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If 7 workers can build 7 cars in 7 days, then how many days would it

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If 7 workers can build 7 cars in 7 days, then how many days would it  [#permalink]

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New post 26 Apr 2011, 08:12
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If 7 workers can build 7 cars in 7 days, then how many days would it take 5 workers to build 5 cars?

(A) 1
(B) 5
(C) 7
(D) 25
(E) 35
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Re: If 7 workers can build 7 cars in 7 days, then how many days would it  [#permalink]

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New post 26 Apr 2011, 18:43
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reatsaint wrote:
If 7 workers can build 7 cars in 7 days, then how many days would it take 5 workers to build 5 cars?

(A) 1 (B) 5(C) 7(D) 25(E) 35


An interesting thing in such questions is 7 workers and 7 cars. Makes me think of each worker working on his own single car and finishing it in 7 days. So 1 worker finishes 1 car in 7 days.
5 workers working on their own individual 5 cars will also take 7 days. 210 workers working on 210 cars will take 7 days too.
210 workers working on 420 cars will take 14 days (each worker makes 1 car in 7 days and then another in another 7 days)
and so on... Sometimes you can just reason it out too.


reatsaint wrote:
I was using a method similar to Fluke but made a calculation mistake, and got stuck. That method work easier for me.


Actually, both are using the same concept of variation. You can do it one step at a time or all together, whatever suits you. Just different ways of looking at the same thing.

Let me tell you how I think of the all together method.

7 workers - 7 cars - 7 days
5 workers - 5 cars - a days

No of days needed = 7 * (5/7) * (7/5)
You get this expression by thinking in the following way: Initially, you needed 7 days so that is the quantity that has to change so write "No of days needed = 7 *"

Just consider cars now. When you need to make only 5 cars (i.e. less cars) as compared to 7 cars, do you need more days or less? Less ofcourse so you multiply above by (5/7) (it is smaller than 1 so will decrease whatever it multiplies)
Now you have: "No of days needed = 7 * (5/7)"

Now just consider workers. If you have fewer workers (5 instead of 7), will you need more days to finish the work or less? More ofcourse so multiply by (7/5) (which is greater than 1)
Now you have: "No of days needed = 7 * (5/7) * (7/5) = 7 days"

On the same lines, try this:
4 people make 28 baskets in 4 days working 8 hrs every day. How many days will 8 people take to make 14 baskets working 2 hrs a day?
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Re: If 7 workers can build 7 cars in 7 days, then how many days would it  [#permalink]

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New post 26 Apr 2011, 08:21
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reatsaint wrote:
If 7 workers can build 7 cars in 7 days, then how many days would it take 5 workers to build 5 cars?

(A) 1 (B) 5(C) 7(D) 25(E) 35


7 Worker - 7 cars - 7days
1 Worker- 7 cars - 7*7 days
1 Worker - 1 car - 7*7/7=7 days
1 Worker - 5 car - 7*5 days
5 Worker - 5 cars - 7*5/5 =7 days

Ans: "C"
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Re: If 7 workers can build 7 cars in 7 days, then how many days would it  [#permalink]

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New post 26 Apr 2011, 08:25
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7w-------7c------7days.
7w-------1c------1day
1w-------1c------7days
1w-------5c------7*5 days
5w-------5c------7*5/5 days= 7days.
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Re: If 7 workers can build 7 cars in 7 days, then how many days would it  [#permalink]

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New post 26 Apr 2011, 08:27
Thanks Fluke and Jami !!
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Re: If 7 workers can build 7 cars in 7 days, then how many days would it  [#permalink]

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New post 26 Apr 2011, 09:57
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any of such problem can be solved easily in the following way

Workers cars days
7 7 7
5 5 x
We have asked about how many days will require to complete the work

now days are inversely proportional to workers and direct proportional to the cars. When there is inverse proportion take number from the opposite line to X to numerator … and when there is direct proportion take number form the same line to X to numerator … and put other numbers to denominator. Also, take number that is above or below X to numerator or denominator respectively

Hence the equation will be X = 7*5*7 / 5*7 = 7

You can use this method when there are only two related quantities or 100 relaed quantities
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Re: If 7 workers can build 7 cars in 7 days, then how many days would it  [#permalink]

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New post 26 Apr 2011, 10:09
vyassaptarashi wrote:
any of such problem can be solved easily in the following way

Workers cars days
7 7 7
5 5 x
We have asked about how many days will require to complete the work

now days are inversely proportional to workers and direct proportional to the cars. When there is inverse proportion take number from the opposite line to X to numerator … and when there is direct proportion take number form the same line to X to numerator … and put other numbers to denominator. Also, take number that is above or below X to numerator or denominator respectively

Hence the equation will be X = 7*5*7 / 5*7 = 7

You can use this method when there are only two related quantities or 100 relaed quantities

I was using a method similar to Fluke but made a calculation mistake, and got stuck. That method work easier for me.
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Re: If 7 workers can build 7 cars in 7 days, then how many days would it  [#permalink]

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New post 27 Apr 2011, 00:33
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VeritasPrepKarishma wrote:
On the same lines, try this:
4 people make 28 baskets in 4 days working 8 hrs every day. How many days will 8 people take to make 14 baskets working 2 hrs a day?


