At a certain company, employees purchase food and beverages from vendi

Question

At a certain company, employees purchase food and beverages from vending machines using two types of company-issued tokens—small tokens and large tokens. Each large token is equal in value to 5 small tokens.

The XJ100 is a vending machine at the company that sells exactly one type of beverage at a price of 3 small tokens. If 1 large token is inserted, 2 small tokens will be returned with the beverage. Employees are equally likely to pay for a beverage from this machine with 1 large token as they are with 3 small tokens. When the XJ100 is serviced, all tokens are removed except for 50 small tokens. This is the only time tokens are removed.

Between the last time it was serviced and today, 400 beverages were sold from the XJ100. In the table, select the number of tokens of each size that would be expected to be in the XJ100 today. Make only two selections, one in each column.

AnishPassi · Accepted Answer

Approach 1

We're given in the passage that
 
So, we can expect 200 beverages (exactly half) bought with large tokens and the remaining 200 bought with small tokens.

For the beverages bought with small tokens 
Total tokens collected: 200 x 3 = 600 small tokens

For the beverages bought with large tokens 
Total tokens collected: 200 large tokens
Total tokens returned: 200 x 2 = 400 small tokens

So, overall we have 200 large tokens
For small tokens: 600 inserted, 400 returned and 50 in the machine from before.
--> 600 - 400 + 50 = 250.

An alternate approach

The machine sold a total of 400 beverages.
The total income from these beverages is 400 x 3 = 1200 small tokens.

There are 50 small tokens in the machine at the start. So, the total worth of tokens in the machine should be 1250 small tokens. 
(Note: I am just saying the total tokens should be  worth  1250 small tokens. I am not commenting on the number of small tokens here.)

Now I'll go through the table, dealing with the large tokens column first.

1. If # large tokens = 50, their total worth = 250 small tokens. Even if I add the largest possible number of small tokens (400) to 250, I don't reach 1250. Reject 50 for large tokens.

2. If # large tokens = 150, their total worth = 750 small tokens. Even on adding 400 small tokens, the total doesn't reach 1250 small tokens. Reject 150 for large tokens.

3. If # large tokens = 200, their total worth = 1000 small tokens. I could then select 250 for # of small tokens column to get the total to 1250 small tokens. It fits. I could mark this answer and move on at this point.

For peace of mind, let me check the remaining two choices also.

4. If # large tokens = 250, their total worth = 1250 small tokens. That's already the total I need. Since 0 is not an option, the overall worth will certainly be more than 1250 small tokens. Rejected.

5. If # large tokens = 400, their total worth = 2000 small tokens. Already more than what we need the total worth to be (1250). Rejected.

Combining the two approaches

Of the 400 beverages, half (200) would have been bought with large tokens. And a large token is never returned. So, once a large token is in, it'll stay there until the machine is serviced. For 200 beverages, there will be 200 large tokens in the machine.

The total tokens should be  worth  1250 small tokens.

200 large tokens = 1000 small tokens.

There need to be 1250 - 1000 = 250 small tokens in the machine to get the total worth to 1250 small tokens.

Done.

Small tokens: 250
Large tokens: 200

Sajjad1994 · Answer

Official Explanation

The machine contained only 50 small tokens following its last service. Employees are equally likely to pay for a beverage from this machine with 1 large token as they are with 3 small tokens, so it is expected that out of 400 beverages sold, 200 will be purchased with 3 small tokens. These purchases will account for a total of 200(3) = 600 small tokens added to the machine. The other 200 beverages will be purchased with 1 large token, and for each of these purchases, 2 small tokens will be removed from the machine. Therefore, the purchases with a large token result in a total of 200(2) = 400 small tokens removed from the machine. The total number of small tokens expected to be in the machine today is thus 50+600−400=250.

The correct answer is 250.

RO2

The machine contains no large tokens following its last service. As explained in the discussion of RO1, 200 employees are expected to purchase a beverage using 1 large token, so 200 large tokens would be expected to be in the machine today.

The correct answer is 200.

yashikaaggarwal · Answer

50 coins are left in the vending machine.
Every time 1 large coin valued at 5 small coins is inserted in vending machine 2 small coins is given out by machine with the beverage or The beverage is simply valued at 3 small coins.

total 400 beverage is been taken out from vending machine. amounting 400*3 = 1200 small coins

Case 1: let say 400 large coins are used to get beverages, therefore the machine have to return 400*2 small coins = 800 coins. 
but the machine only have 50 small coins as no one used small coins to purchase beverage. So the case is automatically nullified.

Case 2: let say 250 large coins are used to get beverages, therefore the machine have to return 250*2 small coins = 500 coins plus 150 times small coins for 150 more beverages which is equal to 150*3 = 450 small coins
the vending machine have total of 450+50 = 500 small coins to return to the employees, leaving 500-500 = 0 small coins and 250 large coins in vending machine. But we don't have zero as option for small coins. Case is again nullified.

