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Orange08
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Leo can buy a certain computer for p1 dollars in State A, where the sa 05 Sep 2010, 06:58
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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55% (hard)

Question Stats:

63% (02:02) correct 37% (01:48) wrong based on 3252 sessions

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Leo can buy a certain computer for \(p_1\) dollars in State A, where the sales tax is \(t_1\) percent, or he can buy the same computer for \(p_2\) dollars in State B, where the sales tax is \(t_2\) percent. Is the total cost of the computer greater in State A than in State B?


(1) \(t_1 > t_2\)

(2) \(p_1t_1 > p_2t_2\)
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Leo can buy a certain computer for p1 dollars in State A, where the sa 05 Sep 2010, 07:54
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Orange08
Leo can buy a certain computer for p1 dollars in State A, where the sales tax is t1 percent,or he can buy the same computer for p2 dollars in State B, where the sales tax is t2 percent. Is the total cost of the computer greater in State A than in State B?

(1) t1 > t2
(2) p1t1 > p2t2
Show more
You can solve this question algebraically, but number plugging is easier here.

Total cost = p*(1 + t/100).

(1) \(t_1>t_2\)

No information about the prices. Not sufficient.

(2) \(p_1*t_1>p_2*t_2\)

The dollar amount of tax is higher in A than in B. But if \(t_1 > 0%\) and \(t_2 = 0%\), then this holds for any positive \(p_1\) and \(p_2\). Still, this does not guarantee which total cost is higher. Not sufficient.

(1)+(2) Again, if \(t_1 = 10% > t_2 = 0%\) (statement 1), then \(p_1 * t_1 > p_2 * t_2 = 0\) (statement 2). But even with both statements, we cannot establish the relationship between the total costs in State A and State B. For example, if \(p_1 = p_2\), the total cost in A would be higher than in B, since B’s cost would be just \(p_2\) (as \(t_2 = 0%\)) and A’s cost would be \(p_1 * 1.1 = p_2 * 1.1\). However, if \(p_1 = 1\) and \(p_2 = 100\), the total cost in A would be lower than in B, since B’s cost would be \(p_2 = 100\) and A’s cost would be \(p_1 * 1.1 = 1.1\). Not sufficient.

Answer: E.
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Leo can buy a certain computer for p1 dollars in State A, where the sa 05 Sep 2010, 09:22
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i always find it better to replace all the t1, p1, blah blah with easy-on-the-eyes variables
e.g. replace p1,p2,t1,t2 with a,b,c,d respectively
Question is total price greater in State A --> is ac+a > bd+b
--> a(c+1) > b(d+1) ?

Quote:
(1) c> d
Show more
we don't know anything about a and b --> insufficient

Quote:
(2) ac > bd
Show more
all we know is that ac > bd ...again, we don't know anything about a,b,c,d individually--> insufficient

Quote:
(1) & (2) combined
Show more
again, we don't have any info about a and b --> Both statements together are also insufficient

-->
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E
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Leo can buy a certain computer for p1 dollars in State A, where the sa 21 Oct 2010, 10:29
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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.
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Leo can buy a certain computer for p1 dollars in State A, where the sa 21 Oct 2010, 16:27
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gurpreetsingh
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.
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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.
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Leo can buy a certain computer for p1 dollars in State A, where the sa 17 Sep 2012, 21:18
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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.
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Leo can buy a certain computer for p1 dollars in State A, where the sa 17 Sep 2012, 22:29
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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.
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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.
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Leo can buy a certain computer for p1 dollars in State A, where the sa 14 Apr 2014, 08:45
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\(p1 = c1 + \frac{t1}{100}*c1\) => \(t1 = \frac{100(p1 - c1 )}{c1}\)

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

\(1) t1 > t2\)

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

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
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Leo can buy a certain computer for p1 dollars in State A, where the sa 11 Sep 2018, 16:21
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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
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Leo can buy a certain computer for p1 dollars in State A, where the sa 22 Feb 2020, 14:54
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Bunuel
Orange08
Leo can buy a certain computer for p1 dollars in State A, where the sales tax is t1 percent,or he can buy the same computer for p2 dollars in State B, where the sales tax is t2 percent. Is the total cost of the computer greater in State A than in State B?
10
(1) t1 > t2
(2) p1t1 > p2t2


I chose B. However, OA is different. please explain.
You can solve this question algebraically, but number plugging is easier here.