I recall that I used this formula in 10th grade. Dont know if it is exact - pls verify

Man * Days / Work done = constant

or

Man * Hours / Workdone = constant

4 people * (4 * 8) hrs / 28 baskets = constant = 8 people * (2*D) hrs / 14 baskets

D = 4 days

Plus there is one more variation of this formula when efficiency of the worker comes into play -

Man * Days * efficiency / Work done = constant
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Re: If 7 workers can build 7 cars in 7 days, then how many days would it  [#permalink]

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New post 27 Apr 2011, 02:07
7 (1car/xday) * 7 days = 7 cars
49/x=7
x=7

Therefore, rate per worker is 1car/7days.

5(1/7)(t)=5cars
t=(5)(7/5)
t=7days

Answer: 7 days to build 5 cars by 5 workers!
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Re: If 7 workers can build 7 cars in 7 days, then how many days would it  [#permalink]

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New post 27 Apr 2011, 18:24
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gmat1220 wrote:
VeritasPrepKarishma wrote:
On the same lines, try this:
4 people make 28 baskets in 4 days working 8 hrs every day. How many days will 8 people take to make 14 baskets working 2 hrs a day?


I recall that I used this formula in 10th grade. Dont know if it is exact - pls verify

Man * Days / Work done = constant

or

Man * Hours / Workdone = constant

4 people * (4 * 8) hrs / 28 baskets = constant = 8 people * (2*D) hrs / 14 baskets

D = 4 days

Plus there is one more variation of this formula when efficiency of the worker comes into play -

Man * Days * efficiency / Work done = constant


Yes, it is correct.
The formula is again nothing but application of variation.
You say, Man * Days / Work done = constant
It implies that 'Man' varies directly with 'Work done' which is obvious since if you need to do more work, you need more men to do it in the same time.
Also, 'Man' varies inversely with 'Days' which is again obvious since if you need to do the work in fewer days, you need more men (keeping work done the same)

The clubbing of more than two variables is just called 'joint variation'.

When you include efficiency, we see that 'man' varies inversely as 'efficiency' which makes sense too. If men are more efficient, you need fewer of them to finish the same work in same time.
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Re: If 7 workers can build 7 cars in 7 days, then how many days would it  [#permalink]

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New post 11 Aug 2011, 06:38
7 workers --- 7 days --- 7cars
5 workers --- x days --- 5cars

x = 7*7*5/7*5 = 7 days
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If 7 workers can build 7 cars in 7 days, then how many days would it  [#permalink]

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New post Updated on: 19 May 2019, 21:30
If 7 workers can build 7 cars in 7 days, then how many days would it take 5 workers to build 5 cars?

(A) 1
(B) 5
(C) 7
(D) 25
(E) 35

let r=rate per worker per day
7*r*7=7→
r=1/7
let t=time
5*1/7*t=5→
t=7 hours
C

Originally posted by gracie on 13 Jan 2016, 16:22.
Last edited by gracie on 19 May 2019, 21:30, edited 1 time in total.
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Re: If 7 workers can build 7 cars in 7 days, then how many days would it  [#permalink]

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New post 20 Jan 2016, 09:10
I made a silly mistake cause I saw was a low level question and thought "solve it quickly and move on"....and this was the reason why I picked B.

Then, I thought of it and solved in this way:

If 7 workers can build 7 cars in 7 days, also 1 worker can build 7 cars in 49 days and the same worker can build 1 car in 7 days.
Multiply it by 5 and you get that 5 workers can build 5 cars in 7 days.

I wanted to use the work=rate*time formula but I had some difficulty. Can someone show me how to solve the problem with that formula please?
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Re: If 7 workers can build 7 cars in 7 days, then how many days would it  [#permalink]

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New post 20 Jan 2016, 23:28
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pepo wrote:
I made a silly mistake cause I saw was a low level question and thought "solve it quickly and move on"....and this was the reason why I picked B.

Then, I thought of it and solved in this way:

If 7 workers can build 7 cars in 7 days, also 1 worker can build 7 cars in 49 days and the same worker can build 1 car in 7 days.
Multiply it by 5 and you get that 5 workers can build 5 cars in 7 days.

I wanted to use the work=rate*time formula but I had some difficulty. Can someone show me how to solve the problem with that formula please?



Yes, you can use that formula too but you have to be careful about the number of workers.

In 7 days, 7 cars are made (by 7 workers.)
So Work = 7 cars
Time = 7 days

7 cars = Rate * 7 days
Rate = 1 car/day
(assuming 7 workers are working on it)

If 5 workers are working on it, rate = (1/7)*5 = 5/7 car/day

Time = Work/Rate
Time = 5 cars/(5/7) car/day = 7 days

I suggest you to look at the variation approach. It will be easier.
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Re: If 7 workers can build 7 cars in 7 days, then how many days would it  [#permalink]

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New post 21 Jan 2016, 09:34
VeritasPrepKarishma wrote:
pepo wrote:
I made a silly mistake cause I saw was a low level question and thought "solve it quickly and move on"....and this was the reason why I picked B.

Then, I thought of it and solved in this way:

If 7 workers can build 7 cars in 7 days, also 1 worker can build 7 cars in 49 days and the same worker can build 1 car in 7 days.
Multiply it by 5 and you get that 5 workers can build 5 cars in 7 days.

I wanted to use the work=rate*time formula but I had some difficulty. Can someone show me how to solve the problem with that formula please?



Yes, you can use that formula too but you have to be careful about the number of workers.

In 7 days, 7 cars are made (by 7 workers.)
So Work = 7 cars
Time = 7 days

7 cars = Rate * 7 days
Rate = 1 car/day
(assuming 7 workers are working on it)

If 5 workers are working on it, rate = (1/7)*5 = 5/7 car/day

Time = Work/Rate
Time = 5 cars/(5/7) car/day = 7 days

I suggest you to look at the variation approach. It will be easier.



Thanks for your help.

What is the variation approach?

Thanks again!
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Re: If 7 workers can build 7 cars in 7 days, then how many days would it  [#permalink]

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New post 21 Jan 2016, 20:46
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pepo wrote:
VeritasPrepKarishma wrote:
pepo wrote:
I made a silly mistake cause I saw was a low level question and thought "solve it quickly and move on"....and this was the reason why I picked B.

Then, I thought of it and solved in this way:

If 7 workers can build 7 cars in 7 days, also 1 worker can build 7 cars in 49 days and the same worker can build 1 car in 7 days.
Multiply it by 5 and you get that 5 workers can build 5 cars in 7 days.

I wanted to use the work=rate*time formula but I had some difficulty. Can someone show me how to solve the problem with that formula please?



Yes, you can use that formula too but you have to be careful about the number of workers.

In 7 days, 7 cars are made (by 7 workers.)
So Work = 7 cars
Time = 7 days

7 cars = Rate * 7 days
Rate = 1 car/day
(assuming 7 workers are working on it)

If 5 workers are working on it, rate = (1/7)*5 = 5/7 car/day

Time = Work/Rate
Time = 5 cars/(5/7) car/day = 7 days

I suggest you to look at the variation approach. It will be easier.



Thanks for your help.

What is the variation approach?

Thanks again!


Check out this post: http://www.veritasprep.com/blog/2015/10 ... made-easy/
Understand the methodology (shown in the first question of the post) and use the same for this question. It will get solved in seconds.
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Re: If 7 workers can build 7 cars in 7 days, then how many days would it  [#permalink]

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New post 14 Feb 2016, 03:30
Here is my approach,

No. of workers(w) is directly proportional to no. of cars(c)
No. of days(d) is also directly proportional to no. of cars(c)
But no. of workers(w) is inversely proportional to no. of days(d)

So simply put down, the logic becomes d * w = c

Per worker effort is 1/7th a car per day

Finally d * 5(1/7) = 5, this gives the no. of days for 5 workers to make 5 cars as 7 days.

Hope this helps :)
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If 7 workers can build 7 cars in 7 days, then how many days would it  [#permalink]

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New post 18 Mar 2018, 08:38
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Quote:
I wanted to use the work=rate*time formula but I had some difficulty. Can someone show me how to solve the problem with that formula please?

reatsaint wrote:
If 7 workers can build 7 cars in 7 days, then how many days would it take 5 workers to build 5 cars?

(A) 1
(B) 5
(C) 7
(D) 25
(E) 35

You can use the (rate*time) = work formula. Doing so is quick.

Just change the LHS a little.
Add "# of workers" to the LHS, this way:

(# of workers) * rate * time = work

Then manipulate the formula exactly as you would the "regular" formula. (This little change works for "number of machines" questions, too.)

(1) Find the rate of one individual worker from the first scenario. The rate is in cars per day.

(Number of Workers) * R * T = W, so

\(7*R*7=7\)
\(R=\frac{7}{(7*7)}=\frac{1}{7}\)

That is (manipulating the amended formula first):
\(R = \frac{W}{(No.OfWorkers)*(T)}\)

\(R= \frac{7}{(7*7)}=\frac{1}{7}\)

(2) Now solve for time:
At that rate, how many days will it take 5 workers (# of workers) to build 5 cars (Work)?

(Number of Workers) * R * T = W, so

\(5*\frac{1}{7}*T=5\)
\(\frac{5}{7}*T=5\)
\(T=(5*\frac{7}{5})=7\) days

Or:
\(Time= \frac{W}{(No.Of.Workers)*(R)}\)

\(T = \frac{5}{5*\frac{1}{7}}=\frac{5}{\frac{5}{7}}= 5*\frac{7}{5}=7\) days

Answer C
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