A positive integer N satisfies all of the following:

Question

When N is divided by 6, the remainder is 1. 
 When N is divided by 8, the remainder is 5. 
 When N is divided by 9, the remainder is 7. 
 N<2000.

Let S be the sum of all possible values of N that satisfy the above conditions. What is the value of S?

A. 24,948
B. 25,596
C. 26,496
D. 26,919
E. 27,864

SamMenon · Accepted Answer

So This was my approach:

1. When N =6p +1 possible solutions are 7,13,19,25,31,37,43,49,55,61...
2.When N= 8q + 5 possible solutions are 5,13,21,29,...61....
3. When N = 9R + 7 possible solutions are 13,21,29,37...61...

We note first common term is 61

Now the LCM of divisors 6,8 and 9 are 72

Hence 61 + 72k <2000 (where k is common term multiple)

Solving this yields k≤26

Hence At k= 26 there last factor become 61 + 72*26 = 1933

Now the Sum is asked we used summation formulae:

S=27/2*(61+1933)=26,919

Brindac2 · Answer

My intuition says the answer should be D 26,919. This is purely by looking at the numbers because I couldn't solve it first. So, will wait for OA.

vicentewagener · Answer

The sum of numbers divisible by 6 (with 0 remainder), is divisible by 6. 6+12+18+24 = 60. 60/6 = 10.
Same holds for any number.
So any number N divisible by 6, 8 or 9 with 0 remainder, summed up to S, should also be divisible by 6, 8 or 9.
The only number which is NOT divisible by 6, 8, or 9 (with no remainder) is 26,919. Only number that would satisfy initial condition of leaving a remainder when dividing by 6, 8 or 9.
This won't work in all cases, since the sum of divisibles by 6 8 and 9 could eventually lead to a number that is divisible by 6 8 and 9, but in this case, where there's only one possible option, it worked.

A positive integer N satisfies all of the following:

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GMAT Problem Solving (PS) Questions

A positive integer N satisfies all of the following:

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