Sequence

Question

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?

Geva@EconomistGMAT · Answer

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

top_business_2011 · Answer

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.

Whitney Garner · Answer

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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