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A factory normally produces x units per working day. In a month with 2  [#permalink]

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A factory normally produces x units per working day. In a month with 22 working days, no units are produced in the first y working days because of a strike. How many units must be produced per day on each of the rest of the working days of the month in order to have an average of x units per working day for the entire month?

(A) $$11x$$

(B) $$22x$$

(C) $$\frac{22x}{y}$$

(D) $$\frac{22x}{22-y}$$

(E) $$\frac{22x}{22xy-y}$$

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Re: A factory normally produces x units per working day. In a month with 2  [#permalink]

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HKD1710 wrote:
A factory normally produces x units per working day. In a month with 22 working days, no units are produced in the first y working days because of a strike. How many units must be produced per day on each of the rest of the working days of the month in order to have an average of x units per working day for the entire month?

(A) $$11x$$

(B) $$22x$$

(C) $$\frac{22x}{y}$$

(D) $$\frac{22x}{22-y}$$

(E) $$\frac{22x}{22xy-y}$$

In a month with 22 working days, no units are produced in the first y working days because of a strike.
Number of days in which units were produced = 22 - y
Let k = units produced each day in which units were produced
So, TOTAL number of units produced in the month = k(22 - y)

How many units must be produced per day on each of the rest of the working days of the month in order to have an average of x units per working day for the entire month?
We want: (total number of units produced)/(# of work days) = x
In other words, we want: k(22 - y)/22 = x

We must solve the above equation for k

Take: k(22 - y)/22 = x
Multiply both sides by 22 to get: k(22 - y) = 22x
Divide both sides by (22 - y) to get: k = 22x/(22 - y)

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Joined: 09 Mar 2016
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A factory normally produces x units per working day. In a month with 2  [#permalink]

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HKD1710 wrote:
A factory normally produces x units per working day. In a month with 22 working days, no units are produced in the first y working days because of a strike. How many units must be produced per day on each of the rest of the working days of the month in order to have an average of x units per working day for the entire month?

(A) $$11x$$

(B) $$22x$$

(C) $$\frac{22x}{y}$$

(D) $$\frac{22x}{22-y}$$

(E) $$\frac{22x}{22xy-y}$$

Project PS Butler : Question #44

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say 10 units are produced each day

for whole month 220*10 = 220 units are produced

now if strike lasted for 11 working days

then 11x=220

x = 20

let x be number of units per day 10

let 22-y be number of days left after strike 11

SO JUST PLUG IN THOSE VALUES TO GET 20

clearly A, B, and E are out

Between C and D,

D is more logical i think IMO: D i wonder how would an algebraic solution look like GMATPrepNow and how would you choose between D and C using my method of testing values - both yield the same value
Manager  B
Joined: 02 Oct 2018
Posts: 62
Re: A factory normally produces x units per working day. In a month with 2  [#permalink]

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dave13 wrote:
HKD1710 wrote:
A factory normally produces x units per working day. In a month with 22 working days, no units are produced in the first y working days because of a strike. How many units must be produced per day on each of the rest of the working days of the month in order to have an average of x units per working day for the entire month?

(A) $$11x$$

(B) $$22x$$

(C) $$\frac{22x}{y}$$

(D) $$\frac{22x}{22-y}$$

(E) $$\frac{22x}{22xy-y}$$

Project PS Butler : Question #44

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say 10 units are produced each day

for whole month 220*10 = 220 units are produced

now if strike lasted for 11 working days

then 11x=220

x = 20

let x be number of units per day 10

let 22-y be number of days left after strike 11

SO JUST PLUG IN THOSE VALUES TO GET 20

clearly A, B, and E are out

Between C and D,

D is more logical i think IMO: D i wonder how would an algebraic solution look like GMATPrepNow and how would you choose between D and C using my method of testing values - both yield the same value

dave13

Below is my working. Could let me know where i made a mistake?

Total Units per Month = 22x.

No. of units lost due to strike of y days = xy.

No. of units to be produced in the remainder of the month= 22x+xy

No. of days left in the month after strike y = 22-y.

Hence, per day rate= 22x+xy/ 22-y.
Manager  D
Joined: 17 May 2015
Posts: 247
Re: A factory normally produces x units per working day. In a month with 2  [#permalink]

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Hi,

Given:

A factory normally produces x units per working day. In a month with 22 working days, no. of units required to be produced = 22*x units.

