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If the sum of the minimum and the maximum of 7 consecutive o

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by Max@Math Revolution » Wed Jun 06, 2018 7:18 am

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[GMAT math practice question]

If the sum of the minimum and the maximum of 7 consecutive odd integers is 114, what is the average (arithmetic mean) of the seven integers?

A. 19
B. 38
C. 57
D. 76
E. 114
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by Max@Math Revolution » Fri Jun 08, 2018 1:32 am
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Let the 7 consecutive odd integers be 2n-5, 2n-3, 2n-1, 2n+1, 2n+3, 2n+5, and 2n+7. Then their minimum is 2n-5 and their maximum is 2n+7. The sum of the maximum and minimum is ( 2n - 5 ) + ( 2n + 7 ) = 4n + 2 = 114 and so n = 28.
Since the average and the median of consecutive odd integers are equal, the average is 2n + 1 = 57.

Therefore, the answer is C.

Answer: C

Another way to solve this problem is to note that the average of the consecutive odd integers is equal to the average of the two end points. That is, 114 / 2 or 57.
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by Scott@TargetTestPrep » Fri Jun 08, 2018 10:25 am
Max@Math Revolution wrote:[GMAT math practice question]

If the sum of the minimum and the maximum of 7 consecutive odd integers is 114, what is the average (arithmetic mean) of the seven integers?

A. 19
B. 38
C. 57
D. 76
E. 114

We have to recall that in a set a of consecutive integers or consecutive even integers or consecutive odd integers, the average of the smallest number and the largest number in the set is the average (arithmetic mean) of the entire set. Thus the average (arithmetic mean) of the seven integers is

(min + max)/2 = 114/2 = 57

Answer: C

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by Brent@GMATPrepNow » Fri Jun 08, 2018 1:24 pm
Max@Math Revolution wrote:[GMAT math practice question]

If the sum of the minimum and the maximum of 7 consecutive odd integers is 114, what is the average (arithmetic mean) of the seven integers?

A. 19
B. 38
C. 57
D. 76
E. 114
One more (longer!) solution.

Let x = smallest ODD integer
So, x+2 = next (2nd) ODD integer
x+4 = next (3rd) ODD integer
.
.
.
x + 12 = largest (7th) ODD integer

Sum of the minimum and the maximum is 114
So, x + x + 12 = 114
Simplify: 2x + 12 = 114
So, 2x = 102
Solve: x = 51

So, the 7 numbers are: 51, 53, 55, 57, 59, 61, 63

Since the 7 numbers are EQUALLY SPACED, the mean = the median
The median = the middlemost number = 57

So, median = 57 = mean

Answer: C

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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