12 Days of Christmas GMAT Competition - Day 4: Last year in the North

Question

12 Days of Christmas 🎅 GMAT Competition with Lots of Questions & Fun

Last year in the North Pole, 20% of all elves who crafted toys made wooden toys, while 40% of all elves who specialized in eco-friendly toy production made wooden toys. Last year in the North Pole, what percent of all elves who made wooden toys specialized in eco-friendly toy production?

(1) Last year in the North Pole, a total of 1,000 elves specialized in eco-friendly wooden toy production.

(2) Last year in the North Pole, 35% of all elves who crafted toys specialized in eco-friendly toy production.

Bunuel · Accepted Answer

GMAT Club Official Explanation:

Last year in the North Pole, 20% of all elves who crafted toys made wooden toys, while 40% of all elves who specialized in eco-friendly toy production made wooden toys. Last year in the North Pole, what percent of all elves who made wooden toys specialized in eco-friendly toy production?

Set up a double-set matrix assuming the total number of elves to be x, and the total number of elves who specialized in eco-friendly toy production is y:

The question asks to find the value of \(\frac{0.4y}{0.2x}*100\), so essentially the ratio of y to x.

(1) Last year in the North Pole, a total of 1,000 elves specialized in eco-friendly wooden toy production.

This implies that 0.4y = 1,000:

However, this does not help establish a relationship between x and y. Not sufficient.

(2) Last year in the North Pole, 35% of all elves who crafted toys specialized in eco-friendly toy production.

This implies that y = 0.35x:

With the ratio of y to x as 35:100, we can calculate the value of \(\frac{0.4y}{0.2x}*100\). Sufficient.

Answer: B.

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sj296 · Answer

Let's say total elves in involved in toy production = E

20% made wooden toys = 0.2E

Let's say Z elves were involved in eco-friendly toys production
Ecofriendly wooden = 0.4z

Statement 1:
0.4z = 1000

but we don't know about E. So this statement is insufficient

Statement 2:
z = 0.35 E

We can calculate the required percentage using this information.

Sufficient

IMO OA should be B

jaysea · Answer

(1) Last year in the North Pole, a total of 1,000 elves specialized in eco-friendly wooden toy production. We can calculate the percentage of elves specializing in eco-friendly production. sufficient alone

(2) Last year in the North Pole, 35% of all elves who crafted toys specialized in eco-friendly toy production. this directly answers the question. sufficient alone

boomer1ang · Answer

Answer: C

Lets say total elves made toys = x. Question states 20x/100 made wooden toys and asks to find what percent of these specialized in eco friendly.
Let y be total elves specialize in eco friendly. So elves that produced wooden toys of those 40y/100.

(1) Last year in the North Pole, a total of 1,000 elves specialized in eco-friendly wooden toy production.
This gives us y = 1000, so 40y/100 = 400 elves who specialized in eco friendly made wooden toys. But we don't know how many total elves (x). - NS

(2) Last year in the North Pole, 35% of all elves who crafted toys specialized in eco-friendly toy production.
this tells us 35x/100 specialized in eco friendly. -NS

Combined.
35x/100 = 1000, we can find x and we have y from statement (1) - sufficient.

Kinshook · Answer

Last year in the North Pole, 20% of all elves who crafted toys made wooden toys, while 40% of all elves who specialized in eco-friendly toy production made wooden toys. Last year in the North Pole, what percent of all elves who made wooden toys specialized in eco-friendly toy production?

Wooden toys  ~Wooden toy  Total  
  Eco-friendly toys  .4x%  .6x%  x%  
  ~Eco-friendly toys        
  Total  20%  80%  100%

The percent of all elves who made wooden toys specialized in eco-friendly toy production = .4x%/20%

(1) Last year in the North Pole, a total of 1,000 elves specialized in eco-friendly wooden toy production.
Since value of x can not be derived from absolute figure of 1000.
NOT SUFFICIENT

(2) Last year in the North Pole, 35% of all elves who crafted toys specialized in eco-friendly toy production.
x% = 35%
 
    Wooden toys  ~Wooden toy  Total  
  Eco-friendly toys  .4x%=14%  .6x%=21%  x%=35%  
  ~Eco-friendly toys        
  Total  20%  80%  100%  
 
The percent of all elves who made wooden toys specialized in eco-friendly toy production = .4x%/20% = 14%/20% = 70%
SUFFICIENT

IMO B

$!vakumar.m · Answer

Last year in the North Pole, 20% of all elves who crafted toys made wooden toys, while 40% of all elves who specialized in eco-friendly toy production made wooden toys. Last year in the North Pole, what percent of all elves who made wooden toys specialized in eco-friendly toy production?

