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22 Dec 2022, 07:00
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Difficulty:
65%
(hard)
Question Stats:
55% (01:55) correct
45%
(01:53)
wrong
based on 205
sessions
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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.
(A) Statement 1 alone is sufficient, but statement 2 alone is not.
(B) Statement 2 alone is sufficient, but statement 1 alone is not.
(C) Both statements together are sufficient, but neither alone is sufficient.
(D) Each statement alone is sufficient.
(E) Neither statement is sufficient, even when combined.
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.
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(A) Statement 1 alone is sufficient, but statement 2 alone is not.
(B) Statement 2 alone is sufficient, but statement 1 alone is not.
(C) Both statements together are sufficient, but neither alone is sufficient.
(D) Each statement alone is sufficient.
(E) Neither statement is sufficient, even when combined.
23 Dec 2022, 05:51
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GMATWhiz Official Explanation:
Step 1: Analyse Question Stem
- Ron is giving each friend v drawing books, w sketch pens, and x stationary boxes.
- o We need to find the number of friends who attended his party.
- Let’s assume that “n” friends attended his party.
- Then Ron must have given a total of n* v drawing books, n* w sketch pens, and n* x stationary boxes.
Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE
Statement 1: The number of drawing books, sketch pens, and stationery boxes each friend gets is in the ratio 3: 4: 2
- From this statement, we can infer each friend get 3y drawing books, 4y sketch pens, and 2y stationary boxes
Thus, total friends who attended his birthday party =nv/3y=nw/4y=nx/2y
However, we don’t know the exact value of v, w, z and y. Hence, we won’t be able to find the total number of friends who attended his birthday party
Hence, statement 1 is not sufficient and we can eliminate answer options A and D.
Statement 2: Ron gave a total of 36 drawing books, 48 sketch pens, and 24 stationary boxes.
- From this statement, we know that his speed nv = 36, nw = 48, nx = 24
- The common factors of 36, 48 and 24 are 1, 2, 3, 4, 6,12.
- n can take any value from the common factors.
Step 3: Analyse Statements by Combining
From statement 1: Total friends who attended his birthday party =nv/3y=nw/4y=nx/2y
From statement 2: nv = 36, nw = 48, nx = 24
Combining, we can say that:
Total friends who attended the party =ny/3y=36/3y=12/y OR
Total friends who attended the party =ny/4y=48/3y=12/y OR
Total friends who attended the party =ny/2y=24/3y=12/y
Note, that we don’t know the value of y.
Hence, we won’t be able to find the total friends who attended the party.
Hence, the correct answer is Option E.
General Discussion
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 number of friends be N.
So, total drawing books = N * v
total sketch pens = N * w, and
and total stationary boxes = N * x,
(1) The number of drawing books, sketch pens, and stationery boxes each friend gets is in the ratio 3: 4: 2.
No information about total drawing books, sketch pens, and stationery boxes can be found out..
N can't be determined
Hence, INSUFFICIENT
(2) Ron gave a total of 36 drawing books, 48 sketch pens, and 24 stationary boxes.
total drawing books = N * v = 36
total sketch pens = N * w = 48, and
total stationary boxes = N * x = 24,
N still can't be determined; since values of v, w, x are not known
Hence, INSUFFICIENT
(1) & (2)
number of drawing books, sketch pens, and stationery boxes each friend gets is in the ratio 3: 4: 2.
thus, v:w:x = 3:4:2
If say ---> v, w, x be 3.4.2 then N= 12
If say ---> v, w, x be 9.12.6 then N= 4
If say ---> v, w, x be 18.24.12 then N= 2
N still can't be uniquely determined
Hence, INSUFFICIENT
Hence, the correct option is (E)
Let the number of friends be N.
So, total drawing books = N * v
total sketch pens = N * w, and
and total stationary boxes = N * x,
(1) The number of drawing books, sketch pens, and stationery boxes each friend gets is in the ratio 3: 4: 2.
No information about total drawing books, sketch pens, and stationery boxes can be found out..
N can't be determined
Hence, INSUFFICIENT
(2) Ron gave a total of 36 drawing books, 48 sketch pens, and 24 stationary boxes.
total drawing books = N * v = 36
total sketch pens = N * w = 48, and
total stationary boxes = N * x = 24,
N still can't be determined; since values of v, w, x are not known
Hence, INSUFFICIENT
(1) & (2)
number of drawing books, sketch pens, and stationery boxes each friend gets is in the ratio 3: 4: 2.
thus, v:w:x = 3:4:2
If say ---> v, w, x be 3.4.2 then N= 12
If say ---> v, w, x be 9.12.6 then N= 4
If say ---> v, w, x be 18.24.12 then N= 2
N still can't be uniquely determined
Hence, INSUFFICIENT
Hence, the correct option is (E)