Total cost = p*(1 + t/100).

(1) \(t_1>t_2\)

No information about the prices. Not sufficient.

(2) \(p_1*t_1>p_2*t_2\)

The dollar amount of tax is higher in A than in B. But if \(t_1 > 0%\) and \(t_2 = 0%\), then this holds for any positive \(p_1\) and \(p_2\). Still, this does not guarantee which total cost is higher. Not sufficient.

(1)+(2) Again, if \(t_1 = 10% > t_2 = 0%\) (statement 1), then \(p_1 * t_1 > p_2 * t_2 = 0\) (statement 2). But even with both statements, we cannot establish the relationship between the total costs in State A and State B. For example, if \(p_1 = p_2\), the total cost in A would be higher than in B, since B’s cost would be just \(p_2\) (as \(t_2 = 0%\)) and A’s cost would be \(p_1 * 1.1 = p_2 * 1.1\). However, if \(p_1 = 1\) and \(p_2 = 100\), the total cost in A would be lower than in B, since B’s cost would be \(p_2 = 100\) and A’s cost would be \(p_1 * 1.1 = 1.1\). Not sufficient.

Answer: E.
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Hello Bunuel
Is there any chance the tax to be 0% in B (in this regard)?
Thanks__
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Leo can buy a certain computer for p1 dollars in State A, where the sa 23 Feb 2020, 03:59
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Orange08
Leo can buy a certain computer for p1 dollars in State A, where the sales tax is t1 percent,or he can buy the same computer for p2 dollars in State B, where the sales tax is t2 percent. Is the total cost of the computer greater in State A than in State B?
10
(1) t1 > t2
(2) p1t1 > p2t2


I chose B. However, OA is different. please explain.

You can solve this question algebraically, but number plugging is easier here.

Total cost = p*(1 + t/100).

(1) \(t_1>t_2\)

No information about the prices. Not sufficient.

(2) \(p_1*t_1>p_2*t_2\)

The dollar amount of tax is higher in A than in B. But if \(t_1 > 0%\) and \(t_2 = 0%\), then this holds for any positive \(p_1\) and \(p_2\). Still, this does not guarantee which total cost is higher. Not sufficient.

(1)+(2) Again, if \(t_1 = 10% > t_2 = 0%\) (statement 1), then \(p_1 * t_1 > p_2 * t_2 = 0\) (statement 2). But even with both statements, we cannot establish the relationship between the total costs in State A and State B. For example, if \(p_1 = p_2\), the total cost in A would be higher than in B, since B’s cost would be just \(p_2\) (as \(t_2 = 0%\)) and A’s cost would be \(p_1 * 1.1 = p_2 * 1.1\). However, if \(p_1 = 1\) and \(p_2 = 100\), the total cost in A would be lower than in B, since B’s cost would be \(p_2 = 100\) and A’s cost would be \(p_1 * 1.1 = 1.1\). Not sufficient.

Answer: E.
Hello Bunuel
Is there any chance the tax to be 0% in B (in this regard)?
Thanks__
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Why not? Nothing in the question restricts that and so we can have some tax heaven state.
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Leo can buy a certain computer for p1 dollars in State A, where the sa 20 Jul 2021, 07:28
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Leo can buy a certain computer for p1 dollars in State A, where the sales tax is t1 percent,or he can buy the same computer for p2 dollars in State B, where the sales tax is t2 percent. Is the total cost of the computer greater in State A than in State B?
10
(1) t1 > t2
(2) p1t1 > p2t2


I chose B. However, OA is different. please explain.

You can solve this question algebraically, but number plugging is easier here.

