prernamalhotra wrote:If integer k is equal to the sum of all even multiples of 15 between 295 and 615, what is the greatest prime factor of k?
1)5
2)7
3)11
4)13
5)17
Thank you,
Prerna
For any EVENLY SPACED SET:
Number of terms = (biggest-smallest)/interval + 1, where the interval is the distance between successive terms.
Average = median = (biggest + smallest)/2.
Sum = (number of terms)(average).
The even multiples of 15 between 295 and 615 are the MULTIPLES OF 30 between 295 and 615.
Thus:
k = 300 + 330 + 360 + ... + 600.
Here, the interval between successive terms is 30.
Thus:
Number of terms = (600-300)/30 + 1 = 11.
Average = (600+300)/2 = 450.
Sum = 11*450.
Prime-factoring k = (11)(450), we get:
(11)(2*3*3*5*5).
Thus, the greatest prime factor of k is 11.
The correct answer is
C.
Last edited by
GMATGuruNY on Fri May 30, 2014 8:09 am, edited 1 time in total.
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