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# Working together at their respective constant rates, Tom and Matt made

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Re: Working together at their respective constant rates, Tom and Matt made [#permalink]
chetan2u wrote:
Bhavz10 wrote:
Working together at their respective constant rates, Tom and Matt made pots. Did Tom take more time than Matt to make 100 pots?
1. Tom takes 4 hours more than Matt to produce twice the number of pots.
2. Tom takes twice the time as Matt to produce thrice the number of pots.

The answer would depend on the rates of both.

1. Tom takes 4 hours more than Matt to produce twice the number of pots.
If M takes x hrs to make y pots, T will take x+4 to make 2y pots.
So, if M takes 1 hr for 1 pot ( $$R_M = 1$$ per hour), T will take 1+4 or 5 hrs to make 2*1 or 2 pots ( $$R_T = \frac{2}{5}$$ per hour). M>T
But, if M takes 20 hr for 40 pot ( $$R_M = 2$$ per hour), T will take 20+4 or 24 hrs to make 2*40 or 80 pots ( $$R_T = \frac{80}{24}=3.33$$ per hour). M<T

2. Tom takes twice the time as Matt to produce thrice the number of pots.
If M takes x hrs to make y pots, T will take 2x to make 3y pots OR x hrs to make 3y/2 pots. 3y/2>y, so T will always make more pots in the given time
Suff

B

Is there any other way to solve this without taking numbers as example? By equations? In under 2 minutes.

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Re: Working together at their respective constant rates, Tom and Matt made [#permalink]
Bunuel Sir,
Is there any better method to solve this question without plugging values?
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Re: Working together at their respective constant rates, Tom and Matt made [#permalink]
1
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Bhavz10 wrote:
Working together at their respective constant rates, Tom and Matt made pots. Did Tom take more time than Matt to make 100 pots?
1. Tom takes 4 hours more than Matt to produce twice the number of pots.
2. Tom takes twice the time as Matt to produce thrice the number of pots.

Another method.
Let the time taken be M and T, so we are looking for - Is M>T?

Statement I
Matt takes M hrs for 100 pots, so Tom takes M+4 to produce 2*100 pots, that is (M+4)/2 to produce 200/2 pots.
Thus T=(M+4)/2.
Question was is T>M or is (M+4)/2>M.....M+4>2M or Is M<4?
Maybe or maybe not

Statement II
Matt takes M hrs for 100 pots, so Tom takes 2M to produce 3*100 pots, that is 2M/3 to produce 300/3 pots.
Thus T=2M/3
Question was - is T>M or is 2M/3>M?
Since M is positive, answer is NO.
Sufficient

B

Hope it helps
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Working together at their respective constant rates, Tom and Matt made [#permalink]
Bhavz10 wrote:
Working together at their respective constant rates, Tom and Matt made pots. Did Tom take more time than Matt to make 100 pots?
1. Tom takes 4 hours more than Matt to produce twice the number of pots.
2. Tom takes twice the time as Matt to produce thrice the number of pots.

From the Question stem it is clear that we need comparison ( Ratio) of respective rates of T and M
From 1
T*(X+4)=200
MX=100
T/M=2X/X+4
at X=4
T=M
but at X=2
T/M=2/3
Not Sufficient

From 2
T*2X=300
M*X=100
T/M=3/2
Sufficient
B:)
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Working together at their respective constant rates, Tom and Matt made [#permalink]
RaghavKhanna wrote:
Bunuel Sir,
Is there any better method to solve this question without plugging values?

I know the way I solved this problem might look weird but here's how I did it , I didn't use calculation at all ,I know we can answer this question if we find Tom is faster than Foster or vice versa , if I find it I can answer the question , in order to find the work rate and since they are using a comparison , the comparison needs to be on the same ground , I will explain how I solved this problem logically (yes in DS you can save time by not calculating)

Quote:
Tom takes 4 hours more than Matt to produce twice the number of pots.

in just two examples i will show how with this statement can make Tom faster than Matt and vice versa

let's say that Matt produces X amount of pots in 1 hour , so Tom produces 2X in five hours , the work rate of matt is X pot/hour , and Tom is Xpots/2.5 hours , matt is faster than Tom , so under these conditions , Matt is faster.

