Target question: What is the average (arithmetic mean) of 11 consecutive integers?kop wrote:What is the average (arithmetic mean) of 11 consecutive integers?
1. The average of first nine integers is 7
2. The average of last nine integers is 9
Brent@GMATPrepNow wrote:Target question: What is the average (arithmetic mean) of 11 consecutive integers?kop wrote:What is the average (arithmetic mean) of 11 consecutive integers?
1. The average of first nine integers is 7
2. The average of last nine integers is 9
Statement 1: The average of first nine integers is 7
IMPORTANT: There's a nice rule that says, "In a set where the numbers are equally spaced, the mean will equal the median."
For more on this concept, see https://www.beatthegmat.com/mba/2012/05/ ... d-the-mean
We can apply this rule to this question, since consecutive integers are equally spaced.
So, if the mean of the first nine integers is 7, then the median of the first nine integers is 7.
So, the first nine integers must be 3, 4, 5, 6, 7, 8, 9, 10, 11
This means the 11 numbers are 3,4,5,6,7,8,9,10,11,12,13
Since the median of this set is 8, the mean must be 8
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: The average of last nine integers is 9
If the mean of the last nine integers is 9, then the median of the last nine integers is 9.
So, the last nine integers must be 5, 6, 7, 8, 9, 10, 11, 12, 13
This means the 11 numbers are 3,4,5,6,7,8,9,10,11,12,13
Since the median of this set is 8, the mean must be 8
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer = D
Cheers,
Brent
Brent@GMATPrepNow wrote:Target question: What is the average (arithmetic mean) of 11 consecutive integers?kop wrote:What is the average (arithmetic mean) of 11 consecutive integers?
1. The average of first nine integers is 7
2. The average of last nine integers is 9
Statement 1: The average of first nine integers is 7
IMPORTANT: There's a nice rule that says, "In a set where the numbers are equally spaced, the mean will equal the median."
For more on this concept, see https://www.beatthegmat.com/mba/2012/05/ ... d-the-mean
We can apply this rule to this question, since consecutive integers are equally spaced.
So, if the mean of the first nine integers is 7, then the median of the first nine integers is 7.
So, the first nine integers must be 3, 4, 5, 6, 7, 8, 9, 10, 11
This means the 11 numbers are 3,4,5,6,7,8,9,10,11,12,13
Since the median of this set is 8, the mean must be 8
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: The average of last nine integers is 9
If the mean of the last nine integers is 9, then the median of the last nine integers is 9.
So, the last nine integers must be 5, 6, 7, 8, 9, 10, 11, 12, 13
This means the 11 numbers are 3,4,5,6,7,8,9,10,11,12,13
Since the median of this set is 8, the mean must be 8
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer = D
Cheers,
Brent
Perfect approach, Sri - great work!gmattesttaker2 wrote:Brent@GMATPrepNow wrote:Target question: What is the average (arithmetic mean) of 11 consecutive integers?kop wrote:What is the average (arithmetic mean) of 11 consecutive integers?
1. The average of first nine integers is 7
2. The average of last nine integers is 9
Statement 1: The average of first nine integers is 7
IMPORTANT: There's a nice rule that says, "In a set where the numbers are equally spaced, the mean will equal the median."
For more on this concept, see https://www.beatthegmat.com/mba/2012/05/ ... d-the-mean
We can apply this rule to this question, since consecutive integers are equally spaced.
So, if the mean of the first nine integers is 7, then the median of the first nine integers is 7.
So, the first nine integers must be 3, 4, 5, 6, 7, 8, 9, 10, 11
This means the 11 numbers are 3,4,5,6,7,8,9,10,11,12,13
Since the median of this set is 8, the mean must be 8
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: The average of last nine integers is 9
If the mean of the last nine integers is 9, then the median of the last nine integers is 9.
So, the last nine integers must be 5, 6, 7, 8, 9, 10, 11, 12, 13
This means the 11 numbers are 3,4,5,6,7,8,9,10,11,12,13
Since the median of this set is 8, the mean must be 8
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer = D
Cheers,
Brent
Hello Brent,
I was just wondering if the following approach is OK?
We need the average of 11 consecutive integers.
Let the integers be: x, x+1, x+2 ,..., x+10
Since the integers are evenly spaced, Average = x + (x+10)/2
Hence, x = ?
1) Given, x + (x+8) / 2 = 7
=> x = 3
Hence, Sufficient
2) Given, (x+2)+(x+10)/2 = 9
=> x = 3
Hence, Sufficient
Hence D
Thanks a lot for your help.
Best Regards,
Sri
Hello Brent,Brent@GMATPrepNow wrote:Perfect approach, Sri - great work!gmattesttaker2 wrote:Brent@GMATPrepNow wrote:Target question: What is the average (arithmetic mean) of 11 consecutive integers?kop wrote:What is the average (arithmetic mean) of 11 consecutive integers?
1. The average of first nine integers is 7
2. The average of last nine integers is 9
Statement 1: The average of first nine integers is 7
IMPORTANT: There's a nice rule that says, "In a set where the numbers are equally spaced, the mean will equal the median."
For more on this concept, see https://www.beatthegmat.com/mba/2012/05/ ... d-the-mean
We can apply this rule to this question, since consecutive integers are equally spaced.
So, if the mean of the first nine integers is 7, then the median of the first nine integers is 7.
So, the first nine integers must be 3, 4, 5, 6, 7, 8, 9, 10, 11
This means the 11 numbers are 3,4,5,6,7,8,9,10,11,12,13
Since the median of this set is 8, the mean must be 8
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: The average of last nine integers is 9
If the mean of the last nine integers is 9, then the median of the last nine integers is 9.
So, the last nine integers must be 5, 6, 7, 8, 9, 10, 11, 12, 13
This means the 11 numbers are 3,4,5,6,7,8,9,10,11,12,13
Since the median of this set is 8, the mean must be 8
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer = D
Cheers,
Brent
Hello Brent,
I was just wondering if the following approach is OK?
We need the average of 11 consecutive integers.
Let the integers be: x, x+1, x+2 ,..., x+10
Since the integers are evenly spaced, Average = x + (x+10)/2
Hence, x = ?
1) Given, x + (x+8) / 2 = 7
=> x = 3
Hence, Sufficient
2) Given, (x+2)+(x+10)/2 = 9
=> x = 3
Hence, Sufficient
Hence D
Thanks a lot for your help.
Best Regards,
Sri
Cheers,
Brent