Case 3: let say 200 large coins are used to get beverages, therefore the machine have to return 200*2 small coins = 400 coins plus 200 times small coins for 200 more beverages which is equal to 200*3 = 600 small coins
the vending machine have total of 600+50 = 650 small coins to return to the employees, leaving 650-400 =250 small coins and 200 large coins in vending machine. Which is satisfying the value given in options ( Correct)

Therefore value of small coins in vending machine is 250
and value of large coins in vending machine = 200

Babineaux · Answer

IMO,

1LT = 5ST;
And for one beverage 1LT required with 2ST out.
With previous servicing, 50ST are already within the vending machine.

Case 1:
As per given options, let's say with only LT,  150  beverages were sold today
Takes  150  LT and 2 x  150  =  300 ST have to come out,
Remaining beverages 400 -  150  =  250 ;
For  250  beverages  250  x 3 = 750 ST required.
Thus 750 -  300  = 450 ST remains for today with 50 previous ST.
Total 500ST 
No such option given.

Case 2:
Let say with only LT,  200  beverages were sold,
Takes  200  LT and 2 x  200  =  400 ST have to come out,
Remaining beverages 400 -  200  =  200 ;
For  200  beverages  200  x 3 = 600 ST required.
Thus 600 -  400  = 200 ST remains for today with 50 previous ST.
Total 250ST.
Voila!!
It matches the given options.

Thus 200LT and 250ST.

Apt0810 · Answer

Let large token = L
Small token= S
Now 5S=L
And beverage costs 3S ,so if we give L we get 2S in return.50S tokens are already there in the machine.

Now it's given in the question that since the last time and today 400 beverages are sold,

So if we go by the answer options:

1)Case 1: Let L=400,so in 400 L =2000S and 400 beverages require = 400*3= 1200S so remaining would be 800S+50S(already present)=850S,but there is no such option,so this case is rejected.

2)Case 2:Let L=250,so in 250 L =1250S and 400 beverages require = 400*3= 1200S so remaining would be 50S+50S(already present)=100S,but there is no such option,so this case is rejected.

3)Case3:Let L=200,so in 200 L =1000S and 400 beverages require = 400*3= 1200S so here we would be requiring 200S+50S(already present)=250S,and 50S should be required at the time of servicing,so Total 250S and 200L coins would be there in machine

Posted from my mobile device

MrChalo · Answer

ok, i didnt do it with cases, i like first to get an equation to work with and then tryu the values of the posible solutions.

the stem gives us this info:
400 is the total number or purchases, so i defined L the number of TIMES someone used a large coin (it equals to number of large coins for this case) wich gave me this equation for the number of small coins depending on number of Large coins and N the number of times someone purchased with small coins
  N+L=400
3*N+2*L+50=S 
combining these 2 equations gave us:
 (400-L)*3-2*L+50=S 
1250-5L=S  
with that equation i tried and got L=200 -> S=250

pappal · Answer

50 tokens are in machine after service.
for 400 bev=>total small tokens required=1200s
if 150 Large tokens inserted, value equals 150*5=750s
1200s-750s=450s
now substracting 150*2=300s returned by the machine against large tokens;
450s-300s=150s+50s(left earlier after service)=200s

result::>150L ,200s also suffices the conditions.
please guide me if wrong?

AnishPassi · Answer

1200 small tokens is the worth of 400 beverages. At the end of all the purchases and the give and take, the machine will have tokens worth 1250 small tokens (1200 + 50 small tokens that were already in).

This is the final worth that should be in the machine. The small tokens that are returned against large tokens would have been extra. I'll not subtract those tokens from this figure of 1250.

The final number of large and small tokens should add up to 1250 small tokens in worth. With 150 L and 200 s, the total worth is less than 1250.

CorporateAsset · Answer

Equation: 
S = Small
L = Large
Number of Large = x units
Beverage Cost for Large = xL-2xS
Beverage Cost for Small = 3S

Token Left = 50S(past) + xL -2xS + (400-X)3S

Now impute for X using trial and error,

X can't be 400 since S would be 0 (not an option),
try for the other values but putting in the equation to get the answer.

Eg. x = 200
Token Left = 50S + 200L -2*200S + (400-200)*3S
 = 50S + 200L -400S + 600S
 = 250S + 200L

MBAToronto2024 · Answer

KarishmaB  Is thee any framework how to solve this kind of questions quickly?

KarishmaB · Answer

Yes, the question can be solved fairly quickly. We are given: 
 "Employees are   equally likely   to pay for a beverage from this machine with 1 large token as they are with 3 small tokens."

and we are asked: select the number of tokens of each size that   would be expected   to be in the XJ100 today

Basically, 1 large token and 3 small token are equally likely. 
So I expect that out of 400 beverages, 200 were purchased with 1 large token each and 200 were purchased with 3 small tokens.

For 200 beverages, 600 small tokens will be given taking the total to 650 small tokens.
For 200 beverages, 200 large tokens will be given (which will stay intact) and 400 small tokens will be returned out. So the machine will be left with 250 small tokens.

Select 250 and 200

At a certain company, employees purchase food and beverages from vendi

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At a certain company, employees purchase food and beverages from vendi

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