Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 03 Jul 2015, 20:24

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If the sum of four consecutive positive integers a three

Author Message
TAGS:
GMAT Instructor
Joined: 04 Jul 2006
Posts: 1266
Followers: 24

Kudos [?]: 167 [0], given: 0

If the sum of four consecutive positive integers a three [#permalink]  01 Oct 2006, 01:13
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 1 sessions
If the sum of four consecutive positive integers a three digit multiple of 50, the mean of the these integers must be one of k possible values, where k=

(A) 7 (B) 8 (C) 9 (D) 10 (E) more than 10
VP
Joined: 21 Aug 2006
Posts: 1026
Followers: 1

Kudos [?]: 21 [0], given: 0

Theare are 9 possible 3 digit numbers: 100, 200, ...900

9 means.

K will be 9.
_________________

The path is long, but self-surrender makes it short;
the way is difficult, but perfect trust makes it easy.

Senior Manager
Joined: 30 Aug 2006
Posts: 374
Followers: 3

Kudos [?]: 24 [0], given: 0

E more than 10

100,150,200,250,300,350...950
Senior Manager
Joined: 30 Aug 2006
Posts: 374
Followers: 3

Kudos [?]: 24 [0], given: 0

thinking about this the multiples of 100 don't work. the number has to be not divisible by 4 for this to work as otherwise you cannot find 4 cons digits that add up.

so 150,250,350,450,550,650,750,850,950
Senior Manager
Joined: 11 Jul 2006
Posts: 383
Location: TX
Followers: 1

Kudos [?]: 6 [0], given: 0

londonluddite wrote:
thinking about this the multiples of 100 don't work. the number has to be not divisible by 4 for this to work as otherwise you cannot find 4 cons digits that add up.

so 150,250,350,450,550,650,750,850,950

C

Yes , all these numbers can be put in the from 4n+ 6 .
Senior Manager
Joined: 30 Aug 2006
Posts: 374
Followers: 3

Kudos [?]: 24 [0], given: 0

could you explain how you derived 4n+6 please? thanks
Senior Manager
Joined: 11 Jul 2006
Posts: 383
Location: TX
Followers: 1

Kudos [?]: 6 [0], given: 0

londonluddite wrote:
could you explain how you derived 4n+6 please? thanks

sum of 4 consecutive numbers

n + n+1 + n+2 + n+3 = 4n + 6
VP
Joined: 21 Aug 2006
Posts: 1026
Followers: 1

Kudos [?]: 21 [0], given: 0

the word "integers" is important
_________________

The path is long, but self-surrender makes it short;
the way is difficult, but perfect trust makes it easy.

Manager
Joined: 12 Sep 2006
Posts: 92
Followers: 1

Kudos [?]: 2 [0], given: 0

guys,

but mutiples of 100 work for 4n+6 as well

4n+6=200, n=49
4n+6=300, n=64

and so on...

so all mutiples of 50 work for 4n+6
GMAT Instructor
Joined: 04 Jul 2006
Posts: 1266
Followers: 24

Kudos [?]: 167 [0], given: 0

Re: PS: Multiple of 50 [#permalink]  03 Oct 2006, 08:01
kevincan wrote:
If the sum of four consecutive positive integers a three digit multiple of 50, the mean of the these integers must be one of k possible values, where k=

(A) 7 (B) 8 (C) 9 (D) 10 (E) more than 10

Let the four integers be x,x+1,x+2 and x+3=4x+6

4x+6 has to be a multiple of 50 i.e 4x+6=50m mâ‚¬{2,3...,19}

But x=(50m-6)/4= (25m-3)/2 must be an integer, so m must be odd.

Thus m can be any odd integer from 3 to 19 3=1+1*2 19=1+9*2

So there are 9 different values for m, x and 4x+6, as well as (4x+6)/4
Re: PS: Multiple of 50   [#permalink] 03 Oct 2006, 08:01
Similar topics Replies Last post
Similar
Topics:
31 If a is the sum of x consecutive positive integers. b is the 15 05 Mar 2012, 23:36
11 If the sum of n consecutive positive integers is 33, what of 11 10 Dec 2010, 06:58
7 The sum of three consecutive integers is 312. What is the 8 09 Oct 2010, 07:16
2 If the sum of 4 consecutive positive integers is divisible b 9 28 Sep 2009, 18:40
If the sum of five consecutive positive integers is a, then 5 21 Jul 2006, 12:00
Display posts from previous: Sort by