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

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chetan2u
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There are 3 types of machines working together to fill soda bottles [#permalink] New post   07 May 2019, 08:49
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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!!...
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There are 3 types of machines working together to fill soda bottles [#permalink] New post   08 May 2019, 12:26
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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

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There are 3 types of machines working together to fill soda bottles [#permalink] New post   Updated on: 09 May 2019, 09:16
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chetan2u wrote:
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!!...


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

Originally posted by Archit3110 on 07 May 2019, 09:13.
Last edited by Archit3110 on 09 May 2019, 09:16, edited 2 times in total.
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Re: There are 3 types of machines working together to fill soda bottles [#permalink] New post   07 May 2019, 09:24
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Archit3110 wrote:
chetan2u wrote:
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!!...


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; chetan2u ; i hope here we have to assume that only machine a & b are working?
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
total 12
IMO C ...


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.
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Re: There are 3 types of machines working together to fill soda bottles [#permalink] New post   07 May 2019, 09:29
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.
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Re: There are 3 types of machines working together to fill soda bottles [#permalink] New post   09 May 2019, 09:17
chetan2u
understood where i did error.. thanks

chetan2u wrote:
Archit3110 wrote:
chetan2u wrote:
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!!...


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; chetan2u ; i hope here we have to assume that only machine a & b are working?
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
total 12
IMO C ...


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.
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Re: There are 3 types of machines working together to fill soda bottles [#permalink] New post   20 Jun 2019, 14:57
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.

chetan2u wrote:
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!!...
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Re: There are 3 types of machines working together to fill soda bottles [#permalink] New post   21 Jun 2019, 13:02
Vinit800HBS wrote:
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

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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
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Re: There are 3 types of machines working together to fill soda bottles [#permalink] New post   21 Jun 2019, 20:08
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
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Re: There are 3 types of machines working together to fill soda bottles [#permalink] New post   21 Jun 2019, 23:10
MSIMBA wrote:
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


Hi,

I don't understand why the combinations add upto 12.
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Re: There are 3 types of machines working together to fill soda bottles [#permalink] New post   05 Nov 2019, 07:51
chetan2u wrote:
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.


(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)
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Re: There are 3 types of machines working together to fill soda bottles [#permalink] New post   07 Aug 2022, 03:43
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
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Re: There are 3 types of machines working together to fill soda bottles [#permalink] New post   10 Nov 2023, 03:14
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