word problem4

[gmatnmein2010]

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.

[sars72]

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.

if there were 20 baskets--> 1 orange/basket
if this is halved, --> 10 baskets -> 2 oranges/basket --> twice as many organes/ basket

if there were 10 baskets -> 2 oranges/basket
if halved --> 5 baskets -> 4 organes/basket

since we do not have more than one possible answer, this alone is not sufficient --> A, D are eliminated!

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

possible choices are factors of 20 --> 1,2,4,5,10,20

only 20 if doubled would make it no longer possible to place at least one orange in every basket

--> B is the correct answer

[gmatmachoman]

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.

if there were 20 baskets--> 1 orange/basket
if this is halved, --> 10 baskets -> 2 oranges/basket --> twice as many organes/ basket

if there were 10 baskets -> 2 oranges/basket
if halved --> 5 baskets -> 4 organes/basket

since we do not have more than one possible answer, this alone is not sufficient --> A, D are eliminated!

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

possible choices are factors of 20 --> 1,2,4,5,10,20

only 20 if doubled would make it no longer possible to place at least one orange in every basket

--> B is the correct answer

[spoiler]
IMO [/spoiler]C

Can't it be like Initial number of baskets =20
No .of oranges/baskets: 20/20=1

Now both the statements are true.

St 1:

if there were 20 baskets--> 1 orange/basket
if this is halved, --> 10 baskets -> 2 oranges/basket --> twice as many organes/ basket

St2 :
If the number of baskets were doubled, it would no longer be possible to place at least one orange in every basket

Agreed.. No of baskets will become 40 and we cannot place atleast 1 orange in each basket...

SO st 2 is also true..

IMO C

[Ian Stewart]

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.

I find the language of the question simply bizarre. Are we to assume that the oranges can indeed be distributed equally among the current baskets? That isn't made clear. If so, then from the stem, the number of baskets must be a divisor of 20; it could be 1, 2, 4, 5, 10 or 20.

From Statement 1, we learn that we can indeed halve the number of baskets, meaning their number must be even. Of course if you cut the number of baskets in half each basket will then contain twice as many oranges, so we get no further information; there may be 2, 4, 10 or 20 baskets.

From Statement 2, we learn that when we double the number of baskets, we have more baskets than oranges. Since (if my understanding of the language is correct, something I'm not at all sure about) the number of baskets must be a divisor of 20, the only possibility is that we have 20 baskets, and therefore 1 orange per basket.

That would make the answer B, but I find it a strange question.