set of 16 consecutive multiples of 6 with the first term 78 and the last term 168, their average 39 + 84, sum of all is number times average, which is 16(123), and here you are perfect why D.

In fact, your approach is the shortcut!

The mind is everything. What you think you become. –Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

Matt@VeritasPrep · Answer

One time-saving device here: since you have an EVEN number of evenly spaced terms in the set, you don't need to average them, you can just treat them as pairs.

For instance, take the set {2, 4, 6, 8, 10, 12}

Notice that 2 + 12 = 4 + 10 = 6 + 8, so the sum is just 14 * 3.

Similarly, in your set, you'll have 8 pairs, each with a sum of (78+168), so your sum is 8*(78+168), or 8*(250-4) = 2000 - 32 = 1968.

GMATGuruNY · Answer

gmattesttaker2 wrote:Hello,

Can you please tell me what is the best approach to solve this problem:

If S is the infinite sequence S1 = 6, S2 = 12, ..., Sn = Sn-1 + 6,..., what is the sum of all terms in the set {S13, S14, ..., S28}?

1,800
1,845
1,890
1,968
2,016

OA: 1,968

My approach:

S13 = 78
S28 = 168

Number of terms, n = ( 28 - 13 ) + 1 = 16

Average = Sum/n

=> (78 + 168)/2 = Sum/16
=> 246/2 = Sum/16
=> 123 = Sum/16
=> Sum = 123 x 16

Since only D has a unit's digit ending in 8, answer is D

I was just wondering if there is a quicker approach to solving this problem? Thanks a lot.

Regards,
Sri

Shortcut maybe the fact that the average (arithmetic mean) of evenly spaced numbers is equal to the average of first and last numbers in the list, which is a set of 16 consecutive multiples of 6 with the first term 78 and the last term 168, their average 39 + 84, sum of all is number times average, which is 16(123), and here you are perfect why D.

In fact, your approach is the shortcut!

Choose how you want to prepare

Get Ready for GMAT Test Day Faster with Live Online Classes

Target Test Prep EA OnDemand

Target Test Prep GMAT OnDemand

Sum of all terms in the set {S13, S14, ..., S28}?

GMAT/MBA Expert

Chicago Booth

GMAT Course Reviews

Admissions Consulting Reviews

FREE GMAT PREP RESOURCES

GMAT PREP DEAL TRACKER