Tricky one- Got stumped

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ankur.agrawal: Master | Next Rank: 500 Posts; Posts: 261; Joined: Wed Mar 31, 2010 8:37 pmFollowed by: 3 members; Location: Varanasi; Thanked: 11 times

by ankur.agrawal » Tue Mar 22, 2011 9:16 am

Set S contains seven distinct integers. The median of set S is the integer m, and all values in set S are equal to or less than 2m. What is the highest possible average (arithmetic mean) of all values in set S ?

m

10m/7

10m/7 - 9/7

5m/7 + 3/7

5m

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Source: Beat The GMAT — Problem Solving | Tue Mar 22, 2011 9:16 am

HSPA: Legendary Member; Posts: 1101; Joined: Fri Jan 28, 2011 7:26 amFollowed by: 13 members; Thanked: 47 times; GMAT Score:640

by HSPA » Tue Mar 22, 2011 9:23 am

I got C
the seven numbers i took are
m-3, m-2, m-1, m, 2m-2,2m-1,2m

10m/7 - 9/7... what is the OA

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AIM GMAT: Legendary Member; Posts: 857; Joined: Wed Aug 25, 2010 1:36 amFollowed by: 15 members; Thanked: 56 times

by AIM GMAT » Tue Mar 22, 2011 9:30 am

IMO C.

Max number = 2m

median = m

[m-3 , m-2 , m-1 , m , 2m-2 , 2m-1 , 2m ]

sum of all 7 numbers = 10m - 9
mean = (10m - 9 )/ 7

Thanks & Regards,
AIM GMAT

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rohu27: Legendary Member; Posts: 586; Joined: Tue Jan 19, 2010 4:38 amFollowed by: 5 members; Thanked: 31 times; GMAT Score:730

by rohu27 » Tue Mar 22, 2011 9:31 am

may i knw the source?

ankur.agrawal wrote:Set S contains seven distinct integers. The median of set S is the integer m, and all values in set S are equal to or less than 2m. What is the highest possible average (arithmetic mean) of all values in set S ?

m

10m/7

10m/7 - 9/7

5m/7 + 3/7

5m

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AIM GMAT: Legendary Member; Posts: 857; Joined: Wed Aug 25, 2010 1:36 amFollowed by: 15 members; Thanked: 56 times

by AIM GMAT » Tue Mar 22, 2011 9:37 am

What is the highest possible average (arithmetic mean) of all values in set S ?

[m-3 , m-2 , m-1 , m , 2m-2 , 2m-1 , 2m ]

If it would have been lowest possible then i guess the below mentioned whud be the numbers :-

[m-3 , m-2 , m-1 , m , m+1 , m+2 , 2m ]

sum = 8m - 3
mean = (8m-3)/7

Guys let me know if my approach is wrong.

Thanks & Regards,
AIM GMAT

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HSPA: Legendary Member; Posts: 1101; Joined: Fri Jan 28, 2011 7:26 amFollowed by: 13 members; Thanked: 47 times; GMAT Score:640

by HSPA » Tue Mar 22, 2011 9:42 am

what if the first element is (m-12345), m-1,m,m+1...blah balh

how did you come to lowest possible conclusion... havent understood AIM

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AIM GMAT: Legendary Member; Posts: 857; Joined: Wed Aug 25, 2010 1:36 amFollowed by: 15 members; Thanked: 56 times

by AIM GMAT » Tue Mar 22, 2011 9:52 am

HSPA wrote:what if the first element is (m-12345), m-1,m,m+1...blah balh

how did you come to lowest possible conclusion... havent understood AIM

For highest avg we need to maximize sum so the terms tht are gonna make diff are 5th and 6th terms.

1st : 2nd : 3rd : 4th : 5th : 6th : 7th

m-3 : m-2 : m-1: m :2m-2 : 2m-1 : 2m ---- To maximize sum

m-3 : m-2 : m-1: m :m+1 : m+2 : 2m ---- To minimize sum

Hope that helps.

