Leo can buy a certain computer for p1 dollars in State A, where the sa

Bunuel don't you think the question is ambiguous?

it does not clearly mention that the overall p1 includes the tax or not. We can not assume whether he can buy inclusive of tax or exclusive. What do you think.

In either way the answer will be E, but I was little confused before starting the question.

Yes, the question is indeed ambiguous (at least for me too). Though you are also right in saying that it doesn't really matters and either way the answer is E.

It is clear that 1 or 2 individually cannot answer.

Both 1 and 2 combined, we have from 2) that p1t1 > p2t2 and from 1) we have t1 > t2, which means that p1 >= p2. Hence p1 + (p1t1/100) > p2 + (p2t2/100) can be determined. This is my understanding. Please let me know if it is otherwise.

p1 >= p2 - is not a correct assumption.

Consider Case1 - (t1, t2) = (100, 10) & (p1, p2 ) = (3,2)
Here, t1 > t2 and p1t1 > p2t2 and p1 > p2

Consider Case2 - (t1, t2) = (100, 10) & (p1, p2 ) = (2,5)
Here as well, t1 > t2 and p1t1 > p2t2 but p1 < p2

Hope it helps! Cheers!
P.S. - Always try to substitute few values and test in these kind of scenario based questions.

\(p1 = c1 + \frac{t1}{100}*c1\) => \(t1 = \frac{100(p1 - c1 )}{c1}\)

\(p2 = c2 + \frac{t2}{100}*c2\) => \(t2 = \frac{100(p2 - c2 )}{c2}\)

\(1) t1 > t2\)

\(\frac{100(p1 - c1 )}{c1} > \frac{100(p2 - c2 )}{c2}\) => \(\frac{p1}{c1} > \frac{p2}{c2}\)

Not sufficient to tell p1 > p2.

\(1) p1t1 > p2t2\)

\(p1*\frac{100(p1 - c1 )}{c1} > p2*\frac{100(p2 - c2 )}{c2}\) => \(\frac{p1^2}{c1} > \frac{p2^2}{c2}\)

Not sufficient to tell p1 > p2.

As option 2 also includes option 1; both options together are not sufficient.

Ans: E

Hi ,

here are my two cents for this question

In county A let \(p_1\) be price before tax, \(t_1\)be the tax
then total price in county A is say M=\(p_1\)+\(p_1t_1\)
In county B let \(p_2\) be price before tax, \(t_2\)be the tax
then total price in county B is say N= \(p_2\)+\(p_2t_2\)

We are0 asked if M>N
To answer this question we need to know that tax rates at each county, and base price at each county / or we need to know the ratio of prices and ratio of taxes to come to conclusion about the comparison of prices.

Now Stmt 1:\(t_1\)> \(t_2\). OK we can have two case results from this.

Case a:\(p_1\)>\(p_2\) Say \(p_1\)= 150, \(p_2=100,\)\(t_1=20\), \(t_2=10\), then we have
\(t_1\)> \(t_2\)
M= 150+30 & N=100+10. (Here we have\(p_1t_1\)> \(p_2t_2\), or 30>10)
So M=180,N=110
We have from this that M>N

Case b:\(p_1\)<\(p_2\) Say \(p_1\)= 100, \(p_2=150,\)\(t_1=20\), \(t_2=10\), then we have
\(t_1\)> \(t_2\)
M= 100+20 & N=150+15. (Here we have\(p_1t_1\)> \(p_2t_2\), or 20>15)
So M=120,N=165
We have from this that M<N

So Stm1 Insufficient

Now Stmt 2: \(p_1t_1\)> \(p_2t_2\). We can have several cases from this , however if we refer our stmt 1 (the highlighted portion ) we already have \(p_1t_1\)> \(p_2t_2\). and we did get different answers on each case.

So Stm2 Insufficient
Other cases except those not discussed in statement 1 can be
Say \(p_1=p_2\) & \(t_1\)> \(t_2\)

Say Say \(p_1=p_2\) =150 and \(t_1\)= 20 and \(t_2\)=10

we will have M= 150+30 &N= 150+10 so 180>160or M>N

Say \(p_1>p_2\) & \(t_1\)= \(t_2\) Say \(t_1\)= \(t_2\) = 20 Say\(p_1\)= 150 and \(p_2\)= 100,then we have
M= 150+30
N=100+20
we have M>N



Now if we combine both statements , there is no new information, Hence E

Probus

Hello Bunuel
Is there any chance the tax to be 0% in B (in this regard)?
Thanks__

Why not? Nothing in the question restricts that and so we can have some tax heaven state.

Thanks for the previous response.
One more thing:
Leo can buy SAME computers by p2 dollars. Are the cost of computers considered adding tax or without adding tax? Here, There could be 2 scenario:
Assuming......
State A:
p1=$50; tax (p1)=$70--->Total $120
State B:
p2=$100; tax (p2)=$$20-->Total $120

Or,
After adding tax (don't know exactly the tax):
Total cost of computers in State A=$120
Total cost of computers in State B=$120

Which one is the real scenario of this DS?
Thanks__

\(p_1*t_1>p_2*t_2\) --> amount of tax in $ is more in A than in B.

I DIDNT GET THIS PART. How can we conclude that? it maybe because the base price in state A is much higher than in state B

A price multiples by the sales tax is the amount of the tax. For example, if p1 = $100 and t1 = 10%, then p1*t1=$10 is the amount of the tax to be paid in dollars. So, \(p_1*t_1>p_2*t_2\) simply means that the amount of tax in $ is more in A than in B.

Hi could anyone help explain here that statement 2 is clearly mentioned that (2) p1∗t1>p2∗t2. Therefore even though p2 might be greater than p1 in extreme case but it's asking for total cost of the computer ( which mean including tax). Therefore why is statement 2 can not be sufficient? Thanks

Thanks sarathy, why do you have to add a and b to ac+a > bd+b? Thanks

Think I got it now. a is the price itself and ac is tax of a. Not sure my understanding is correct? Thanks

same computer ???????? not used by one one in their assertion

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Bunuel - 

I have 2 things here:-
1. Why are we assuming tax is over the price? According to me, price should be inclusive of tax since question mentions that that "Leo can buy at P1", i.e. he would have to pay P1 cash to buy the computer. 
2. Also, why are we assuming base price (i.e. exclusing sales tax) of the two computers separate in two states? The question mentions that the price of the same computer in other state. So, according to me, since the computer model is same, the base price in both states is same and the sales tax rates are different leading to differen overall price P1 and P2.

When I take these two conditions, my answer comes out to be D.

I think the question is ambiguous.

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1. That's not how sales tax works. It's added to the price. For example, if the price is $100 and the sales tax is 10%, the customer pays $110.

2. Prices can differ between two shops next to each other, so they can obviously differ across state borders.

3. Note that this is an official question, so its wording is as precise as possible.­