When posting questions, please use the spoiler function to hide the correct answer. This will allow others to attempt the question without seeing the final answer.josh80 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?
-5
-7
-11
-13
-17
Ans. C
NOTE: I doubt that the GMAT would use the term "even multiples."
Yes, this term MAY BE intuitively apparent, but I believe the GMAT test-makers would provide additional text to avoid any ambiguity. Presumably even multiples of 15 are 30, 60, 90, etc.
In other words, we're looking for multiples of 30
So, k = 300 + 330 + 360 + ... + 570 + 600
Let's examine some terms in this series. . . .
300 = 30(10)
330 = 30(11)
360 = 30(12)
390 = 30(13)
.
.
.
570 = 30(19)
600 = 30(20)
So k = 30(10 + 11 + 12 + ... + 19 + 20)
------------------------------------------------------
Now, let's examine this sum: 10 + 11 + 12 + ... + 19 + 20
Since 20 - 10 + 1 = 11, we know there are 11 numbers to add together.
Since these red numbers are equally spaced (consecutive integers), their sum = (# of values)(average of first and last values)
= [11][(10+20)/2]
= [11][15]
= (11)(15)
-------------------------------------------------
So, k = 30(10 + 11 + 12 + ... + 19 + 20)
= 30(11)(15)
= (2)(3)(5)(11)(3)(5)
We can see that 11 is the greatest prime factor of k
Answer: C
Cheers,
Brent