Thanks & Regards,
AIM GMAT

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue Mar 22, 2011 9:57 am

ankur.agrawal wrote:Set S contains seven distinct integers. The median of set S is the integer m, and all values in set S are equal to or less than 2m. What is the highest possible average (arithmetic mean) of all values in set S ?

m

10m/7

10m/7 - 9/7

5m/7 + 3/7

5m

Make the situation concrete by plugging in a value for m.

Let m=5.

For the median to be 5, we need to choose 3 distinct integers that are smaller than 5 and 3 distinct integers that are larger than 5. Since we're trying to maximize the average, we want each integer to be as large as possible.

The largest allowed value is 2m = 2*5 = 10. So the 3 largest integers must be 8, 9, 10.
For the 3 distinct integers smaller than 5, the largest possible are 2, 3, 4.
So our 7 integers are 2, 3, 4, 5, 8, 9, 10.
Average = (2 + 3 + 4 + 5 + 8 + 9 + 10)/7 = 41/7. This is our target.

Now we plug m=5 into all the answers to which yields our target of 41/7.

Only answer choice C works:
10m/7 - 9/7 = (10*5)/7 - 9/7 = 50/7 - 9/7 = 41/7.

The correct answer is C.

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ankur.agrawal: Master | Next Rank: 500 Posts; Posts: 261; Joined: Wed Mar 31, 2010 8:37 pmFollowed by: 3 members; Location: Varanasi; Thanked: 11 times

by ankur.agrawal » Tue Mar 22, 2011 10:19 am

may i knw the source?

Hi rohu,

The Source is MGMAT CAT 1 . Any specific reasons for asking about the source?

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ankur.agrawal: Master | Next Rank: 500 Posts; Posts: 261; Joined: Wed Mar 31, 2010 8:37 pmFollowed by: 3 members; Location: Varanasi; Thanked: 11 times

by ankur.agrawal » Tue Mar 22, 2011 10:21 am

HSPA wrote:I got C
the seven numbers i took are
m-3, m-2, m-1, m, 2m-2,2m-1,2m

10m/7 - 9/7... what is the OA

OA is C. You nailed it.

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rohu27: Legendary Member; Posts: 586; Joined: Tue Jan 19, 2010 4:38 amFollowed by: 5 members; Thanked: 31 times; GMAT Score:730

by rohu27 » Tue Mar 22, 2011 5:34 pm

yes ankur. i somehow felt it must be from the MGMAT CAT as i did get a similar sort of question.
can i reuqst u to mention the source, especially whn u r posting qustions from CAT's as many of us would not have taken them and reading it before hand would do us no good. hope u dnt mind.

ankur.agrawal wrote:
may i knw the source?

Hi rohu,

The Source is MGMAT CAT 1 . Any specific reasons for asking about the source?

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ankur.agrawal: Master | Next Rank: 500 Posts; Posts: 261; Joined: Wed Mar 31, 2010 8:37 pmFollowed by: 3 members; Location: Varanasi; Thanked: 11 times

by ankur.agrawal » Wed Mar 23, 2011 8:05 pm

can i reuqst u to mention the source, especially whn u r posting qustions from CAT's as many of us would not have taken them and reading it before hand would do us no good. hope u dnt mind.

I am extremely sorry for being so careless. I would take care of this from now. Thanks rohu.

https://gmatkey-takaways.blocked/

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rohu27: Legendary Member; Posts: 586; Joined: Tue Jan 19, 2010 4:38 amFollowed by: 5 members; Thanked: 31 times; GMAT Score:730

by rohu27 » Wed Mar 23, 2011 8:20 pm

no need for an apology buddy.glad tht u liked my suggestion

ankur.agrawal wrote:
can i reuqst u to mention the source, especially whn u r posting qustions from CAT's as many of us would not have taken them and reading it before hand would do us no good. hope u dnt mind.
I am extremely sorry for being so careless. I would take care of this from now. Thanks rohu.

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