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If each term in the sum a1 + a2 + a3.....+ an is either 7 or 77 and the sum is 350, What is n ?

Note: a1,a2 represent the first term,second...and NOT a*1, a*2 !

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

Let x and y be the number of term 7 and the number of term 77 respectively. WE have :
7x+ 77y= 350 ---> x+11y = 50 ---> x+y= 50- 10y
we have : x+y= n = 50- 10y ---> n must have the unit digit of 0 because 50 - 10y must be a number which has unit digit of 0

Among the answer choices provided, only C matches.

For example: as units digit of 350 is zero then # of terms must be multiple of 10. Only answer choice which is multiple of 10 is C (40).

To illustrate consider adding:

*7 *7 ... 77 77 ---- =350

So, several 7's and several 77's, note that the # of rows equals to the # of terms. Now, to get 0 for the units digit of the sum the # of rows (# of terms) must be multiple of 10. Only answer choice which is multiple of 10 is C (40).

Answer: C.

Or: \(7x+77y=350\), where \(x\) is # of 7's and \(y\) is # of 77's, so # of terms \(n\) equals to \(x+y\);

\(7(x+11y)=350\) --> \(x+11y=50\) --> now, if \(x=39\) and \(y=1\) then \(n=x+y=40\) and we have this number in answer choices.

If each term in the sum a1 + a2 + a3.....+ an is either 7 or 77 and the sum is 350, What is n ?

Note: a1,a2 represent the first term,second...and NOT a*1, a*2 !

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

Let x and y be the number of term 7 and the number of term 77 respectively. WE have : 7x+ 77y= 350 ---> x+11y = 50 ---> x+y= 50- 10y we have : x+y= n = 50- 10y ---> n must have the unit digit of 0 because 50 - 10y must be a number which has unit digit of 0

Among the answer choices provided, only C matches.

If each term in the sum a1 + a2 + a3.....+ an is either 7 or 77 and the sum is 350, What is n ?

Note: a1,a2 represent the first term,second...and NOT a*1, a*2 !

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

Let x and y be the number of term 7 and the number of term 77 respectively. WE have : 7x+ 77y= 350 ---> x+11y = 50 ---> x+y= 50- 10y we have : x+y= n = 50- 10y ---> n must have the unit digit of 0 because 50 - 10y must be a number which has unit digit of 0

Among the answer choices provided, only C matches.

I go for C.

I like this method because it attacks the the question dead on by representing each term as x and y and then deductively finding the answer through POE. Hope I can think this quickly on the exam!

I used a different method altogether. I observed that since all the numbers are 7s, the total number of sevens has to be a multiple of 5 in order to get to 350. out of the answer choices, only 40 is a multiple of 5, So eliminate everything but choice C. I guess, if there were other multiples of 5 then you could use one of the methods above. But as a quick elimination strategy it helped to do the least amount of work.

+1 C 7(50)=350 Since 50 is not there in ANSWERS so 77 needs to be ther 77=7(11) So : number of terms if one 77 is there 50-11+1=50-10=40 --> Check the Ans. C matches..
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A beautiful variant of this problem - If each term in the sum a1 + a2 + a3.....+ an is either 7 or 77 and the sum is 350

Note: a1,a2 represent the first term,second...and NOT a*1, a*2 ! n has a value of : I. 30 II. 45 III. 10 IV. 50 V. 25

Which of the following can be True ? A - I,II,III B - II,III,V C - I,III,IV D - All C - None

Apply the same concepts and you can figure out the solution
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Re: If each term in the sum a1 + a2 + a3.....+ an is either 7 or [#permalink]

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30 Oct 2013, 04:23

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