Total cost = p*(1 + t/100).

(1) \(t_1>t_2\)

No information about the prices. Not sufficient.

(2) \(p_1*t_1>p_2*t_2\)

The dollar amount of tax is higher in A than in B. But if \(t_1 > 0%\) and \(t_2 = 0%\), then this holds for any positive \(p_1\) and \(p_2\). Still, this does not guarantee which total cost is higher. Not sufficient.

(1)+(2) Again, if \(t_1 = 10% > t_2 = 0%\) (statement 1), then \(p_1 * t_1 > p_2 * t_2 = 0\) (statement 2). But even with both statements, we cannot establish the relationship between the total costs in State A and State B. For example, if \(p_1 = p_2\), the total cost in A would be higher than in B, since B’s cost would be just \(p_2\) (as \(t_2 = 0%\)) and A’s cost would be \(p_1 * 1.1 = p_2 * 1.1\). However, if \(p_1 = 1\) and \(p_2 = 100\), the total cost in A would be lower than in B, since B’s cost would be \(p_2 = 100\) and A’s cost would be \(p_1 * 1.1 = 1.1\). Not sufficient.

Answer: E.
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\(p_1*t_1>p_2*t_2\) --> 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
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Leo can buy a certain computer for p1 dollars in State A, where the sa 20 Jul 2021, 09:17
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Bunuel
Orange08
Leo can buy a certain computer for p1 dollars in State A, where the sales tax is t1 percent,or he can buy the same computer for p2 dollars in State B, where the sales tax is t2 percent. Is the total cost of the computer greater in State A than in State B?
10
(1) t1 > t2
(2) p1t1 > p2t2


I chose B. However, OA is different. please explain.

You can solve this question algebraically, but number plugging is easier here.

Total cost = p*(1 + t/100).

(1) \(t_1>t_2\)

No information about the prices. Not sufficient.

(2) \(p_1*t_1>p_2*t_2\)

The dollar amount of tax is higher in A than in B. But if \(t_1 > 0%\) and \(t_2 = 0%\), then this holds for any positive \(p_1\) and \(p_2\). Still, this does not guarantee which total cost is higher. Not sufficient.

(1)+(2) Again, if \(t_1 = 10% > t_2 = 0%\) (statement 1), then \(p_1 * t_1 > p_2 * t_2 = 0\) (statement 2). But even with both statements, we cannot establish the relationship between the total costs in State A and State B. For example, if \(p_1 = p_2\), the total cost in A would be higher than in B, since B’s cost would be just \(p_2\) (as \(t_2 = 0%\)) and A’s cost would be \(p_1 * 1.1 = p_2 * 1.1\). However, if \(p_1 = 1\) and \(p_2 = 100\), the total cost in A would be lower than in B, since B’s cost would be \(p_2 = 100\) and A’s cost would be \(p_1 * 1.1 = 1.1\). Not sufficient.

Answer: E.


\(p_1*t_1>p_2*t_2\) --> 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
Show more

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.
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Leo can buy a certain computer for p1 dollars in State A, where the sa 29 May 2024, 07:46
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Bunuel

Orange08
Leo can buy a certain computer for p1 dollars in State A, where the sales tax is t1 percent,or he can buy the same computer for p2 dollars in State B, where the sales tax is t2 percent. Is the total cost of the computer greater in State A than in State B?
10
(1) t1 > t2
(2) p1t1 > p2t2


I chose B. However, OA is different. please explain.
You can solve this question algebraically, but number plugging is easier here.

Total cost = p*(1 + t/100).

(1) \(t_1>t_2\)

No information about the prices. Not sufficient.

(2) \(p_1*t_1>p_2*t_2\)

The dollar amount of tax is higher in A than in B. But if \(t_1 > 0%\) and \(t_2 = 0%\), then this holds for any positive \(p_1\) and \(p_2\). Still, this does not guarantee which total cost is higher. Not sufficient.

