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# At a certain factory, each employee working the second shift

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At a certain factory, each employee working the second shift [#permalink]

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29 Mar 2014, 03:58
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At a certain factory, each employee working the second shift produced 2/3 as many widgets as each employee working the first shift. If the first shift has 3/4 as many employees, what fraction of the total widgets did the second shift produce?

A. 8/17
B. 1/2
C. 8/9
D. 9/8
E. 17/8
[Reveal] Spoiler: OA

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Last edited by Bunuel on 29 Mar 2014, 08:40, edited 2 times in total.
Edited the question.
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Re: At a certain factory, each employee working the second shift [#permalink]

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29 Mar 2014, 08:40
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Expert's post
Mountain14 wrote:
At a certain factory, each employee working the second shift produced 23 as many widgets as each employee working the first shift. If the first shift has 34 as many employees, what fraction of the total widgets did the second shift produce?[/color]

A. 8/17
B. 1/2
C. 8/9
D. 9/8
E. 17/8

PLEASE CHECK QUESTIONS WHEN POSTING. THANK YOU.

At a certain factory, each employee working the second shift produced 2/3 as many widgets as each employee working the first shift. If the first shift has 3/4 as many employees, what fraction of the total widgets did the second shift produce?

A. 8/17
B. 1/2
C. 8/9
D. 9/8
E. 17/8

Pick some smart numbers:

Let the first shift have 3 employee and each produce 3 widgets, so the total number of widgets produced by the first shift is 3*3=9;

Then the second shift would have 4 employees and each second shift employee would produce 3*2/3=2 widgets, so the total number of widgets produced by the second shift employees would be 4*2=8;

The ratio of the second shift production to the total is 8/(9+8)=8/17.

This question is almost exact copy of the following OG question:
Quote:
At a loading dock, each worker on the night crew loaded 3/4 as many boxes as each worker on the day crew. If the night crew has 4/5 as many workers as the day crew, what fraction of all the boxes loaded by the two crews did the day crew load?

(A) 1/2
(B) 2/5
(C) 3/5
(D) 4/5
(E) 5/8

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Re: At a certain factory, each employee working the second shift [#permalink]

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31 Mar 2014, 03:03
Bunuel wrote:
Mountain14 wrote:
At a certain factory, each employee working the second shift produced 23 as many widgets as each employee working the first shift. If the first shift has 34 as many employees, what fraction of the total widgets did the second shift produce?[/color]

A. 8/17
B. 1/2
C. 8/9
D. 9/8
E. 17/8

PLEASE CHECK QUESTIONS WHEN POSTING. THANK YOU.

At a certain factory, each employee working the second shift produced 2/3 as many widgets as each employee working the first shift. If the first shift has 3/4 as many employees, what fraction of the total widgets did the second shift produce?

A. 8/17
B. 1/2
C. 8/9
D. 9/8
E. 17/8

Pick some smart numbers:

Let the first shift have 3 employee and each produce 3 widgets, so the total number of widgets produced by the first shift is 3*3=9;

Then the second shift would have 4 employees and each second shift employee would produce 3*2/3=2 widgets, so the total number of widgets produced by the second shift employees would be 4*2=8;

The ratio of the second shift production to the total is 8/(9+8)=8/17.

This question is almost exact copy of the following OG question:
Quote:
At a loading dock, each worker on the night crew loaded 3/4 as many boxes as each worker on the day crew. If the night crew has 4/5 as many workers as the day crew, what fraction of all the boxes loaded by the two crews did the day crew load?

(A) 1/2
(B) 2/5
(C) 3/5
(D) 4/5
(E) 5/8

Hi Bunuel,
Did not understand the method. Here is one method which I tried, but is not working. Please help.

Picking smart numbers

let the total number of employees be 12.

1st shift has 3/4 of the total hence 3/4*12 = 9
2nd shift has 3.

2nd shift emp gadgets = 3* (2/3 as they produce 2/3 as many gadgets as 1st shift) = 2
1st shift emp gadgets = 9*1 = 9

total fraction for 2nd shift = 2/11.
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Re: At a certain factory, each employee working the second shift [#permalink]

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31 Mar 2014, 04:02
seabhi wrote:
Bunuel wrote:
Mountain14 wrote:
At a certain factory, each employee working the second shift produced 23 as many widgets as each employee working the first shift. If the first shift has 34 as many employees, what fraction of the total widgets did the second shift produce?[/color]

A. 8/17
B. 1/2
C. 8/9
D. 9/8
E. 17/8

PLEASE CHECK QUESTIONS WHEN POSTING. THANK YOU.

At a certain factory, each employee working the second shift produced 2/3 as many widgets as each employee working the first shift. If the first shift has 3/4 as many employees, what fraction of the total widgets did the second shift produce?

A. 8/17
B. 1/2
C. 8/9
D. 9/8
E. 17/8

Pick some smart numbers:

Let the first shift have 3 employee and each produce 3 widgets, so the total number of widgets produced by the first shift is 3*3=9;

Then the second shift would have 4 employees and each second shift employee would produce 3*2/3=2 widgets, so the total number of widgets produced by the second shift employees would be 4*2=8;

The ratio of the second shift production to the total is 8/(9+8)=8/17.

