The Jock wrote:A box contains bags of marbles. All of the bags hold the same number of marbles except one bag, which holds one marble more than each of the other bags hold. If the box contains a total of 2001 marbles, how many bags are in the box?
(1) The number of bags is between 13 and 23 inclusive
(2) There is an even number of bags, and there is an even number of marbles in the bag containing the extra marble.
Step 1 of the Kaplan Method for DS: Analyze the Stem
Let's call the number of bags n and and the marbles per bag x. So, the total number of marbles is nx + 1, since the last bag has 1 extra marble.
Accordingly:
nx + 1 = 2001
nx = 2000
By the indivisible nature of the items, we also know that both n and x must be positive integers.
Q: what's the value of n?
Step 2 of the Kaplan Method for DS: Evaluate the Statements
(1) 13 <= n <= 23
We know that n is a factor of 2000. So, is there more than one factor of 2000 in this range?
Breaking 2000 into primes:
2000 = 10 * 200 = 2 * 5 * 10 * 20 = 2 * 5 * 2 * 5 * 2 * 2 * 5
2 * 2 * 2 * 2 = 16; 2 * 2 * 5 = 20; n could be either 16 or 20 - insufficient, eliminate A and D.
(2) n is even and x is odd (since x + 1 is even).
even * odd = 2000
We could pick n = 2000 and x = 1 or n = 400 and x = 5; n could be either 2000 or 400 - insufficient, eliminate B.
Combined:
From (1), we know that n is 16 or 20.
If n = 16, then x = 5*5*5 = 125
If n = 20, then x = 2*2*5*5 = 100
From (2), we know that x must be odd - accordingly, only n=16 works; sufficient, choose C!