Another case , Matt produces X amount of pots in 20 hours , so Tom produces 2X in 25 hours , the work rate of Matt is 0.2X/hour , and Tom rate is 0.25X/hour, now Tom in this case is faster

1 insufficient.

for the statement 2: this one will always give us one answer (sufficient)

for example Tom takes 2* T to produce 3* X (T is time for matt to produce X matt) , so Tom has a work rate of 3*X/2*T it means 1.5 X pots / T hours , whereas matt takes X pot/ T hours , so here Tom is always faster

B is correct.

understanding this concept makes you answer this question in 50 seconds.
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Re: Working together at their respective constant rates, Tom and Matt made [#permalink]
1
Kudos
Bhavz10 wrote:
Working together at their respective constant rates, Tom and Matt made pots. Did Tom take more time than Matt to make 100 pots?
1. Tom takes 4 hours more than Matt to produce twice the number of pots.
2. Tom takes twice the time as Matt to produce thrice the number of pots.

Question stem, rephrased:
Is Tom slower than Matt?

Statement 1:
Case 1: Matt produces 1 pot in 1 hour, with the result that Matt's rate = work/time = 1/1 = 1 pot per hour
Since Tom takes 4 more hours to produce twice the number of pots, Tom takes 5 hours to produce 2 pots, with the result that Tom's rate = work/time = 2/5 pot per hour.
In this case, Tom is SLOWER than Matt, so the answer to the rephrased question stem is YES.

Case 2: Matt produces 10 pots in 10 hours, with the result that Matt's rate = work/time = 10/10 = 1 pot per hour
Since Tom takes 4 more hours to produce twice the number of pots, Tom takes 14 hours to produce 20 pots, with the result that Tom's rate = work/time = 20/14 = 10/7 pots per hour
In this case, Tom is FASTER than Matt, so the answer to the rephrased question stem is NO.

Since the answer is YES in Case 1 but NO in Case 2, INSUFFICIENT.

Statement 2:
If Tom and Matt were to work at the same rate, Tom would take 3 times as long as Matt to produce 3 times the number of pots.
Since Tom only takes TWICE as long as Matt to produce 3 times the number of pots, Tom must be FASTER than Matt.
Thus, the answer to the rephrased question stem is NO.
SUFFICIENT.

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Working together at their respective constant rates, Tom and Matt made [#permalink]
chetan2u wrote:
Bhavz10 wrote:
Working together at their respective constant rates, Tom and Matt made pots. Did Tom take more time than Matt to make 100 pots?
1. Tom takes 4 hours more than Matt to produce twice the number of pots.
2. Tom takes twice the time as Matt to produce thrice the number of pots.

The answer would depend on the rates of both.

1. Tom takes 4 hours more than Matt to produce twice the number of pots.
If M takes x hrs to make y pots, T will take x+4 to make 2y pots.
So, if M takes 1 hr for 1 pot ( $$R_M = 1$$ per hour), T will take 1+4 or 5 hrs to make 2*1 or 2 pots ( $$R_T = \frac{2}{5}$$ per hour). M>T
But, if M takes 20 hr for 40 pot ( $$R_M = 2$$ per hour), T will take 20+4 or 24 hrs to make 2*40 or 80 pots ( $$R_T = \frac{80}{24}=3.33$$ per hour). M<T

2. Tom takes twice the time as Matt to produce thrice the number of pots.
If M takes x hrs to make y pots, T will take 2x to make 3y pots OR x hrs to make 3y/2 pots. 3y/2>y, so T will always make more pots in the given time
Suff

B

Hi,
KarishmaB ScottTargetTestPrep chetan2u Bunuel
Isnt statement 1 ambiguous? Can't A mean that T takes 4 hours more than M does to make twice the number of pots?
Say M takes m hours to make x pots, thus will take 2m hours to make 2x pots. I considered- T will take 2m+4 hours to make twice the number of pots (2x)
TIA!
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Re: Working together at their respective constant rates, Tom and Matt made [#permalink]
RenB wrote:
chetan2u wrote:
Bhavz10 wrote:
Working together at their respective constant rates, Tom and Matt made pots. Did Tom take more time than Matt to make 100 pots?
1. Tom takes 4 hours more than Matt to produce twice the number of pots.
2. Tom takes twice the time as Matt to produce thrice the number of pots.

