Bunuel wrote:

A bag contains blueberry candies, each weighing 9 grams, and mango candies, each weighing 7 grams. How many blueberry candies are in the bag?

(1) The total weight of the candies in the bag is 75 grams.

(2) The bag contains twice as many blueberry candies as mango candies.

To know the number of blueberry candies, we need to know their total weight.

We'll look for a statement that gives us this information, a Logical approach.

(1) There are two methods to see that there can be only one unique solution.

Say we've found one solution and we're looking for another one. That is, we've found values of b,m such that 9b+ 7m = 75.

Since we want to maintain the equality, then every time we increase the total number of blueberries by 9b, we need to decrease the total number of mulberries by 7m.

That is, we need to find values of b and m such that 9b = 7m.

Since the LCM of 9 and 7 is 63, then this happens only once every 63 berries. That is, every pair of answer choices will be exactly 63 berries larger or smaller than another pair.

But the total number of berries is only 75! That means that we can only 'fit' one answer pair into our data.

Then there must be one unique solution (even if we don't know what it is).

If all this is confusing, we'll try all the options:

9b + 7m = 75.

We'll look through possible values of b:

9b = 9 --> 7m = 75 - 9 = 66 --> not divisible by 7. No

9b = 18 --> 7m = 66 - 9 --> 57 --> not divisible by 7. No (Note that we already know 75 - 9 so instead of calculating 75 - 18 we can just subtract another 9 from 75 - 9, which is what we did)

9b = 27 --> 7m = 57 - 9 = 48 --> No.

9b = 36 --> 7m = 48 - 9 = 39. No

9b = 45 --> 7m = 39 - 9 = 30. No

9b = 54 --> 7m = 30 -9 = 21. Yes.. this is our first answer.

9b = 63 --> 7m = 21 - 9 = 12. No

9b = 72 --> 7m = 12 - 9 = 3. No

So only 9b = 54, 7m = 21 is an answer.

(2) Without having any information on the total this is insufficient.

(A) is our answer.

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