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13 Jul 2021, 04:15
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The average of a set of 18 consecutive integers is 22.5. What is the smallest integer in the set?
(A) 10
(B) 12
(C) 13
(D) 14
(E) 15
(A) 10
(B) 12
(C) 13
(D) 14
(E) 15
13 Jul 2021, 05:14
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If we have 18 consecutive integers, we have an equally spaced list, and the mean equals the median, so our median is 22.5. Since we have 18 consecutive integers, the largest integer is 17 greater than the smallest. The median in any equally spaced set is halfway between the smallest and largest things, so the median is 8.5 away from the smallest value. So the smallest value is 22.5 - 8.5 = 14.
General Discussion
13 Jul 2021, 04:32
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Explanation:
Sum = 18x22.5 = 405
Let, first term is x
So last term will be x+17
Sum of n term of ap = n(a+l)/2
405 = 18(x+x+17)/2
810/18 = 2x + 17
45 = 2x + 17
28 = 2x
x = 14
IMO-D
Posted from my mobile device
Sum = 18x22.5 = 405
Let, first term is x
So last term will be x+17
Sum of n term of ap = n(a+l)/2
405 = 18(x+x+17)/2
810/18 = 2x + 17
45 = 2x + 17
28 = 2x
x = 14
IMO-D
Posted from my mobile device