This question is almost exact copy of the following OG question:
Quote:
At a loading dock, each worker on the night crew loaded 3/4 as many boxes as each worker on the day crew. If the night crew has 4/5 as many workers as the day crew, what fraction of all the boxes loaded by the two crews did the day crew load?

(A) 1/2
(B) 2/5
(C) 3/5
(D) 4/5
(E) 5/8

Hi Bunuel,
Did not understand the method. Here is one method which I tried, but is not working. Please help.

Picking smart numbers

let the total number of employees be 12.

1st shift has 3/4 of the total hence 3/4*12 = 9
2nd shift has 3.

2nd shift emp gadgets = 3* (2/3 as they produce 2/3 as many gadgets as 1st shift) = 2
1st shift emp gadgets = 9*1 = 9

total fraction for 2nd shift = 2/11.

This part is wrong. You have to multiply by 4/5 not 3/4
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Re: At a certain factory, each employee working the second shift [#permalink]

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31 Mar 2014, 05:15
why should i multiply with 4/5. Please correct me if I am wrong.
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Re: At a certain factory, each employee working the second shift [#permalink]

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31 Mar 2014, 10:44
seabhi wrote:
why should i multiply with 4/5. Please correct me if I am wrong.

3/4 as many boxes

4/5 as many workers

So 12 should be multiplied with workers not boxes....

~M14
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Re: At a certain factory, each employee working the second shift [#permalink]

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31 Mar 2014, 10:55
Assume that each employee working the first shift produces 3 widgets. Then each employee working the second shift will produce 2 widgets.

Assume that there are 100 second shift employees. Then there will be 75 first shift employees.

So fraction of total widgets produced by the second shift = [100*2]/[(100*2)+(75*3)] = 200/425 = 8/17.

(A) it is.
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Re: At a certain factory, each employee working the second shift [#permalink]

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31 Mar 2014, 21:39
1
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Expert's post
seabhi wrote:
Picking smart numbers

let the total number of employees be 12.

1st shift has 3/4 of the total hence 3/4*12 = 9
2nd shift has 3.

2nd shift emp gadgets = 3* (2/3 as they produce 2/3 as many gadgets as 1st shift) = 2
1st shift emp gadgets = 9*1 = 9

total fraction for 2nd shift = 2/11.

Your understanding of the question is not quite correct.

"each employee working the second shift produced 2/3 as many widgets as each employee working the first shift"
This does not mean that employees of second shift produced 2/3 of the total widgets produced. It means that each employee of second shift produced 2/3 of the widgets produced by each employee of the first shift. If each first shift employee produced 3 widgets, each second shift employee produced 2 widgets (2/3rd of 3).

"If the first shift has 3/4 as many employees"
This does not mean that the first shift has 3/4 the total number of employees. It means that the first shift has 3/4 of the number of employees in the second shift. i.e. if the second shift has 4 employees, the first shift has only 3 (which is 3/4th of 4)

Assuming these numbers, first shift has 3 employees producing 3 widgets each i.e. total 9 widgets.
Second shift has 4 employees producing 2 widgets each i.e. total 8 widgets.

Fraction of total widgets produced by the second shift = 8/(9+8) = 8/17
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Re: At a certain factory, each employee working the second shift [#permalink]

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23 Apr 2014, 07:03
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My Approach:

Let the number of employees work in the second shift be "x" and the number of widgets produced in 1st shift be w.
Now first shift workers produced -> 3x/4 * w widgets = 3xw/4
Second shift workers produced -> x * 2w/3 widgets = 2xw/3 widgets
Total widgets produced = 3xw/4 + 2xw/3 = 17xw/12. Now the second shift workers produced
2xw/3 * 12/17xw fraction of total 17xw/12 widgets. This comes to 8/17.

Hence option A
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Re: At a certain factory, each employee working the second shift [#permalink]

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23 Apr 2014, 23:22
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.................. First Shift.................... Second Shift
Widgets.........$$\frac{2w}{3} .......................... w$$
Employees...... $$x ................................ \frac{3x}{4}$$
Total.............. $$\frac{2wx}{3} ......................... \frac{3wx}{4}$$

Total Widgets$$= \frac{17wx}{12}$$

Fraction $$= \frac{\frac{2wx}{3}}{\frac{17wx}{12}}$$

Answer $$= \frac{8}{17}$$
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Re: At a certain factory, each employee working the second shift [#permalink]

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01 May 2014, 10:28
1
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No of widgets produced in 1st shift = X
No of people in 1st shift = 3/4 Y

No of widgets produced in 2nd shift = 2/3 X
No of people in 2nd shift = Y

Total no of widgets produced in 1st shift = 3/4 XY and total no of widgets produced in 2nd shift = 2/3 XY

Ratio asked = No of widgets produced in 2nd shift / total no of widgets produced
= 8/17
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Re: At a certain factory, each employee working the second shift [#permalink]

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06 Jun 2014, 01:16
Hi!
The wording of this question confused me and it resulted in the wrong answer.
"If the first shift has 3/4 as many employees" I took as if it referred to the overall number of employees.
So, if the number of employees is 4, than there are 3 employees working the first shift and 1 employee working the second.
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Re: At a certain factory, each employee working the second shift [#permalink]

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22 Jun 2014, 16:57
Bunuel wrote:
Mountain14 wrote:
At a certain factory, each employee working the second shift produced 23 as many widgets as each employee working the first shift. If the first shift has 34 as many employees, what fraction of the total widgets did the second shift produce?[/color]

A. 8/17
B. 1/2
C. 8/9
D. 9/8
E. 17/8

PLEASE CHECK QUESTIONS WHEN POSTING. THANK YOU.

