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A number of apples and oranges are to be distributed evenly [#permalink]

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21 Jul 2008, 07:58

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

A number of apples and oranges are to be distributed evenly among a number of baskets. Each basket will contain at least one of each type of fruit. If there are 20 oranges to be distributed, what is the minimum number of apples needed so that every basket contains less than twice as many apples as oranges?

(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 oranges were halved, it would no longer be possible to place an orange in every basket.

I'm having difficulty with understanding less than twice as many apples as oranges Does this mean: if there are 10 oranges in a basket then twice as many apples will be 20; since it says less than, should the number of apples be 21 and oranges 10

I would really appreciate if you guys can help me understand this. Also, try to answer the question.

Re: MGMAT - Problem with understanding the language [#permalink]

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22 Jul 2008, 09:49

stingraybullray wrote:

I'm having difficulty with understanding less than twice as many apples as oranges

To understand the question, it may be useful to cover certain words...

Original: "every basket contains less than twice as many apples as oranges?"

New: "every basket contains ... as many apples as oranges?" Okay, we agree that if this were the question, we'd be looking for equal numbers of apples and oranges.

New: "every basket contains ... twice as many apples as oranges?" Now we're looking for 2 apples for every orange.

Original: "every basket contains less than twice as many apples as oranges? The question is looking for LESS THAN 2 apples for every orange.

Statement 1 tells us that we have an even number of baskets... 2, 4, 10, or 20 (since oranges have to be distributed evenly). Statement 2 (alone) tells us that 10 oranges would be insufficient, thus we have 11 - 20 baskets.

Together, we can deduce that there must be exactly 20 baskets, so together we can answer the question.

Re: MGMAT - Problem with understanding the language [#permalink]

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22 Jul 2008, 10:02

stingraybullray wrote:

A number of apples and oranges are to be distributed evenly among a number of baskets. Each basket will contain at least one of each type of fruit. If there are 20 oranges to be distributed, what is the minimum number of apples needed so that every basket contains less than twice as many apples as oranges?

(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 oranges were halved, it would no longer be possible to place an orange in every basket.

I'm having difficulty with understanding less than twice as many apples as oranges Does this mean: if there are 10 oranges in a basket then twice as many apples will be 20; since it says less than, should the number of apples be 21 and oranges 10

I would really appreciate if you guys can help me understand this. Also, try to answer the question.

Answer is C)

Statement 1) tells that baskets are exact even factors of oranges which is 20,10,4,2 Statement 2) tells that baskets are between 11-20

Combining both tells number of baskets are 20. Therefore number of apples required should be 2*20=40

Re: MGMAT - Problem with understanding the language [#permalink]

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23 Jul 2008, 20:17

paul & nmohindru - Thanks for your reply. Here is the OE from MGMAT.

Quote:

Each basket must contain at least one of each type of fruit. We also must ensure that every basket contains less than twice as many apples as oranges. Therefore, the minimum number of apples that we need is equal to the number of baskets, since we can simply place one apple per basket (even if we had only 1 apple and 1 orange per basket, we would not be violating any conditions). If we are to divide the 20 oranges evenly, we know we will have 1, 2, 4, 5, 10, or 20 baskets (the factors of 20). But because we don't know the exact number of baskets, we do not know how many apples we need. Thus, the question can be rephrased as: "How many baskets are there?"

(1) INSUFFICIENT: This tells us only that the number of baskets is even (halving an odd number of baskets would result in half of a basket). Since we have 20 oranges that must be distributed evenly among an even number of baskets, we know we have 2, 4, 10, or 20 baskets. But because we still do not know exactly how many baskets we have, we cannot know how many apples we will need.

(2) SUFFICIENT: This tells us that 10 oranges (half of the original 20) would not be enough to place an orange in every basket. So we must have more than 10 baskets. Since we know the number of baskets is 1, 2, 4, 5, 10, or 20, we know that we must have 20 baskets. Therefore, we know how many apples we will need.

Re: MGMAT - Problem with understanding the language [#permalink]

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25 Jul 2008, 09:33

Let there be n baskets. Since the oranges are evenly distributed, n should be a factor of 20. This produces 4 scenarios: Oranges Baskets 5 x 4 4 x 5 10 x 2 2 x 10 i.e, there are 4 possible combinations.

Statement 1: If n becomes n/2, oranges become double. This condition is satisfied by 5 x 4 and 10 x 2 above. Therefore, there could be 4 baskets, each containing 5 oranges.. Therefore, min. number of apples that could be evenly distributed among the 4 baskets and would be < 2 x oranges in each basket = 6 x 4 =24.

Statement 2: Out of all the 4 combinations, there is only 1 where if no. of oranges is halved, one cannot place oranges evenly in the baskets, i.e, 10 oranges in 4 baskets. Therefore, there must be 5 oranges in each of the 4 baskets, which again brings us to the original answer that we derived from the 1st statement. Therefore, the answer should be D.

Re: MGMAT - Problem with understanding the language [#permalink]

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25 Jul 2008, 12:39

I would go for B

Remember we need to find minimum no. of apples

No. of Oranges = 20 minimum there will be 1 orange per basket

also no. of apples per basket < 2( no. of oranges per basket) => no. of apples per basket < 2(1) ( as 1 is the least no of oranges possible per basket)

so we need only 1 apple per basket ( as even if there are more than 1 orange per basket no of apples will be less than twice of oranges)

so if know how many baskets are there our problem is solved

stmt 1 - talks abt if baskets are halved so we know tht no. of baskets are even so it can be 2, 4, 10 or 20

not suff

stmt 2 - if oranges are halved they cannot be placed. so 10 oranges can't be placed so no of baskets has to be > 10

also because oranges/apples are placed evenly so no. of baskets has to be 20

As no. of baskets is known , minimum no. of apples is known = 20 hence B is ans