6 from 6 to 510 inclusive

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 am; Location: India; Thanked: 267 times; Followed by:80 members; GMAT Score:760

6 from 6 to 510 inclusive

by sanju09 » Sat Jun 19, 2010 12:31 am

What is the average (arithmetic mean) of all multiples of 6 from 6 to 510 inclusive?
(A) 252
(B) 258
(C) 516
(D) 1510
(E) 1530

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

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Source: Beat The GMAT — Problem Solving | Sat Jun 19, 2010 12:31 am

amising6: Master | Next Rank: 500 Posts; Posts: 294; Joined: Wed May 05, 2010 4:01 am; Location: india; Thanked: 57 times

by amising6 » Sat Jun 19, 2010 12:44 am

sanju09 wrote:What is the average (arithmetic mean) of all multiples of 6 from 6 to 510 inclusive?
(A) 252
(B) 258
(C) 516
(D) 1510
(E) 1530

so basically of the number of form 6K where k will take value of 1,2,3 integer to give the multiple of 6
so first will be 6 i.e k=1 and last willl 510/6= i.e k= 85
so total number of terms 85
sum of all the terms =(85/2) *(516)
now artihmetic mean=(85*258)/85=258

arithmetic means =258

Ideation without execution is delusion

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 am; Location: India; Thanked: 267 times; Followed by:80 members; GMAT Score:760

by sanju09 » Sat Jun 19, 2010 12:47 am

in more simple words?

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

Quote

amising6: Master | Next Rank: 500 Posts; Posts: 294; Joined: Wed May 05, 2010 4:01 am; Location: india; Thanked: 57 times

by amising6 » Sat Jun 19, 2010 12:55 am

sanju09 wrote:in more simple words?

first observation is both 6 and 510 divisible by 6
so it is a APseries with 6 as first term and common difference of 6

6,12,18,24,................510
now 510 will be 85 th term
and then formula of sum to get sum as 85*256
then arithmetic mean =sum/number of term

Ideation without execution is delusion

Quote

sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 am; Location: India; Thanked: 267 times; Followed by:80 members; GMAT Score:760

by sanju09 » Sat Jun 19, 2010 1:09 am

amising6 wrote:
sanju09 wrote:in more simple words?
first observation is both 6 and 510 divisible by 6
so it is a APseries with 6 as first term and common difference of 6

6,12,18,24,................510
now 510 will be 85 th term
and then formula of sum to get sum as 85*256
then arithmetic mean =sum/number of term

Can we say that the average of terms in an AP is the average of its first and last terms?

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