At a certain factory, each employee working the second shift produced 2/3 as many widgets as each employee working the first shift. If the first shift has 3/4 as many employees, what fraction of the total widgets did the second shift produce?

A. 8/17
B. 1/2
C. 8/9
D. 9/8
E. 17/8

Pick some smart numbers:

Let the first shift have 3 employee and each produce 3 widgets, so the total number of widgets produced by the first shift is 3*3=9;

Then the second shift would have 4 employees and each second shift employee would produce 3*2/3=2 widgets, so the total number of widgets produced by the second shift employees would be 4*2=8;

The ratio of the second shift production to the total is 8/(9+8)=8/17.

This question is almost exact copy of the following OG question:
Quote:
At a loading dock, each worker on the night crew loaded 3/4 as many boxes as each worker on the day crew. If the night crew has 4/5 as many workers as the day crew, what fraction of all the boxes loaded by the two crews did the day crew load?

(A) 1/2
(B) 2/5
(C) 3/5
(D) 4/5
(E) 5/8

Bunuel,

The OG questions specifically states 'If the night crew has 4/5 as many workers as the day crew' whereas this verities prep questions says 'If the first shift has 3/4 as many employees' makes it confusing. 3/4 as many as TOTAL EMPLOYEES or SECOND SHIFT EMPLOYEES?

Don't you think so too?
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Re: At a certain factory, each employee working the second shift [#permalink]

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12 Jul 2014, 09:05
Mountain14 wrote:
At a certain factory, each employee working the second shift produced 2/3 as many widgets as each employee working the first shift. If the first shift has 3/4 as many employees, what fraction of the total widgets did the second shift produce?

A. 8/17
B. 1/2
C. 8/9
D. 9/8
E. 17/8

Not sure if this is shortest way to solve this question but it worked for me within 45 seconds:

1st shift emp = x widgets, 2nd shift em = 2/3*x widgets
2nd shift= n emp's, 1st shift = 3/4*n emp's

total widgets (1st shift) = 3/4*n*x, total widgets (2nd shift) - 2/3*n*x

Total widget (both shifts) = (3/4+2/3)*n*x=17/12*n*x

total widgets (2nd shift) = (2/3*n*x)/(17/12*n*x) = 8/17
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Re: At a certain factory, each employee working the second shift [#permalink]

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18 Oct 2014, 12:44
Bunuel wrote:
Mountain14 wrote:
At a certain factory, each employee working the second shift produced 23 as many widgets as each employee working the first shift. If the first shift has 34 as many employees, what fraction of the total widgets did the second shift produce?[/color]

A. 8/17
B. 1/2
C. 8/9
D. 9/8
E. 17/8

PLEASE CHECK QUESTIONS WHEN POSTING. THANK YOU.

At a certain factory, each employee working the second shift produced 2/3 as many widgets as each employee working the first shift. If the first shift has 3/4 as many employees, what fraction of the total widgets did the second shift produce?

A. 8/17
B. 1/2
C. 8/9
D. 9/8
E. 17/8

Pick some smart numbers:

Let the first shift have 3 employee and each produce 3 widgets, so the total number of widgets produced by the first shift is 3*3=9;

Then the second shift would have 4 employees and each second shift employee would produce 3*2/3=2 widgets, so the total number of widgets produced by the second shift employees would be 4*2=8;

The ratio of the second shift production to the total is 8/(9+8)=8/17.

This question is almost exact copy of the following OG question:
Quote:
At a loading dock, each worker on the night crew loaded 3/4 as many boxes as each worker on the day crew. If the night crew has 4/5 as many workers as the day crew, what fraction of all the boxes loaded by the two crews did the day crew load?

(A) 1/2
(B) 2/5
(C) 3/5
(D) 4/5
(E) 5/8

exactly bunuel, i thought something was amiss too, because when we dont know how many employees were present in the second half, how can we come to a conclusion. I spent 5 mins solving this because once i tried with 1/4 remaining employees and once with all the employees.
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Re: At a certain factory, each employee working the second shift [#permalink]

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27 Oct 2014, 02:19
I prefer the tabular form for such question ( might be useful for some).

emp widget widget / employee
1st shift 3e/4 w 4w/3e
2nd shift e x 8w/9e

thus x = emp * widget/employee = 8w/9

ratio of x/w+x = (8w/9) / w + (8w/9) = 8/17
Re: At a certain factory, each employee working the second shift   [#permalink] 27 Oct 2014, 02:19
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