I31-15

Question

"Sweetness" is defined as sugar content per unit of weight. At a fruit stand, mangoes are sweeter than apples, and apples are sweeter than lemons. A fruit salad is made using equal weights of exactly two of these fruits and no other ingredients. Does the fruit salad contain mango?

(1) The fruit salad is less sweet than apples.
 
(2) The fruit salad is sweeter than a fruit salad made using equal weights of apples and lemons and no other ingredients.

Bunuel · Answer

Official Solution:

"Sweetness" is defined as sugar content per unit of weight. At a fruit stand, mangoes are sweeter than apples, and apples are sweeter than lemons. A fruit salad is made using equal weights of exactly two of these fruits and no other ingredients. Does the fruit salad contain mango? 
 
Given: mangoes > apples > lemons.
 
(1) The fruit salad is less sweet than apples.
 
This means the salad cannot be made of mangoes and apples, since that salad would be sweeter than apples. However, the salad could be made of apples and lemons, or it could be made of mangoes and lemons. So the salad may or may not contain mango. Not sufficient.
 
(2) The fruit salad is sweeter than a fruit salad made using equal weights of apples and lemons and no other ingredients.
 
Among the three possible equal-weight salads, the apples and lemons salad has the lowest sweetness. If the fruit salad is sweeter than that, it cannot be apples and lemons. The remaining options are mangoes and apples or mangoes and lemons, and both contain mango. Sufficient.
 
Answer: B

LuvleenPanda · Answer

In option B, it says salad is sweeter than salad with equal weight of apple and lemon.
Possibility 1: Salad has more apple than lemon
Possibility 2: Salad has mango and apple or mango and lemon
So, we cannot infer if mango is present in salad.
Please confirm the loop hole in such explanation.

For me Ans was E.

Bunuel · Answer

The correct answer is B. “More apple than lemon” is impossible here because the salad must be 50/50 by weight. With 50/50 fixed, apple+lemon is the least sweet pair, so if the salad is sweeter than that, it cannot be apple+lemon, and the remaining pairs both include mango.

natusadipisci · Answer

I did not quite understand the solution. Hi, 
I got confused by this.
(2) The fruit salad is sweeter than a fruit salad made using equal weights of apples and lemons and no other ingredients.

As per my thought, if the sweetness are in this fashion Mango> Apple>Lemon
The salad is said to be sweeter than 1:1 by weight of apples and lemons(i.e than the sweetness at the absolute midpoint in between Apple and lemon. )Apple.....x.....Lemon
And our salad's sweetness is greater than that.

Now, what about a case where the salad contains only apples, or more of apples than lemons. In all the cases the salad sweetness will be greater than 50-50 by weight of apple and lemon.
So, like option A, the salad may/may not contain mango.

Hence I chose E.

Can you please tell me where is my logic wrong?

Bunuel · Answer

In (2), the salad must use equal weights of exactly two fruits, so “only apples” or “more apples than lemons” is not allowed.

With equal weights, the apple lemon salad is the least sweet of the three possible mixes (MA, ML, AL). If the salad is sweeter than AL, it cannot be AL, so it must be MA or ML, and both include mango.

natusadipisci · Answer

Yeah, I got it now, moreover I found my fault. I missed the part in the question where it clearly mentioned "the salad must contain 2 of the 3 fruits."
Thanks for the clarification.

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