vaibhav101 wrote:find the sum of all even numbers from 10 to 300, excluding those which are multiples of 8.
A 17014
B 2345
C 4562
D 9128
E none of these
For any EVENLY SPACED SET:
Count = (biggest - smallest)/(increment) + 1.
Average = (biggest + smallest)/2.
Sum = (count)(average).
The INCREMENT is the difference between successive values.
Even numbers between 10 and 300, inclusive:
Here, the integers are EVEN, so the increment = 2.
Count = (300-10)/2 + 1 = 146.
Average = (300 + 10)/2 = 155.
Sum = (146)(155) = 22,630.
Multiples of 8 between 10 and 300, inclusive:
Here, the integers are MULTIPLE OF 8, so the increment = 8.
Smallest multiple of 8 = 16.
Biggest multiple of 8 = 296.
Thus:
Count = (296-16)/8 + 1 = 36.
Average = (296+16)/2= 156.
Sum = (36)(156) = 5616.
Subtracting the second sum from the first, we get:
22630 - 5616 = 17,014.
The correct answer is
A.
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