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# If each term in the sum a1+a2+a3+...+an is either 7 or 77 and the sum

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Intern
Joined: 20 Aug 2018
Posts: 25
Re: If each term in the sum a1+a2+a3+...+an is either 7 or 77 and the sum  [#permalink]

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24 Nov 2018, 18:51
There are a few different approaches.

A video explanation of two of them can be found here:

One approach is to think about the maximum and minimum number of 7s we would need in order to reach a sum of 350. The maximum is 350/7 = 50, but 50 isn't an answer choice. We need a number that's lower than 50, so lets find the second-highest number by subtracting a 77 from 350

350 - 77 = 273

273/7 = 39, i.e. our list of numbers could have a 77 and thirty-nine "7s" and the sum would be 350

The video covers this approach and a second one, as well.
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Re: If each term in the sum a1+a2+a3+...+an is either 7 or 77 and the sum  [#permalink]

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01 Nov 2019, 11:12
Great question, and thanks for the explanation Bunuel!
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Re: If each term in the sum a1+a2+a3+...+an is either 7 or 77 and the sum  [#permalink]

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14 Dec 2019, 14:00
LM wrote:
If each term in the sum $$a_1+a_2+a_3+...+a_n$$ is either 7 or 77 and the sum equals 350, which of the following could be equal to n?

A. 38
B. 39
C. 40
D. 41
E. 42

350 / 7 = 50, but it is too large, so we must have at least one 77

350 - 77 = 273

273 / 7 = 39 (number of 7s)

39 + 1 (add one for 77) = 40
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Re: If each term in the sum a1+a2+a3+...+an is either 7 or 77 and the sum  [#permalink]

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14 Dec 2019, 14:26
LM wrote:
If each term in the sum $$a_1+a_2+a_3+...+a_n$$ is either 7 or 77 and the sum equals 350, which of the following could be equal to n?

A. 38
B. 39
C. 40
D. 41
E. 42

Let x = the number of 7's and y = the number of 77's.

Total number of terms:
Since the OA represents the total number of terms, we get:
x + y = OA.

Sum of the terms:
Since the sum of the terms is 350, we get:
7x + 77y = 350
7(x + 11y) = 350
x + 11y = 50.

Subtracting the red equation from the blue equation, we get:
(x + 11y) - (x + y) = 350 - OA
10y = 350 - OA
OA = 350 - 10y = (multiple of 10) - (multiple of 10) = multiple of 10.

.
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Re: If each term in the sum a1+a2+a3+...+an is either 7 or 77 and the sum   [#permalink] 14 Dec 2019, 14:26

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