GmatKiss wrote:There are five jars in a row, each of which contains some marbles in them in strictly increasing order. From left to right, the number of marbles in each jar (except the first one) is multiple of the number of marbles in the jar just before it. The total number of marbles in those five jars is 43. What is the number of marbles in the jar with maximum number of marbles in it?
If anyone is looking for the conventional algebraic method, here it is. But this is very lengthy and cumbersome method.
Say, the number of marbles in the jars are p, pq, pqr, pqrs, and pqrst, where q, r, s, and t are the multiplication factors which are integers greater than 1.
So, (p + pq + pqr + pqrs + pqrst) = 43
--> p*(1 + q + qr + qrs + qrst) = 43
As 43 is a prime integer, only possible factorization for 43 is 1*43.
Hence, p must be equal to 1 and the expression in bracket must be equal to 43.
So, (1 + q + qr + qrs + qrst) = 43
--> q*(1 + r + rs + rst) = 42
Now, 42 = 1*42 = 2*21 = 3*14 = 6*7
We have to check for each of the above factorization.
Note that 1*42 is not allowed as that will lead us to q = 1, which is not permissible. Let us check with 42 = 2*21
- q must be equal to 2 and the expression in bracket must be equal to 21.
So, (1 + r + rs + rst) = 21
--> r*(1 + s + st) = 20
Now, 20 = 1*20 = 2*10 = 4*5
We have to check for each of the above factorization.
Note that 1*20 is not allowed as that will lead us to r = 1, which is not permissible. Let us check with 20 = 2*10
- r must be equal to 2 and the expression in bracket must be equal to 10.
So, (1 + s + st) = 10
--> s*(1 + t) = 9
Now, 9 = 1*9 = 3*3
We have to check for each of the above factorization.
Note that 1*9 is not allowed as that will lead us to s = 1, which is not permissible. Let us check with 9 = 3*3
- s must be equal to 3 and the expression in bracket must be equal to 3.
So, (1 + t) = 3
--> t = 2
Hence, p = 1, q = r = 2, s = 3, and t = 2.
Hence, number of marbles in the jars are 1, 2, 4, 12, and 24.
Hence, number of marbles in the jar with maximum number of marbles in it = 24
The correct answer is D.
Note : We are lucky that all our assumptions on the selection of the factorization was correct. If for example, we ended up with t = 1 we have to go back to any point on the past where an assumption took place and take another factorization like 20 = 4*5 or 42 = 3*14 etc.
