12 Days of Christmas GMAT Competition - Day 9: Ron has invited his fri

Ron has invited his friends to his birthday party, and he plans to give his friends drawing books, sketch pens, and stationery box as a return gift. Each of his friends gets “v” drawing books, “w” sketch pens, and “x” stationary boxes. How many of Ron’s friends attended his birthday party?

(1) The number of drawing books, sketch pens, and stationery boxes each friend gets is in the ratio 3: 4: 2.-- We do not know total people or total ratio to be able to derive the number of people NS

(2) Ron gave a total of 36 drawing books, 48 sketch pens, and 24 stationary boxes.--- We get a ratio of 3:4:2 but we do not know how many were distributed to each person. It could 3,4,2 to each or 6,8,4 or 9,12,6 or 18,24,12 or 36,48,24 Thus NS

Together also NS because we already know ratio of distribution in B so A is not dding anything new

Ans E

Number of friends = x

Statement 1:
The ratio of books, pens, and boxes given to each friend = 3:4:2
No. of friends could be anything as the total number of items is not given.
Insufficient

Statement 2:
Total items given to friends are given
36 Books, 48 Pens & 24 Boxes
If x = 12 => 3 books, 4 pens & 2 boxes per friend (3:4:2)
If x = 6 => 6 books, 8 pens & 4 boxes per friend (3:4:2)
No. of friends cannot be calculated.
Insufficient

Combining both statements:
Redundant information.
Insufficient

IMO E

(1) The number of drawing books(D), sketch pens(S), and stationery boxes(B) each friend gets is in the ratio 3: 4: 2.

We cannot determine the number of Ron’s friends who attended his birthday party from the given ratios.
For e.g if 3 friends attended, then the number of D,S & B will be 9,12 & 6 resp.
If 5 friends attended, then the number of D,S & B will be 15,20 & 10 resp.

Insufficient.

(2) Ron gave a total of 36 drawing books, 48 sketch pens, and 24 stationary boxes.

From the given data on return , we cannot determine the number of friends.

Insufficient.

Combining (1) +(2) , Taking number of friends as n, we get that 3nx:4nx:2nx = 36:48:24
We cannot directly take 3x=36 and x = 12, since we do not know the number of friends.
For example,
If n = 6, then the gifts distribution can be 6:8:4
If n = 12, then the gifts distribution can be 3:4:2
If n = 3, then the gifts distribution can be 12:24:8.
In all these scenarios , the given ration of gifts doesn't change. And we cannot determine the unique value of number of friends.

Answer - E

In order to find the number friends, if we are to establish it from the V, W and X quantities, we need to know the following things:

- how many items were distributed in total
- how many items are presented per person

So, unless the conditions give us both, there's no way of finding the answer.

The ratio is good, but it does nothing to address the task. How many items? 6, 8 and 4? 30, 40 and 20? And how many friends got this all? Anyway, Condition 1 is insufficient.

This is already better, because it addresses one of our bullet points - the total number of things. However, how many per person? This is unclear.
We can have 12 friends, or 1 friend getting everything - it isn't decisive at all. Therefore, Condition 2 is insufficient.

Now if we combine the two things, unfortunately, nothing changes still: 12 friends can get 3/4/2 items each, or 2 friends can get 18/24/12 gifts each.
Therefore, even two conditions together are insufficient - so the answer is E.

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