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# What is the sum of the first 50 multiples of a positive integer K?

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Math Expert
Joined: 02 Sep 2009
Posts: 50044
What is the sum of the first 50 multiples of a positive integer K?  [#permalink]

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18 Apr 2018, 18:21
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Difficulty:

45% (medium)

Question Stats:

58% (01:13) correct 42% (01:13) wrong based on 46 sessions

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What is the sum of the first 50 multiples of a positive integer K?

(A) 1,225K
(B) 1,275K
(C) 2,450K
(D) 2,550K
(E) 1,326K

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What is the sum of the first 50 multiples of a positive integer K?  [#permalink]

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18 Apr 2018, 19:23
1
Bunuel wrote:
What is the sum of the first 50 multiples of a positive integer K?

(A) 1,225K
(B) 1,275K
(C) 2,450K
(D) 2,550K
(E) 1,326K

We have to find Sum of progression (1+2+..+50)K = (50+1)/2*50 *K =1 275 K

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What is the sum of the first 50 multiples of a positive integer K?  [#permalink]

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19 Apr 2018, 11:28
Bunuel wrote:
What is the sum of the first 50 multiples of a positive integer K?

(A) 1,225K
(B) 1,275K
(C) 2,450K
(D) 2,550K
(E) 1,326K

Zero is a multiple of every integer.

The first 50 multiples of $$K$$ are
$$0K, 1K, 2K, 3K, . . . . 47K, 48K, 49K$$

Factor K out (we're interested in the arithmetic progression)

Sum of first 50 multiples of $$K$$:
$$K(0 + 1 + 2 + 3 . . . + 47 + 48 + 49)$$

Sum of evenly spaced integers=
(Average)*(# of terms)

Average = $$\frac{FirstTerm+LastTerm}{2}$$
Number of terms: 50 (given)

SUM (of K's multiples' coefficients) =
(Average)*(number of terms)

Sum: $$(\frac{(0 + 49)}{2}*50) = (25 * 49)= 1,225$$

Sum of first 50 multiples of K:
$$(1,225*K) = 1,225K$$

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Re: What is the sum of the first 50 multiples of a positive integer K?  [#permalink]

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19 Apr 2018, 12:59
1
Top Contributor
Bunuel wrote:
What is the sum of the first 50 multiples of a positive integer K?

(A) 1,225K
(B) 1,275K
(C) 2,450K
(D) 2,550K
(E) 1,326K

The answer to this question boils down to what is meant by "the first 50 multiples"
For example, some might say that the first 3 multiples of 5 are 5, 10, 15
Others might say that the first 3 multiples of 5 are 0, 5, 10
Of course, we might also even go in the other direction and say that the first 3 multiples of 5 are -5, -10, -15

I think the test-makers would add a few extra words to remove any ambiguity.

Cheers,
Brent
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Re: What is the sum of the first 50 multiples of a positive integer K? &nbs [#permalink] 19 Apr 2018, 12:59
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