Sequence

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ktn11: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Sat Aug 20, 2011 5:09 am; Thanked: 1 times

by ktn11 » Sun Aug 21, 2011 5:55 pm

Sequence A consists of 10 consecutive odd numbers and B consists of 5 consecutive even numbers. If the
least number in A is 7 greater than the least number in B, the average of the numbers in A is how much
greater than average of numbers in B?

oa: 14

if my least no in B is 2 then i have

B= {2,4,6,8,10}
And since its given the least no in A is 7 greater than least no in B i will have
A = {9,11,13,15,17,19,21,23,25,27}

Avg of A is (17+19)/2 =18
Avg of B is 6

therefore Avg of A is 12 greater than avg of B
But OA says ans is 14. How is this? Am i doing wrong somewhere?

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Source: Beat The GMAT — Problem Solving | Sun Aug 21, 2011 5:55 pm

Geva@EconomistGMAT: GMAT Instructor; Posts: 905; Joined: Sun Sep 12, 2010 1:38 amFollowed by: 123 members; Thanked: 378 times; GMAT Score:760

by Geva@EconomistGMAT » Mon Aug 22, 2011 6:27 am

ktn11 wrote:Sequence A consists of 10 consecutive odd numbers and B consists of 5 consecutive even numbers. If the
least number in A is 7 greater than the least number in B, the average of the numbers in A is how much
greater than average of numbers in B?

oa: 14

if my least no in B is 2 then i have

B= {2,4,6,8,10}
And since its given the least no in A is 7 greater than least no in B i will have
A = {9,11,13,15,17,19,21,23,25,27}

Avg of A is (17+19)/2 =18
Avg of B is 6

therefore Avg of A is 12 greater than avg of B
But OA says ans is 14. How is this? Am i doing wrong somewhere?

Are you sure the OA is 14?

Geva
Senior Instructor
Master GMAT
1-888-780-GMAT
https://www.mastergmat.com

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top_business_2011: Senior | Next Rank: 100 Posts; Posts: 47; Joined: Wed Sep 03, 2008 11:18 pmFollowed by: 1 member; Thanked: 5 times

by top_business_2011 » Mon Aug 22, 2011 6:55 am

ktn11 wrote:Sequence A consists of 10 consecutive odd numbers and B consists of 5 consecutive even numbers. If the
least number in A is 7 greater than the least number in B, the average of the numbers in A is how much
greater than average of numbers in B?

oa: 14

if my least no in B is 2 then i have

B= {2,4,6,8,10}
And since its given the least no in A is 7 greater than least no in B i will have
A = {9,11,13,15,17,19,21,23,25,27}

Avg of A is (17+19)/2 =18
Avg of B is 6

therefore Avg of A is 12 greater than avg of B
But OA says ans is 14. How is this? Am i doing wrong somewhere?

The OA must be incorrect.
Sequence A = { 2n+1, 2n+3, 2n+5,...2n+19}
sequence B = { 2m, 2m+2, 2m+4, 2m+6, 2m+8}
It is also given that the least number in A is 7 greater than the least number in B.
2n+1 = 2m+7
n=m+3

Required: Average of A - Average of B?

Average of A = [The sum of the last term and the first term]/2 = [2n+1+ 2n+19]/2 =2n+10
Average of B = The third term[since there are odd number of terms]= 2m+4

Therefore,Average of A -Average of B = 2n+10 -[2m+4]
But since n=m+3, Average of A -Average of B = 2[m+3]+10 -[2m+4]
= 2m +6+10-2m-4 = 12.

Thus, the answer is 12.

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GMAT/MBA Expert

Whitney Garner: GMAT Instructor; Posts: 273; Joined: Tue Sep 21, 2010 5:37 amFollowed by: 74 members; Location: Durham, NC; Thanked: 154 times; GMAT Score:770

by Whitney Garner » Mon Aug 22, 2011 8:35 am

ktn11 wrote:Sequence A consists of 10 consecutive odd numbers and B consists of 5 consecutive even numbers. If the
least number in A is 7 greater than the least number in B, the average of the numbers in A is how much
greater than average of numbers in B?

oa: 14

if my least no in B is 2 then i have

B= {2,4,6,8,10}
And since its given the least no in A is 7 greater than least no in B i will have
A = {9,11,13,15,17,19,21,23,25,27}

Avg of A is (17+19)/2 =18
Avg of B is 6

therefore Avg of A is 12 greater than avg of B
But OA says ans is 14. How is this? Am i doing wrong somewhere?

Your logic is Spot-On: The OA is incorrect. I would contact the company or person who created the question and let them know so they can correct this in their errata. If you are not sure who that would be, I caution you against using the questions as study material. Only use material from reputable sites/companies (but even we make typos now and again)!!

Whit

Whitney Garner
GMAT/GRE/EA Instructor & Anxiety/Accommodations Coach
www.whitneygarner.com

Contributor to Beat The GMAT!

Math is a lot like love - a simple idea that can easily get complicated

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