(1)+(2) Again, if \(t_1 = 10% > t_2 = 0%\) (statement 1), then \(p_1 * t_1 > p_2 * t_2 = 0\) (statement 2). But even with both statements, we cannot establish the relationship between the total costs in State A and State B. For example, if \(p_1 = p_2\), the total cost in A would be higher than in B, since B’s cost would be just \(p_2\) (as \(t_2 = 0%\)) and A’s cost would be \(p_1 * 1.1 = p_2 * 1.1\). However, if \(p_1 = 1\) and \(p_2 = 100\), the total cost in A would be lower than in B, since B’s cost would be \(p_2 = 100\) and A’s cost would be \(p_1 * 1.1 = 1.1\). Not sufficient.

Answer: E.
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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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Bunuel
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Leo can buy a certain computer for p1 dollars in State A, where the sa 29 May 2024, 08:12
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Bunuel

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Leo can buy a certain computer for p1 dollars in State A, where the sales tax is t1 percent,or he can buy the same computer for p2 dollars in State B, where the sales tax is t2 percent. Is the total cost of the computer greater in State A than in State B?
10
(1) t1 > t2
(2) p1t1 > p2t2


I chose B. However, OA is different. please explain.
You can solve this question algebraically, but number plugging is easier here.

Total cost = p*(1 + t/100).

(1) \(t_1>t_2\)

No information about the prices. Not sufficient.

(2) \(p_1*t_1>p_2*t_2\)

The dollar amount of tax is higher in A than in B. But if \(t_1 > 0%\) and \(t_2 = 0%\), then this holds for any positive \(p_1\) and \(p_2\). Still, this does not guarantee which total cost is higher. Not sufficient.

(1)+(2) Again, if \(t_1 = 10% > t_2 = 0%\) (statement 1), then \(p_1 * t_1 > p_2 * t_2 = 0\) (statement 2). But even with both statements, we cannot establish the relationship between the total costs in State A and State B. For example, if \(p_1 = p_2\), the total cost in A would be higher than in B, since B’s cost would be just \(p_2\) (as \(t_2 = 0%\)) and A’s cost would be \(p_1 * 1.1 = p_2 * 1.1\). However, if \(p_1 = 1\) and \(p_2 = 100\), the total cost in A would be lower than in B, since B’s cost would be \(p_2 = 100\) and A’s cost would be \(p_1 * 1.1 = 1.1\). Not sufficient.

Answer: E.
­
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.­
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Leo can buy a certain computer for p1 dollars in State A, where the sa 21 Apr 2025, 07:03
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Leo can buy a certain computer for \(p_1\) dollars in State A, where the sales tax is \(t_1\) percent, or he can buy the same computer for \(p_2\) dollars in State B, where the sales tax is \(t_2\) percent. Is the total cost of the computer greater in State A than in State B?


(1) \(t_1 > t_2\)

(2) \(p_1t_1 > p_2t_2\)
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in the question, arent we talking about same computer in different states. Hence the price before taxes could be same in both states and the tax is the only part that makes the difference. Hence both statements can answer and hence D
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Leo can buy a certain computer for p1 dollars in State A, where the sa 21 Apr 2025, 07:56
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RudraaDS
Orange08
Leo can buy a certain computer for \(p_1\) dollars in State A, where the sales tax is \(t_1\) percent, or he can buy the same computer for \(p_2\) dollars in State B, where the sales tax is \(t_2\) percent. Is the total cost of the computer greater in State A than in State B?


(1) \(t_1 > t_2\)

(2) \(p_1t_1 > p_2t_2\)
in the question, arent we talking about same computer in different states. Hence the price before taxes could be same in both states and the tax is the only part that makes the difference. Hence both statements can answer and hence D
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The computer is the same, but the question does not say the price before tax is the same in both states. It's common for the same item to have different base prices in different locations.

That’s why we cannot assume p1 = p2, and without knowing both base prices and tax rates, we cannot determine which total cost is greater.

So, your assumption that the base prices must be the same is not supported by the question and that’s exactly why E is correct, not D.
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