12 Days of Christmas GMAT Competition - Day 9: Ron has invited his fri : Data Sufficiency (DS) - Page 2

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

First of all to get a numerical value , we need numerical information.

Statement 1:

This gives us a ratio of v : w : x, however , we cannot use this ratio information to deduce what the multiplier is to get what the total number of friends attended Ron's party. Therefore, this is INSUFFICIENT

Statement 2:

As mentioned before to find a numerical output, we need numerical information. Here we are given the total number of each item in his return gift.
i.e. total number of drawing books , sketch pens, stationary boxes. We can deduce the ratio of v : w : x using this to 3 : 4: 2 with the multiplier being 12, this means that 12 of Ron's friends attended his birthday party and therefore, we get an exact numerical value answer. SUFFICIENT

Statement 2 sufficient on its own. Answer is B

12 friends attended party. Adding each number of gifts we total number of gifts available with him which is 108 gifts. Now putting ration addition into N =108 ,solving we get number of friends=N.

Answer is E
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. Insufficient. various possibilities.
(2) Ron gave a total of 36 drawing books, 48 sketch pens, and 24 stationary boxes. Insufficient. multiple possibilities

(1) + (2) still. we cannot get a single answer. Insufficient

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

Drawing Sketch Pen Stationary
one friend receives v w x

Statement I : v = 3t w = 4t x = 2t 3t is the total drawing books that were distributed among friends and t is the number of friends. We can not find out value of t -> Insufficient

Statement II: v = 36 w = 48 x = 24 we can write them like this
v w x
12*3 12*4 12*2 or
6*6 6*8 6*4 other factorization is also possible

so friends can be 12, 6 etc. ------> Insufficient

Combining 1 & 2 the number of friends should be 12.
answer should be C

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?

Let the total number of drawing books be Vt
number of drawing books each friend got V (given)

Let the total number of sketch pens be Wt
number of sketch pens each friend got W (given)

Let the total number of stationary boxes be Xt
number of sketch pens each friend got X (given)

If we know the values of any of the pairs i.e, (Vt,V) (Wt,W) and (Xt,X), we can easily find the total number of friends that attended the birthday attended the birthday party.

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

Here we are provided with the ratio of V, W and X (INSUFFICIENT)

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

Here we are provided with the values of Vt, Wt and Xt. But we do not yet know the values of V, T, and W (INSUFFICIENT)

Statement (1)+(2)

Here we are provided with the ratio of V, W and X and the values of Vt, Wt and Xt.

This gives us many possibilities of the total number of friends at a party. The number could be 12 , 6 , 4 .. etc There is no unique answer.

Answer: Choice E

(1) The number of drawing books, sketch pens, and stationery boxes each friend gets is in the ratio 3: 4: 2.
is not enough to know the total of each stuff that will be given.
Hence A and D is wrong
(2) Ron gave a total of 36 drawing books, 48 sketch pens, and 24 stationary boxes.
is not enough to know how many friends are invited.
Maybe he can give all 36 drawing books, 48 sketch pens and 24 boxes to one person or two person.
Hence, it depends on the ratio.
Therefore, B is wrong

from 1 and 2 we know that 12 friends were invited to the birthday.
Hence C is enough

We need to find number of friends(n).

v:w:x = 3:4:2 ( v=3y, w= 4y, x=2y)
possible values of v =3,6,9,......
possible values of w = 4,8,12,.....
possible values of x = 2,4,6,....

we cannot find exact value on n. So not sufficient.

v=36, w= 48, x= 24
still not sufficient.

1 + 2
Here n can be either 12 or 6 or 3. Still not sufficient so the answer is E

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.

information on total distribution of items not available.

so, NOT ADEQUATE

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

information on per friend's share not available in this prompt..

so, NOT ADEQUATE

(1) and (2) together

If v.w,x = 3.4.2; then friends = 12 (given that 36 drawing books, 48 sketch pens, and 24 stationary boxes. were distributed)
If v.w,x = 9.12.6; then friends = 4 (given that 36 drawing books, 48 sketch pens, and 24 stationary boxes. were distributed)

still, NOT ADEQUATE

Thus, (E) should be correct

(1) The number of drawing books, sketch pens, and stationery boxes each friend gets is in the ratio 3: 4: 2.
Insufficient because provides us about the ratio of number of drawing books, sketch pens, and stationery boxes each friend gets
3:4:2 but we don't know about the number of friends.

(2) Ron gave a total of 36 drawing books, 48 sketch pens, and 24 stationary boxes.
Now that we know he gave 36 drawing books, 48 sketch pens, and 24 stationary boxes. This is also insufficient because we don't know as to number of drawing books, sketch pens and stationary boxes each friend gets.

Combining 1 and 2
the ratio of number of drawing books, sketch pens, and stationery boxes each friend gets is 3:4:2
and the total number of 36 drawing books, 48 sketch pens, and 24 stationary boxes were distributed.
From this we can infer that there were 12 friends.
Therefore, option C

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

(1) and (2) are not sufficient as they are giving same information

(1)+(2)
No of friends could be 1,2,3,4,6

Not sufficient

E is the answer

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Bunuel wrote:12 Days of Christmas GMAT Competition with Lots of Fun

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

This question was provided by GMATWhiz for the 12 Days of Christmas Competition. Win $30,000 in prizes: Courses, Tests & more

 

no. of friends = y
no. of items distributed = vy + wy + xy= y(v+w+x) ------1)
st1
no. of books = (3/9)k
no. of sketch pens = (4/9)k
no. of stationary boxes = (2/9)

let k =9 i.e. total items distributed were 9, then only 1 friend attended the party
k =18 i.e. total items distributed were 18, then only 2 friends attended the party

Not sufficient as multiple values are possible

st.2
total books distributed are = 36+48+24 = 12(3+4+2), comparing it with equation 1, we get that number of friend's that visited ron's party were 12

sufficient, correct answer should be B

Bunuel wrote:12 Days of Christmas GMAT Competition with Lots of Fun

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

This question was provided by GMATWhiz for the 12 Days of Christmas Competition. Win $30,000 in prizes: Courses, Tests & more

 

Statement 1: Ratio is not enough
6:8:4= 9:12:6=3:4:2

Statement 2:
We know exact numbers, suff

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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.
Statement 1: Insufficient - For a given ratio, any number of friends is possible.

(2) Ron gave a total of 36 drawing books, 48 sketch pens, and 24 stationary boxes.
Statement 2: Insufficient - For a given ratio, the number of friends can vary from 2,4,6,12

Combining both statement 1 & 2: Sufficient Only 12 satisfies both the statment.

Ans: C

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

Each statement alone is insufficient.
Taking both statements together.
Total number of return gifts=36+48+24=108
Total number of return gifts per friend=3x+4x+2x=9x
Hence Number of friends attending=108/9x=18
But since we only have the ratio.
Total number of return gifts per friend can also be equal to 18x/27x and more.
Therefore we cannot find exact number of friends. Option E.

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?

Statement 1) The number of drawing books, sketch pens, and stationery boxes each friend gets is in the ratio 3: 4: 2. --> not sufficient
statement 2) Ron gave a total of 36 drawing books, 48 sketch pens, and 24 stationary boxes. --> not sufficient

statement 1 & 2 enough to find the total number friends who attend the party
ans C