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MBA.Aspirant: Master | Next Rank: 500 Posts; Posts: 401; Joined: Tue May 24, 2011 1:14 am; Thanked: 37 times; Followed by:5 members

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by MBA.Aspirant » Fri Jun 03, 2011 6:35 am

What's the average (arithmetic mean) of all multiples of 10 from 10 to 400 inclusive?

A) 190
B) 195
C) 200
D) 205
E) 210

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Source: Beat The GMAT — Problem Solving | Fri Jun 03, 2011 6:35 am

Frankenstein: Legendary Member; Posts: 1448; Joined: Tue May 17, 2011 9:55 am; Location: India; Thanked: 375 times; Followed by:53 members

by Frankenstein » Fri Jun 03, 2011 6:38 am

Hi,
Average of an Arithmetic series(progression) is always the average of first term and last term.
So, Avg = (10+400)/2 = 205.

Hence, D

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vikram4689: Legendary Member; Posts: 1325; Joined: Sun Nov 01, 2009 6:24 am; Thanked: 105 times; Followed by:14 members

by vikram4689 » Fri Jun 03, 2011 7:18 am

If shortcut does not click
Total no of multiples : (400-10)/10 + 1 = 40
Sum of A.P. = 410*20
Average = 410*20/40 =205

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Ozlemg: Master | Next Rank: 500 Posts; Posts: 407; Joined: Tue Jan 25, 2011 9:19 am; Thanked: 25 times; Followed by:7 members

by Ozlemg » Fri Jun 03, 2011 7:34 am

IMO D

There is a short cut formula :

Number of terms in between 2 numbers : [(Last Term-First Term)/ Incremental]+1
Sum of Number of Terms : ([Last Term+First Term)/2]* number of terms

10+20+30+....+400 =

step 1: ((400-10)/10)+1 : 40
step 2: ((400+10)/2)*40 : 8200

8200/40 = 205

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eloquentgent: Junior | Next Rank: 30 Posts; Posts: 10; Joined: Fri Jun 03, 2011 5:34 am; Thanked: 2 times

by eloquentgent » Fri Jun 03, 2011 7:48 am

Many answers already, but if you're not a formula junkie:
10+400 = 410 (1st term)
20+390 = 410 (2nd term)
.
.
.
200+210 = 410 (20th term)

The sum of all the 20 terms mentioned above is the same as the sum of all the 40 multiples of 10 between 10 and 400 (both inclusive)

Hence the average is (20x 410)/40 = 205

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cans: Legendary Member; Posts: 1309; Joined: Mon Apr 04, 2011 5:34 am; Location: India; Thanked: 310 times; Followed by:123 members; GMAT Score:750

by cans » Fri Jun 03, 2011 10:46 am

s = 10+20+30+40+....+400
Arithmetic progression series
no. of terms = 40
to find s/40
a is the first term = 10
l is last term = 400
thus sum = (n/2)*(a+l)
to find avg, or sum/n = (400+10)/2 = 410/2 = 205
IMO D

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