outty 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.
Hey, I made up that question
https://www.beatthegmat.com/a-box-of-bag ... 29612.html
My solution is similar to Rich's but introduces some variables.
Target question: How many bags are in the box?
Let B = # of bags
Let M = # of marbles in MOST bags
So, M + 1 = # of marbles in the bag containing the extra marble.
This means that BM + 1 = 2001
Or we can say that BM = 2000
Let's find the prime factorization of 2000.
We get 2000 = (2)(2)(2)(2)(5)(5)(5)
In other words,
BM = (2)(2)(2)(2)(5)(5)(5)
Statement 1: The number of bags is between 13 and 23 inclusive
If
BM = (2)(2)(2)(2)(5)(5)(5), and B ranges from 13 to 23 inclusive, there are EXACTLY TWO POSSIBLE CASES:
Case a:
B = 16 and M = 125
Case b:
B = 20 and M = 100
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: There is an even number of bags, and there is an even number of marbles in the bag containing the extra marble.
In other words, B is EVEN and (M+1) is EVEN
Or we can say that B is EVEN and M is ODD
If
BM = (2)(2)(2)(2)(5)(5)(5), there are several possible case. Here are two:
Case a:
B = 16 and M = 125
Case b:
B = 80 and M = 25
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1 tells us that
EITHER B = 16 and M = 125
OR B = 20 and M = 100
Statement 2 tells us that M is ODD.
So, it must be the case that
B = 16 and M = 125
Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer =
C
Cheers,
Brent