Let E be Elves who are involved in crafting toys, then 0.2E are involved in making wooden toys.
Let X be Elves who are specialized in making eco-friendly toys, then 0.4 X are the Elves who are involved in making Eco friendly wooden toys
We are required to find, percentage = 0.4X/(0.2E+0.4X)*100 
(1) Last year in the North Pole, a total of 1,000 elves specialized in eco-friendly wooden toy production.
X = 1000. But no information on E. Not Sufficient

(2) Last year in the North Pole, 35% of all elves who crafted toys specialized in eco-friendly toy production.
X = 0.35E
substituting in percentage, we get 0.35*0.4E/(0.2E+0.35*0.4E)*100 = 41% approx
Sufficient
Answer B

paulkim46 · Answer

Answer: (C)

(i) Insufficient. Knowing 1,000 elves specialized in eco-friendly wooden toys tells us there were 2,500 eco-friendly toy production elves, but we do not know how many other elves working on toys there are, to know how many total wooden toy making elves there are.

(ii) Insufficient. Also don't know how many regular toy makers there are.

Combining (i) and (ii), we can get the number of total toy elves. Thus, this tells us how many total wooden toy elves there are, from which we can calculate the % of elves making wooden toys that specialized in eco-friendly toys.

rezk1 · Answer

not enough information because we don't know the total of all elfs

The answer is E

Tukkebaaz · Answer

So here we have W = all elves who crafted toys and E = all elves who specialized in eco-friendly toys Total wooden toys = 0.2W+0.4E What do we need: 0.4E/ 0.2W+0.4E; In other words we need the relation between W and E. S1: E =1000 ( doesnt help) S2: 0.35W = E (seems like we are heading somewhere now). I will mark B at this point but adding on for completeness: 0.4*0.35W/(0.2+0.4*0.35)W *100% B alone is enough. Cheers

AviNFC · Answer

Total elves who craft toys = x
Wooden toys = 0.2x
Ecofriendly toys=y
Wooden as well as Eco friendly toys = 0.4y

Reqd =  \frac{0.4y}{0.2x} ..So, we need y/x

1. 0.4 y =1000...no info about x... No
2. 0.35x = y
 y/x= 0.35... So, Yes

Ans B

missionmba2025 · Answer

Number of elves who made toys = x

Number of elves who made wooden toys = 0.2 x

Number of elves who specialized in eco-friendly toy production = y

Number of elves who specialized in eco-friendly toy production and made wooden toys = 0.4y

Question: ( 0.4y / 0.2x ) * 100 = 2y/x * 100

Hence, if we can find the ratio of y/x we can solve the question.

(1) Last year in the North Pole, a total of 1,000 elves specialized in eco-friendly wooden toy production.

This statement is not sufficient as we don't have the ration of y/x. Eliminate A and D.

(2) Last year in the North Pole, 35% of all elves who crafted toys specialized in eco-friendly toy production.

This is the same number who crafted toys and specialized in eco-friendly toy production.

0.35x = 0.4y

Hence, we can get the ratio of x and y from this statement.

The statement is sufficient to answer the question.

IMO B

Lalykys · Answer

Let's say that x% is the percentage of Elves that specialized in Eco-friendly toys. 100% being the total percentage of elves crafting toys. 20% of them make wooden toys.
We know that 40.x%/100 represents the percentage of all Elves that makes wooden toys that are specialized in eco-friendly toys. We are being asked to find percentage of wooden toys that are specialized in eco-friendly toys. So we want to find the percentage of the 20% that made wooden toys who are specialized eco-friendly toys. We just need for that to find x.

(1) We have the number of elves specialized in eco-friendly toys but since we don't know the total number of elves crafting toys  so (1) is not sufficient .

(2) If 35% of all elves who crafted toys specialized in eco-friendly toy then we have x.  So (2) is sufficient.

So  Answer B

Catman · Answer

Let Total Elves be E = (E1+ Ne2)

E1- who made eco friendly toys.
Ne 2- who made non-eco friendly toys

Out of E1, E1 = w1+ o1
Let w1 - who makes wooden toys
Let o1- who makes other than wooden toys

Out of Ne2, Ne2 = w2+ o2
Let w2- who makes wooden toys
Let o2- who make other than wooden toys

E = (E1+ Ne2)= (w1+ o1)+ (w2+ o2)

Given  w1+ w2 = 20% of E and w1= 40% of E1

Find  : w1/E

(1) Last year in the North Pole, a total of 1,000 elves specialized in eco-friendly wooden toy production.

