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26 Nov 2019, 02:01
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Consider a set of 729 consecutive integers whose smallest element is x. If the arithmetic mean of this set of numbers is 1,072, what is the value of x?
A. 672
B. 708
C. 780
D. 828
E. 1,236
Are You Up For the Challenge: 700 Level Questions
A. 672
B. 708
C. 780
D. 828
E. 1,236
Are You Up For the Challenge: 700 Level Questions
26 Nov 2019, 02:37
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I think this is a fairly straight forward question, although it took me close to 6 minutes to fully resolve .
One property of consecutive numbers is that they are evenly spaced
Because we don't know how many integers there are, we can assume that the arithmetic mean of 729 integers is the middle number
729/2 = 364.
This means that the arithmetic mean of 1072, is the 365th number.
Meaning that there are 364 numbers before 1072, and equally 364 numbers after it ..
Therefore to find the smallest, we simply subteact 364 from 1072.
1072-364 = 708.
If the question said we sbould find the greatest number, we simply add 364 to 1072 and get 1,436.
But since the question asked what the smallest integer is, we stick with our earlier answer of 708.
Answer = B
Posted from my mobile device
One property of consecutive numbers is that they are evenly spaced
Because we don't know how many integers there are, we can assume that the arithmetic mean of 729 integers is the middle number
729/2 = 364.
This means that the arithmetic mean of 1072, is the 365th number.
Meaning that there are 364 numbers before 1072, and equally 364 numbers after it ..
Therefore to find the smallest, we simply subteact 364 from 1072.
1072-364 = 708.
If the question said we sbould find the greatest number, we simply add 364 to 1072 and get 1,436.
But since the question asked what the smallest integer is, we stick with our earlier answer of 708.
Answer = B
Posted from my mobile device
26 Nov 2019, 03:31
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Bunuel
Consider a set of 729 consecutive integers whose smallest element is x. If the arithmetic mean of this set of numbers is 1,072, what is the value of x?
A. 672
B. 708
C. 780
D. 828
E. 1,236
Are You Up For the Challenge: 700 Level Questions
A. 672
B. 708
C. 780
D. 828
E. 1,236
Are You Up For the Challenge: 700 Level Questions
729x+( ( 728*729)/2 )= 1072*729
x= 708
IMO B
