Number Systems

sukhman 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

Hmmmmm, not sure about "even multiples." 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. Is this correct?? Of course, if this is the case, why not just say "multiples of 30"?

What's the source of this question?

Cheers,
Brent

sukhman 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?
A) 5
B) 7
C) 11
D) 13
E) 17

Assuming "even multiples of 15" is the same as "multiples of 30," let's examine some terms to add up.
So k = 300 + 330 + 360 + ... + 570 + 600

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)

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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)

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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