There are 3 types of machines working together to fill soda bottles

Question

There are 3 types of machines working together to fill soda bottles. Machine A fills up 400 bottles in an hour while Machine B fills up 600 bottles in an hour, and machine C is used to seal the cans. How many total number of all 3 types of machines were working from 1700h to 1800h?
(A) There were total 4800 bottles filled in this one hour.
(B) The ratio of number of machines B to machines C working in that hour is 2:1.

Tricky question!!...

Archit3110 · Answer

giving a try

given info a,b are filling and c is for filling 
a= 400 bottles in an hr 
b= 600 bottles in an hr
c = rate is not given to seal 
#1
There were total 4800 bottles filled in this one hour;
if so then we get 400x+600y=4800
value of x , y will vary ; x=3;y=6, x=4,y=4, x=9.y=2 ; insufficient also relation of c not given 
#2
no of machine b/ no of machine c = 2/1
no relation given of how many products mfg from 1700 to 1800 hr in sufficient
from 1 & 2
we can say a=9 and b=2 so c=1
or it can be a=3,b=6 ,c=3
total remains 12 for all possible combinations

IMO C

chetan2u · Answer

Hi,

The machines filling up are only A and B, so statement I would mean that A and B are working together.

However, just a point, A and B could be 9 and 2, but they can be some other combinations too. (4,4) or (3,6). So we will have to check for other combinations too.

Chethan92 · Answer

From S1:

400A+600B = 4800 cans filled in 1 hour.
Reducing this, we get
2A+3B = 24
Possible values of (A,B) = (3,6) (6,4) (9,2).
The total number of machines vary, Hence this statement is INSUFFICIENT.

From S2:

Only ratio is given. No info work rate.
But, no info about the number of cans filled and sealed in that hour.
INSUFFICIENT.

Combining both:

No extra info. Hence INSUFFICIENT.

E is the answer.

Vinit800HBS · Answer

Great question.

Firstly, it’s important to understand that there are multiple machines of type A, B and C.

Rate of machines of type A = 400 bottles per hour
Rate of machines of type B = 600 bottles per hour

Statement 1: 
400A + 600B = 4800
2A + 3B = 24
Now, various combinations that satisfy the above condition are (A,B): (3,6),(6,4) and (9,2)
As no information about C is available, we can’t comment on number of machines working in all.

Statement 1 alone is Insufficient.

Statement 2: 
Number of machines of B:Number of machines of C = 2:1

No information about A.

Statement 2 is insufficient.

Combining statement 1 and 2:
This is where it gets interesting
Number of machines of C is half of that of B. Keeping this thing in mind, let’s evaluate the three combinations that we have got.

First combination (A,B,C) = (3,6,3)
Total machines = 12

Second combination (A,B,C) = (6,4,2)
Total machines = 12

Third combination (A,B,C) = (9,2,1)
Total machines = 12

Hence, Statement 1 and 2 together ARE SUFFICIENT

ANSWER IS OPTION C

HIT KUDOS IF YOU FIND THE ANSWER USEFUL

Posted from my mobile device

Archit3110 · Answer

chetan2u 
understood where i did error.. thanks

Pari28 · Answer

Excellent question !!

Sometime, to save time, we assume that if there are multiple outcomes then there would hence multiple answers.. This one had all outcomes leading to same answer (value of machines)...

Regards,
Parimal.

menonrit · Answer

Hi,

Could you explain this part :

First combination (A,B,C) = (3,6,3)
Total machines = 12

Second combination (A,B,C) = (6,4,2)
Total machines = 12

Third combination (A,B,C) = (9,2,1)
Total machines = 12

MSIMBA · Answer

Given

machines A = 400 bottles per hour
machines B = 600 bottles per hour

Statement 1: 
400A + 600B = 4800
2A + 3B = 24
combinations (A,B): (3,6),(6,4) and (9,2)
nO Info for C - Insufficient

Statement 2: 
machines B:machines C = 2:1
No information about A.

Statement 2 is insufficient.

Combining statement 1 and 2:

Number of machines of C is half of that of B.

First combination (A,B,C) = (3,6,3)
Total machines = 12

Second combination (A,B,C) = (6,4,2)
Total machines = 12

Third combination (A,B,C) = (9,2,1)
Total machines = 12

Statement 1 and 2 together SUFFICIENT

ANSWER IS OPTION C

menonrit · Answer

Hi,

I don't understand why the combinations add upto 12.

exc4libur · Answer

(1) There were total 4800 bottles filled in this one hour.   insufic. 
case 1: 4800/400=12 of A
case 2: 4800/600=7 of B

(2) The ratio of number of machines B to machines C working in that hour is 2:1.   insufic.

(1 & 2)   sufic. 
B/C=2/1…B=2C…C=B/2=integer…(B,C)={2,1;4,2;6,3]
B,C=2,1: 4800-2(600)=3600/400=9 of A; total: 2+1+9=12
B,C=4,2: 4800-4(600)=2400/400=6 of A; total: 4+2+6=12
B,C=6,3: 4800-6(600)=1200/400=3 of A; total: 6+3+3=12

Answer (C)

ANANDHYD · Answer

Statement 1 
400A+600B = 4800 cans filled in 1 hour.
multiple options are possible such as (3,6), (6,4) and (9,2). So Insufficient

Statement 2 
2B=C. If 2B machines work in that hour, then the number of C machines will be B. Since the total number of bottles filled is not given. The provided information will not be sufficient to arrive at the answer.

Combine both the statements,
The total output is 4800 bottles, which is the sole output of machine C as well as the combined output of machine A and Machine B. Assume the number of "B" machines =2X, then the number of machine "C" will be x. The total number of machine B and machine C = 3x. The number of machine "A" be A.

Then the equation will be
(number of machine A *400) + (number of machine B *600) =4800
A*400 + 2x * 600 = 4800
A*400 + x*1200 = 4800
400(A+3x) =4800
Therefore (A+3x) =12
(A+3x) is the total number of machines working in that hour, which is equal to 12

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

There are 3 types of machines working together to fill soda bottles

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

There are 3 types of machines working together to fill soda bottles

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards