Oranges only...

[ketandoshi31]

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 could not understand the explanation.....can somebody help...

Thanks
KD

[gokul_nair1984]

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?

Number of Oranges=20( Given)
Thus, Number of baskets can be 1,2,4,5,10,20

According to Statement 1,

(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.

Number of Oranges=20
Number of Baskets could be 1,2,5,10(* You cannot halve odd nubers here because basket has to be a natural number)
So , number of Oranges/Basket could be 20,10,4 or 2.
Hence A is insufficient

According to Statement 2,

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

Number of baskets can only be 20 in this case because the question stem says that there has to be atleast 1 orange/basket.

In line with Statement 2, if we double it, the number of baskets will be 40 and hence there won't be atleast one orange/basket.
So number of baskets has to be 20 and that means 1orange/basket.

Hence B is sufficient.

-----Hope this helps

[odonnelle22]

"A number of oranges are to be distributed evenly among a number of baskets."

Are we supposed to assume that there can't be any oranges left over after you distribute them evenly over a certain number of baskets?

From the answer given we clearly are, but I'm wondering if this is something I can actually assume from the question - that it's not a trick - that maybe each basket got 2 but then there were 4 left over.

I worry about making these kind of assumptions!

Thanks.

[gokul_nair1984]

Are we supposed to assume that there can't be any oranges left over after you distribute them evenly over a certain number of baskets?

Yes, that is what evenly distributed means. Otherwise the question would have indicated some leftovers.

[tim]

Thanks, Gokul. Odonnelle, let us know if you have any further questions..

[naraenk]

Hi,

I have a doubt regarding this question. I understand the explanation but on point 2, when 4 baskets are doubled it will not satisfy the evenly distributed rule mentioned in the question. Therefore, I chose E as the answer. It will be great if someone can explain what I'm missing.

[tim]

the even distribution condition applies only to the original number of baskets. after the number of baskets is doubled, the only condition is that there are more baskets than oranges..

[adrian_obusan]

I;m not seeing why A is insufficient. I understand that you could have 1, 2, 4, 5, 10, or 20 baskets. But there seems to be only one answer that satisfies the fact that when you reduce the basket count to half, that you double the number of 20 oranges. And that would be 20 baskets. (ie reduced to half or 10 baskets hence orange count increasing from 20 ornge/20 bskt=1 to 20 ornge/10 bskt = 2.)

Am I totally missing something here? :)

[jnelson0612]

I;m not seeing why A is insufficient. I understand that you could have 1, 2, 4, 5, 10, or 20 baskets. But there seems to be only one answer that satisfies the fact that when you reduce the basket count to half, that you double the number of 20 oranges. And that would be 20 baskets. (ie reduced to half or 10 baskets hence orange count increasing from 20 ornge/20 bskt=1 to 20 ornge/10 bskt = 2.)

Am I totally missing something here? :)

Be careful! I think that you're misreading. Let's see the clue again:
"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."

We are not doubling the number of oranges from twenty to forty; instead, we are halving the number of baskets and doubling the number of oranges in each basket. The original number of twenty oranges stays the same.

So I could have one orange in twenty baskets. If I halve the baskets to ten and distribute the oranges, I have two oranges per basket. So this possibilities works.

I could also have two oranges in ten baskets. If I have the baskets to five and distribute the oranges, I have four oranges per basket. This possibility works too.

Thus, A is insufficient because I have two possibilities.

[JbhB682]

Hi Sage --i marked S2 as insufficient because i thought the following are the 2 scenario's

-- 20 baskets @ 1 orange each
-- 4 baskets @ 5 oranges each

My perception is that the rule of even distribution (in the question stem) should be applied to the two statements.

Doing multiple DS questions, the criteria in the question stem does apply to both statements (and then S1 and S2 give additional criteria, thereby allowing one to finalize the list of scenario's when testing)

Hence i thought, 4 baskets @ 5 oranges each is also a possibility

Please let us know your thoughts !

Thank you !

[Sage Pearce-Higgins]

If I understand your point correctly, you're thinking that statement 2 is really saying: If the number of baskets were doubled, it would no longer be possible to place at least one orange in every basket and would no longer be possible to distribute the oranges evenly among the baskets. You're inferring this because the question stem tells you that A number of oranges are to be distributed evenly among a number of baskets.

I don't think you can make a general rule that "conditions in the question stem apply to the statements". They do sometimes, and don't other times. Opening my Official Guide 2020 at random, this seems akin to the DS problems 365 and 366: we have a 'before' and 'after' situation. The conditions that apply to the 'before' situation don't necessarily apply to the 'after'.

For the above problem, perhaps things are more complicated. We could define 3 stages:
Situation 1: a pile of 20 oranges
Situation 2: oranges distributed evenly; at least 1 orange per basket
Situation 3 (according to statement 2): double the number of baskets, no longer possible to put one orange in each basket

It looks like you're claiming that the conditions for situation 2 should apply to situation 3. I disagree: they are separate situations with different constraints. However, I can see that the wording we've chosen for this one is perhaps a little weak. We've got a future tense in the question stem (for situation 2) and then a conditional (for situation 3). All the same, I'd defend the problem as being a good one.