You could work from answer choices. You will find that 40 would be the answer. The sequence would be that it has 39 -7s and 1 -77, such that the sum=(39*7)+77=273+77=350.Fab_Vr6 wrote:If each term in the sum a1+a2+.....an (n-term) is either 7 or 77, and the sum is equal to 350, which of the following could equal to n?
1) 38
2)39
3)40
4)41
5)42
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Prasanna
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When I looked at this problem I didn't look at the answers very closely(big mistake,...I know). I divided 77 into 350 and saw that it went in 4 times with a remainder of 42, which is 6 sevens.
That only gave me n=10, which is the smallest n could be. Then I looked at the answers and realized that in order to be up around 40, there would have to be alot more sevens than seventy-sevens.
So I subtracted seventy seven from 350 leaving 273, and tried dividing that by 7. It went 39 times, leaving me with n=40 which was an available answer.
You can quickly see the other anwers aren't viable by realizing if you have two 77s, n is no where near high enough, and all 7s would be n=50.
I'm sure there is a more "scientific" way to attack it, but that was my approach. Hope it helps.
That only gave me n=10, which is the smallest n could be. Then I looked at the answers and realized that in order to be up around 40, there would have to be alot more sevens than seventy-sevens.
So I subtracted seventy seven from 350 leaving 273, and tried dividing that by 7. It went 39 times, leaving me with n=40 which was an available answer.
You can quickly see the other anwers aren't viable by realizing if you have two 77s, n is no where near high enough, and all 7s would be n=50.
I'm sure there is a more "scientific" way to attack it, but that was my approach. Hope it helps.
Assume that the number of 7s and 77s in the series is x and y respectively.
Then we could form the equation:
7x + 77y = 350
=> 7 (x + 11y) = 350
=> x + 11y = 50
Possible values of (x,y) : (39,1) , (28,2) , (17,3) .. and so on (you just need to calculate with y = 1)
x + y is the total number of terms in the series i.e n = x + y
n can take values : (40, 30, 20) .. and so on
so 40 is the answer ...
Then we could form the equation:
7x + 77y = 350
=> 7 (x + 11y) = 350
=> x + 11y = 50
Possible values of (x,y) : (39,1) , (28,2) , (17,3) .. and so on (you just need to calculate with y = 1)
x + y is the total number of terms in the series i.e n = x + y
n can take values : (40, 30, 20) .. and so on
so 40 is the answer ...
