Data Sufficiency

A number of oranges are to be distributed evenly among a number of baskets. Each basket will contain at least one orange. If there are 20 oranges to be distributed, what is the number of oranges per basket?

(1) If the number of baskets were halved and all other conditions remained the same, there would be twice as many oranges in every remaining basket.

(2) If the number of baskets were doubled, it would no longer be possible to place at least one orange in every basket.

Let N is the number of basket, X is the number of oranges in each basket.

We will have X * N = 20, remember both X & N are integer

so we can guess X & N will be one of the following pairs (interchangeable)

1 - 20, 2 - 10, 4 - 5

I. We will choose 1 - 20, 1 is X and 20 is N. If we halve the number of basket (then now 10) we will have X is 2. So it's sufficient

II. Insufficient.

So answer is A. It's a little bit tricky to solve the problem

There are 20 oranges, and B baskets. Since each basket has at least 1 orange, and the number of oranges per basket is the same, there are only a limited number of possibilities; B must be a factor of 20.

So B can be 1, 2, 4, 5, 10 or 20.

(1) if B was halved, there would be twice as many oranges per basket. This is true for B=2, 4, 10, 20

(2) if B were doubled, there would not be enough oranges to satisfy the constraint. This is only true for B=20 (one orange per basket). If you doubled B=4 to eight baskets, you could not split the oranges evenly, but you could put one orange in each.

Statement (2) is sufficient, and Statement (1) is not sufficient.

Want more Data Sufficiency examples? Try
https://www.testsandtutors.com/course/qu ... ufficiency

praxis is right, I don't pay attention to 2-10 and 4-5 case. and even maximum 20.

Thanks praxis