GMAT Club Around The World!!! Jane and Chris work at a factory produci

IMO B

let Chris produce C widgets per hour
=> rate of work of Chris = C widgets/hour

Jane produces 4 more than Chris per hour
=> rate of work of Jane = (C+4) widgets/hour

combined rate = J+C ?? or 2C+4 ??

(1) Last week, Chris and Jane together produced a total of 96 widgets.
total work = combined rate * total hours worked
- don't know the total hours Jane and Chris worked
Not Sufficient

(2) Last week, Chris worked twice as long as Jane and produced the same number of widgets as she did.
Time taken by Jane = \(T_{Jane}\)
=> Time taken by Chris = \(2 * T_{Jane}\)

total widgets produced by Jane = total widgets produced by Chris
=> rate of Jane * time taken by Jane = rate of Chris * time take by Chris
=> (C+4) * \(T_{Jane}\) = C * 2 * \(T_{Jane}\)
=> C+4 = 2C
=> C = 4
=> J = 8
combined rate = J + C = 12
Sufficient

Let Chris's rate be c, so Jane's rate = c+4.
We need to find the combined rate = c+c+4 = 2c+4

(1) Last week, Chris and Jane together produced a total of 96 widgets.
Let both worked for x hours.

Total widgets = 2cx+4x=96.....eq1

Insufficient


(2) Last week, Chris worked twice as long as Jane and produced the same number of widgets as she did.
Let Jane worked for y hours, so Chris worked for 2y hours. In doing so they both produced equal number of widgets.

2yc = yc+4y.....eq2

Insufficient

Combining 1&2

2yc=48
yc=24.....eq3

Putting value of yc in eq2, y=6
Putting y=6 in eq3, c=4

so, 2c+4=12

Sufficient

IMO Option C

Jane and Chris work at a factory producing widgets. If Jane produces 4 more widgets per hour than does Chris, what is their combined rate?

Given, Jane = 4 +x per hr., where, Chris = x per hr.

Stat1: Last week, Chris and Jane together produced a total of 96 widgets.
We don't know, how many hrs. it took to produce 96 widgets. Not sufficient.

Stat2: Last week, Chris worked twice as long as Jane and produced the same number of widgets as she did.
(4+x)/2 = x or, x = 4 widgets per hr. we can get combined rate now. Sufficient.

So, I think B.

Correct Answer B

Jane and Chris work at a factory producing widgets. If Jane produces 4 more widgets per hour than does Chris, what is their combined rate?
----------------------------------Rate
Jane -----------------------------(x+4)/hrs
Chris ----------------------------x/hrs
Combined Rate ----------------(2x+4)/hrs

(1) Last week, Chris and Jane together produced a total of 96 widgets.
It is not given how many hours they worked. Let say y hrs
(2x+4)*y =96
- Two variable one equation
-Not sufficient

(2) Last week, Chris worked twice as long as Jane and produced the same number of widgets as she did.
Let's say Jane worked for z hrs
then Chris worked for 2z hrs
x*2z =(x+4)*z
x=4
then 2x+4 = 12 /hrs
-Sufficient

W=RT
From the information provided we know that jane produces 4 more widgets per hour than does chris
If Chris produces x widgets in an hour then Jane will produce x+4 widgets in an hour
Lets set the W=RT equation for chris and jane and find their individual work rates
For Chris
x=R*1
RC = x
For Jane
x+4 = R*1
RJ = x+4
We have to find their combined rate which is RC + RJ = x+x+4 = 2x+4

Statement 1
It tells us that Chris and Jane produced total of 96 widgets.
Let t be the time taken by jane and chris to make 96 widgets.
So using W=RT we will get,
96= (2x+4)*t
2 variables and one equation. Not possible to solve for x.
Hence Insufficient

Statement 2
Chris worked twice as long as Jane and produced the same number of widgets
Let w be the number of widgets produced by both of them
If Jane worked for t hours then Chris worked for 2t hours
Set W=RT equation for Chris and Jane using information above
For Chris
w=x*2t
For jane
w=(x+4)*t
Since the number of widgets are same so we can equate both the equations
x*2t = (x+4)*t
2xt = xt + 4t
xt = 4t
x=4
Now that we have value of x we can find their combined rate which is 2x+4= 2*4 + 4= 12
Sufficient

So the answer will be B

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