E1= 1000 , W1=400 and o1= 600. But from this we cannot find any information about Ne2 and Hence cannot determine E.

(2) Last year in the North Pole, 35% of all elves who crafted toys specialized in eco-friendly toy production.

E1= 35% of E.
W1= 40% of E1
W1= 40% * 35% of E
w1= 14% of E.

IMO B.

mayankdgmat · Answer

Let total elves who made toys are  T

We have been given,

Wooden toys = 0.2T 
Non-wooden toys = 0.8T

now let us assume that elves who have made specialized toys are  S

So Specialized toys which are wooden = 0.4S
Non-wooden specialized toys are = 0.6S

we need to find  \frac{0.4S}{0.2T} , in short we need to find ratio of S & T

(1) Last year in the North Pole, a total of 1,000 elves specialized in eco-friendly wooden toy production.

we know 0.4S = 1000, we would get S. We know nothing about T.  Hence we can eliminate A,D

(2) Last year in the North Pole, 35% of all elves who crafted toys specialized in eco-friendly toy production.

S=0.35T

now we know ratio S & T. We could find percent.

Hence answer is (B)

sanjitscorps18 · Answer

Let total elves who made toys is 'a', then elves who crafted wooden toys is 'a/5'
Let total elves who make eco-friendly toys be 'b', such elves who crafted wooden toys are '2b/5'
Required ask is (2b/5)/(a/5) = 2b/a

(1) Last year in the North Pole, a total of 1,000 elves specialized in eco-friendly wooden toy production.
This suggests that b = 1000 elves
However we have no information about 'a'
Sufficient

(2) Last year in the North Pole, 35% of all elves who crafted toys specialized in eco-friendly toy production.
This implies 35% of (a/5) = 2b/5
=> (35/100) * a = 2b
=> 2b/a = 7/20
Sufficient

Option B

DG1989 · Answer

Last year in the North Pole, 20% of all elves who crafted toys made wooden toys, while 40% of all elves who specialized in eco-friendly toy production made wooden toys. Last year in the North Pole, what percent of all elves who made wooden toys specialized in eco-friendly toy production?

(1) Last year in the North Pole, a total of 1,000 elves specialized in eco-friendly wooden toy production.

(2) Last year in the North Pole, 35% of all elves who crafted toys specialized in eco-friendly toy production.

Solution: 
Let Total number of elves who crafted toys = x
Then, number of elves who made wooden toys = 0.2x

Let Total number of elves who who specialized in eco-friendly toy production = y
Then, number of such elves who made wooden toys = 0.4y

Total number of elves who made wooden toys = 0.2x + 0.4y
We need to find what percentage of this total represents elves who specialized in eco-friendly toy production i.e. (0.4y/(0.2x + 0.4y)) * 100

Statement 1:    Last year in the North Pole, a total of 1,000 elves specialized in eco-friendly wooden toy production. 
Here y = 1000
Since we don't know value of x, this information alone is not enough to determine the required percentage.

NOT SUFFICIENT

Statement 2:    Last year in the North Pole, 35% of all elves who crafted toys specialized in eco-friendly toy production. 
This option doesn't provide any specific information about wooden toy production or the percentage of elves who made wooden toys.

NOT SUFFICIENT

Combining statement 1 and statement 2
It tells us that 35% of all elves who crafted toys specialized in eco-friendly toy production, and among all the elves who specialized in eco-friendly toy production, there were 1,000 elves who made wooden toys. However, it still doesn't provide enough information to determine the percentage of all elves who made wooden toys and specialized in eco-friendly toy production.
  NOT SUFFICIENT

Option E   is right answer

Shwetamed · Answer

B.

let total elves who made toys =T
elves who made wooden toys=20% of T
all elves who specialized in eco-friendly toy production =E
elves who specialized in eco-friendly toy production and made wooden toys.=40% of E
1. NOT SUFFICIENT
2. E=35%of T
 percentage required= 40% of 35% of T/20% of T *100 SUFFICIENT

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12 Days of Christmas GMAT Competition - Day 4: Last year in the North

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	Wooden toys	~Wooden toy	Total
Eco-friendly toys	.4x%	.6x%	x%
~Eco-friendly toys
Total	20%	80%	100%

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12 Days of Christmas GMAT Competition - Day 4: Last year in the North

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