The answer would depend on the rates of both.

1. Tom takes 4 hours more than Matt to produce twice the number of pots.
If M takes x hrs to make y pots, T will take x+4 to make 2y pots.
So, if M takes 1 hr for 1 pot ( $$R_M = 1$$ per hour), T will take 1+4 or 5 hrs to make 2*1 or 2 pots ( $$R_T = \frac{2}{5}$$ per hour). M>T
But, if M takes 20 hr for 40 pot ( $$R_M = 2$$ per hour), T will take 20+4 or 24 hrs to make 2*40 or 80 pots ( $$R_T = \frac{80}{24}=3.33$$ per hour). M<T

2. Tom takes twice the time as Matt to produce thrice the number of pots.
If M takes x hrs to make y pots, T will take 2x to make 3y pots OR x hrs to make 3y/2 pots. 3y/2>y, so T will always make more pots in the given time
Suff

B

Hi,
KarishmaB ScottTargetTestPrep chetan2u Bunuel
Isnt statement 1 ambiguous? Can't A mean that T takes 4 hours more than M does to make twice the number of pots?
Say M takes m hours to make x pots, thus will take 2m hours to make 2x pots. I considered- T will take 2m+4 hours to make twice the number of pots (2x)
TIA!

It is not a good question. Statement 1 is ambiguous - I am not sure what it means. We cannot make a generic statement like this.

The question is just this: Is Tom slower than Matt?

1. Tom takes 4 hours more than Matt to produce twice the number of pots.

I wondered here whether they mean Tom takes 4 hours more to make 200 pots? But I wasn't convinced.

To give the information that they intended to give they should have said that on a particular day, Tom took 4 more hours and produced twice the number of pots than Matt did. Then it makes sense because we are talking about one particular instance. We cannot use a generic statement 'Tom takes 4 hours more to produce twice the number of pots' because that will not be true for all n (the number of pots made).

Take an example:
Say Matt takes 4 hours to make 100 pots.
Then Tom takes 8 hrs to make 200 pots.

Say Matt takes 8 hours to make 200 pots.
Then Tom will take 16 hrs to make 400 pots (not 12 hrs)

So this statement cannot hold for all values of n. For only one value of n, will the time taken by Tom be 4 hrs more.
To show an instance, we cannot use a generic statement.

2. Tom takes twice the time as Matt to produce thrice the number of pots.

This is alright. Now we have the ratio in both cases.
Tom does thrice the work in twice the time so he is faster than Matt.
Sufficient alone.
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Re: Working together at their respective constant rates, Tom and Matt made [#permalink]
RenB wrote:
chetan2u wrote:
Bhavz10 wrote:
Working together at their respective constant rates, Tom and Matt made pots. Did Tom take more time than Matt to make 100 pots?
1. Tom takes 4 hours more than Matt to produce twice the number of pots.
2. Tom takes twice the time as Matt to produce thrice the number of pots.

The answer would depend on the rates of both.

1. Tom takes 4 hours more than Matt to produce twice the number of pots.
If M takes x hrs to make y pots, T will take x+4 to make 2y pots.
So, if M takes 1 hr for 1 pot ( $$R_M = 1$$ per hour), T will take 1+4 or 5 hrs to make 2*1 or 2 pots ( $$R_T = \frac{2}{5}$$ per hour). M>T
But, if M takes 20 hr for 40 pot ( $$R_M = 2$$ per hour), T will take 20+4 or 24 hrs to make 2*40 or 80 pots ( $$R_T = \frac{80}{24}=3.33$$ per hour). M<T

2. Tom takes twice the time as Matt to produce thrice the number of pots.
If M takes x hrs to make y pots, T will take 2x to make 3y pots OR x hrs to make 3y/2 pots. 3y/2>y, so T will always make more pots in the given time
Suff

B

Hi,
KarishmaB ScottTargetTestPrep chetan2u Bunuel
Isnt statement 1 ambiguous? Can't A mean that T takes 4 hours more than M does to make twice the number of pots?
Say M takes m hours to make x pots, thus will take 2m hours to make 2x pots. I considered- T will take 2m+4 hours to make twice the number of pots (2x)