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

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
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From first statement
Case 1
Let Matt takes 10 hours to make 10 pots so he will take 100 hours to make 100 pots. Now tom produces 20 pots in 14 hours so he will make 100 pots in 70 hours.
Case 2
Let Matt takes 2 hours to make 10 pots so he will make 100 pots in 20 hours. Now tom produces 20 pots in 6 hours so he will make 100 pots in 30 hours.
Both the cases give different answer so this statement is insufficient.
From statement 2
Tom's rate is 3/2 times the rate of Matt so will take less time than Matt, hence sufficient.
So answer is B

Posted from my mobile device

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

Posted from my mobile device

Bunuel Sir,
Is there any better method to solve this question without plugging values?
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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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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:)

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)

so let's start with the first statement:


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.

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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