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If x is a sum of all even integers on the interval 13...65

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If x is a sum of all even integers on the interval 13...65  [#permalink]

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New post 29 Jun 2014, 07:26
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If x is a sum of all even integers on the interval 13...65 and y is their number, what is the GCD (x, y)?

(A) 1
(B) 13
(C) 26
(D) 52
(E) 1014
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Posts: 52905
If x is a sum of all even integers on the interval 13...65  [#permalink]

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New post 29 Jun 2014, 08:12
Maksym wrote:
If x is a sum of all even integers on the interval 13...65 and y is their number, what is the GCD (x, y)?

(A) 1
(B) 13
(C) 26
(D) 52
(E) 1014


y is the number of even integers from 14 to 64, inclusive = (largest - smallest)/2 + 1 = (64 - 14)/2 + 1 = 26. (Check this: totally-basic-94862.html#p730075)

x = 14 + 16 + ... + 64 = (largest + smallest)/2 *(# of terms) = (14 + 64)/2*26 = 39*26.

GCD of 26 and 39*26 is 26.

Answer: C.

P.S. The wording of the question is not quite GMAT-like.
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Re: If x is a sum of all even integers on the interval 13...65  [#permalink]

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New post 06 Feb 2019, 19:44
Maksym wrote:
If x is a sum of all even integers on the interval 13...65 and y is their number, what is the GCD (x, y)?

(A) 1
(B) 13
(C) 26
(D) 52
(E) 1014


The number of even integers from 14 to 64, inclusive, is:

(64 - 14)/2 + 1 = 26 = y

The sum of these integers is:

(64 + 14)/2 * 26 = 39 * 26 = x

Thus, the GCF(x, y) is 26.

Answer: C
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Re: If x is a sum of all even integers on the interval 13...65   [#permalink] 06 Feb 2019, 19:44
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