Which of the following integers can be written as both the sum of 5 consecutive odd integers and 7 consecutive odd integers?
A. 49
B. 70
C. 140
D. 215
E. 525
A. 49
B. 70
C. 140
D. 215
E. 525
For any evenly spaced set:aishwaryav12 wrote:Which of the following integers can be written as both the sum of 5 consecutive odd integers and 7 consecutive odd integers?
A. 49
B. 70
C. 140
D. 215
E. 525
sum = (number)(median)
We can PLUG IN THE ANSWERS, which represent the sum.
Since the number of integers can be 5 or 7, the sum must be a multiple of both 5 and 7.
Eliminate A, which is not divisible by 5.
Eliminate D, which is not divisible by 7.
The equation in blue can be rephrased as follows:
median = sum/number
Since all of the integers must be odd, the correct answer must yield an odd value for the median.
If B is the sum of 7 consecutive odd integers, we get:
median = sum/number = 70/7 = 10.
Since the yielded median is not odd, eliminate B.
If D is the sum of 7 consecutive odd integers, we get:
median = sum/number = 140/7 = 20.
Since the yielded median is not odd, eliminate D.
The correct answer is E.
