The Farmer in the Deli sandwich shop sells two kinds of sandwich: tuna

Question

Tough and Tricky questions: Word Problems.

The Farmer in the Deli sandwich shop sells two kinds of sandwich: tuna melts and veggie melts. Each customer buys exactly one sandwich. If there were 300 customers yesterday, what fraction of veggie melts sold yesterday were bought by female customers?

(1)  \frac{1}{2}  of all sandwiches sold yesterday were tuna melts, and  \frac{1}{3}  of all customers yesterday were male.

(2) Yesterday, twice as many tuna melts were bought by females as there were veggie melts bought by males.

Kudos for a correct  solution .

DangerPenguin · Answer

statement 1: not sufficient

We are told that there were 150 tuna melts sold and 150 veggie melts sold and that 100 of the customers are male, so we can conclude that there are 200 females. But we still do not know how many females bought tuna vs how many females bought veggie.

statement 2: not sufficient

There could have been 40 tuna melts sold to females and 20 veggie melts sold to males or there could have been 80 tuna melts sold to females and 40 veggie melts sold to males.

Down to answers C and E.

Combined, I chose to pick numbers so I could have a starting point. Knowing that there are 100 males and 200 females and using statement 2 first, I chose 100 for # of tuna melts bought by females which means that there would be 50 veggie melts bought by males. I then combined with statement 1 which tells us that there are 100 males, 150 tuna melts, and 150 veggie melt to fill out a quick table below

total: 300 
tuna, male: 50
tuna, female: 100
veggie, male: 50
veggie, female: 100

Answer C!!

amitshri15 · Answer

Statement 1: T = 150, V=150, Male= 100 , Female = 200
 There are so many combination which gives different value for Female customer bought veggie melts.
 Insufficient
Statement 2: T(Female) = 2 V(Male) no other information. So insufficient.

Statement 1 and Statement 2: V(Female) + V(Male) = 150 and T(Female) = 2 V (Male)
 T(Female) + V(Female) = 200 (no of female customers).
 2V(Male) + V(Female) = 200 but V(male) + V(Female) = 150
 V(Male) = 50 and V (Female) = 100.

So Answer should be C.

akumar5 · Answer

Lets Tuna melts=T
 Veggie melts=V
 Male = M
 Female=F

1) No of T customer=1/2 & No of M=1/3
 Lets Total no of customer= x for simplification in place of 300 as given
 so T=x/2=Tf+Tm ;V=x/2=Vf+Vm
Also Tm+Vm=x/3.............A
 Also Tf+Vf=2x/3............B
 one can't find Vf from above statement.INSUFFICIENT

2) Tf=2Vm. This statement also INSUFFICIENT.

Combining both the statements

Taking equation B 
 Tf+Vf=2x/3
 2Vm+Vf=2x/3; from statement 2.
 2(x/2 - Vf)+Vf=2x/3 ;since V=x/2=Vf+Vm
 Vf=x/3. 
 Hence both equation helps to solve this riddle.

Answer C

Bunuel · Answer

Official Solution:

The Farmer in the Deli sandwich shop sells two kinds of sandwich: tuna melts and veggie melts. Each customer buys exactly one sandwich. If there were 300 customers yesterday, what fraction of veggie melts sold yesterday were bought by female customers?

In this overlapping sets problem, there are two kinds of sandwiches (tuna melts and veggie melts, abbreviated T and V). There are also two kinds of customers: male and female. Since each customer buys exactly one sandwich, customers and sandwiches are interchangeable. Thus, we can set up one table to keep track of both type of sandwich and type of customer, as follows:
 M F Total T V Total 300 
We are looking for the ratio of two numbers on this chart: veggie melts bought by females and the total number of veggie melts. 
 
Statement (1): INSUFFICIENT. We can fill in the chart's total row and total columns, but the four cells in the upper left remain unknown.
 M F Total T 150 ( \frac{1}{2}  of 300) V 150 Total 100 200 300 
Thus, we cannot figure out the needed ratio.
 
Statement (2): INSUFFICIENT. We can use the relationship between "female tuna melts" and "male veggie melts," introducing a variable as follows:
 M F Total T  2x  V  x  Total 300 
However, without more information, we cannot find the needed ratio.
 
Statements (1) and (2) together: SUFFICIENT. Combining the tables above, we get the following:
 
We can fill in the remaining cells with expressions -- for instance, "female veggie melts" can be written as  150 - x , since the veggie row must sum to 150. Now we can add up the female column and solve for  x :
  2x + (150 - x) = 200 
  x + 150 = 200 
  x = 50 
 
We see that  \frac{100}{150} , or  \frac{2}{3} , of the veggie melts sold yesterday were bought by female customers.
 
Note that we could have addressed this problem without knowing the total number of customers (300). We are only looking for a ratio between two numbers on the chart.
 
Answer: C.

Roosterbooster · Answer

Am I the only one that doesn't see answer choices?

(1) 1/2 were TM so the remaining 1/2 must be VM. 1/3 of cust were male so 2/3 must be female

Tot= 300
1/2(Tot)= 150 TM
1/2(Tot)= 150 VM

1/3*300=100 Males
300-100=200 Females

(2) Male tuna melt (MTM) plus Female Tuna Melt (FTM) must total 1/2. Same with the Veggie melt. FVM plus FTM must total 2/3. MTM plus MVM must total 1/3.

So:
MTM+FTM=1/2 or 150
MVM+FVM=1/2 or 150
FTM+FVM=2/3 or 200
MTM+MVM=1/3 or 100
2(MVM)= FTM

my initial "10 second method" was:

That if there were twice as many women as men: 1/3*2 = 2/3
and twice as many FTM as MVM 
And there was an equal breakdown in sandwiches sold at 1/2 & 1/2
Then you could see that MVM= 2/3*1/2= 1/3
3/3-1/3=2/3 ratio for Female Veggie melts

I didn't like that way because it is too easy to get it wrong.

Is it a coincidence that the fraction of F to the total customer base is the same is Female Veggie melt orders.

2/3 of the customers are female 2/3 of the veggie melts sold yesterday were bought buy female customers.

All of this of course is given the conditions listed in the problem.

Educate me sensei bunuel!

Edit: Nevermind, just looked at your solution.

G-Man · Answer

1) This statement gives the number of customers who purchased Veg and Tuna melts. It also gives the male and female count. Not enough to get the specific count of Female customers who bought Tuna sandwich
2) Ratio - Insufficient

Combining two statements to create the attached the table

From the table/matrix, 
we have two equations to solve x
200 - x = 150
100 + x = 150 or 200 + 2x = 300

Adding both equations, 
400 + x = 450
x = 50
2x = 100
Sufficient

C

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The Farmer in the Deli sandwich shop sells two kinds of sandwich: tuna

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