No units are produced in the first y working days because of a strike. => No. of working days reduced to (22 - y) days.

Now, the factory has to produce 22x units in (22-y) days. Hence, new average $$= \frac{22x}{22 - y}$$.

DAVE:

This is very much possible that with a particular set of values more than one option might be true. In such cases, you have to recheck the answer with another set of values.

For example, now consider x = 10, and y = 2. => In 22-y = 20 days factory has to produce 220 units => average = 220/20 = 11 units/day.

(C) 22x/y => (22*10)/2 = 110 units. OUT

(D) 22x/(22-y) => (22*10)/20 = 11 units. Option (D) matches, hence right answer.

ParthSanghavi

Quote:
Below is my working. Could let me know where i made a mistake?

Total Units per Month = 22x.

No. of units lost due to strike of y days = xy.

No. of units to be produced in the remainder of the month= 22x+xy

No. of days left in the month after strike y = 22-y.

Hence, per day rate= 22x+xy/ 22-y

Total production is fixed. Total units in a month = 22x. Hence, no. of units to be produced in a month will also be 22x.

Alternate Solution:

Old average = x units days.

No. of units lost due to strike = x*y units. These x*y units have to be produced on the remaining 22-y days.

No. of remaining working days = 22-y days.

New average $$= x + \frac{xy}{22 - y} = \frac{x*(22 - y) + xy}{22 - y} = \frac{ 22x - xy + xy}{22 - y} = \frac{22x}{22 -y}$$.

Hope this helps.

Thanks.
Manager  B
Joined: 02 Oct 2018
Posts: 62
Re: A factory normally produces x units per working day. In a month with 2  [#permalink]

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ganand wrote:
Hi,

Given:

A factory normally produces x units per working day. In a month with 22 working days, no. of units required to be produced = 22*x units.

No units are produced in the first y working days because of a strike. => No. of working days reduced to (22 - y) days.

Now, the factory has to produce 22x units in (22-y) days. Hence, new average $$= \frac{22x}{22 - y}$$.

DAVE:

This is very much possible that with a particular set of values more than one option might be true. In such cases, you have to recheck the answer with another set of values.

For example, now consider x = 10, and y = 2. => In 22-y = 20 days factory has to produce 220 units => average = 220/20 = 11 units/day.

(C) 22x/y => (22*10)/2 = 110 units. OUT

(D) 22x/(22-y) => (22*10)/20 = 11 units. Option (D) matches, hence right answer.

ParthSanghavi

Quote:
Below is my working. Could let me know where i made a mistake?

Total Units per Month = 22x.

No. of units lost due to strike of y days = xy.

No. of units to be produced in the remainder of the month= 22x+xy

No. of days left in the month after strike y = 22-y.

Hence, per day rate= 22x+xy/ 22-y

Total production is fixed. Total units in a month = 22x. Hence, no. of units to be produced in a month will also be 22x.

Alternate Solution:

Old average = x units days.

No. of units lost due to strike = x*y units. These x*y units have to be produced on the remaining 22-y days.

No. of remaining working days = 22-y days.

New average $$= x + \frac{xy}{22 - y} = \frac{x*(22 - y) + xy}{22 - y} = \frac{ 22x - xy + xy}{22 - y} = \frac{22x}{22 -y}$$.

Hope this helps.

Thanks.

Understood where i went wrong. Thank you :D
Director  G
Joined: 09 Mar 2018
Posts: 995
Location: India
Re: A factory normally produces x units per working day. In a month with 2  [#permalink]

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HKD1710 wrote:
A factory normally produces x units per working day. In a month with 22 working days, no units are produced in the first y working days because of a strike. How many units must be produced per day on each of the rest of the working days of the month in order to have an average of x units per working day for the entire month?

(A) $$11x$$

(B) $$22x$$

(C) $$\frac{22x}{y}$$

(D) $$\frac{22x}{22-y}$$

(E) $$\frac{22x}{22xy-y}$$

Plug in for all the unknown variables
x = 10 units/day
y = 5
Remaining days 17

Average = Sum of the terms/ Total number of terms

whatever was lost in the 5 days needs to be recovered by working in the remaining days at a new rate
17 x = 220
x = 220/17

When plugged back for all the values, Only D gives us the same value
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Many of life's failures happen with people who do not realize how close they were to success when they gave up. Re: A factory normally produces x units per working day. In a month with 2   [#permalink] 10 Feb 2019, 01:07
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