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Leo can buy a certain computer for p1 dollars in State A

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Leo can buy a certain computer for p1 dollars in State A [#permalink] New post 05 Sep 2010, 05:58
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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?

(1) t1 > t2
(2) p1t1 > p2t2
[Reveal] Spoiler: OA
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Re: Total cost of computer [#permalink] New post 05 Sep 2010, 06:54
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Orange08 wrote:
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 think number plugging is better this time.

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

(1) t_1>t_2 --> no info about the prices. Not sufficient.

(2) p_1*t_1>p_2*t_2 --> amount of tax in $ is more in A than in B. Now if t_1>0% and t_2=0% then given statement works for any prices of computers (any positive p_1 and p_2). So not sufficient, to answer whether total cost of the computer greater in State A than in State B.

(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 from this we can not establish relationship between total cost of the computer in State A and in State B. For example if p_1=p_2, then total cost in A would be higher than in B (because total cost in B would be just p_2, as t_2=0% and in A would be higher than p_2=p_1 as t_1>0%), but if p_1=1 and p_2=100 then total cost in A would be lower than in B (because total cost in B would be p_2=100, as t_2=0% and in A would be p_1*1.1=1.1 as t_1=10%). Not sufficient.

Answer: E.
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Re: Total cost of computer [#permalink] New post 05 Sep 2010, 08:22
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

we don't know anything about a and b --> insufficient

Quote:
(2) ac > bd

all we know is that ac > bd ...again, we don't know anything about a,b,c,d individually--> insufficient

Quote:
(1) & (2) combined

again, we don't have any info about a and b --> Both statements together are also insufficient

-->
[Reveal] Spoiler:
E

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Re: Total cost of computer [#permalink] New post 21 Oct 2010, 09:29
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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Re: Total cost of computer [#permalink] New post 21 Oct 2010, 15:27
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gurpreetsingh wrote:
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.
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Total Cost [#permalink] New post 16 Nov 2010, 08:35
I have a more general question, but have an example to show what I am getting at. On the GMAT, for example, is it wrong to assume that Total Cost of a certain product includes tax?

Example from the OG 12th edition:
Data Sufficiency #79
Leo can buy a 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

[Reveal] Spoiler:
E


My rationale:
Statement 1 is insufficient right off the bat.
Statement 2 tells me that the total cost in State A is greater than State B, making is sufficient.

However, the official answer explains that there is no info given on the size of p1 or p2, making it insufficient. In my mind Total Cost is like the final price; all taxes, reductions, discounts, etc. included. Is it not safe to assume that tax should be included in Total Cost?
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Re: Total cost of computer [#permalink] New post 16 Nov 2010, 08:48
My bad Bunnuel, but thank you! I forgot to include what was given to me in statement 1 in my reasoning of statement 2, a common error (soon to be fixed!) of mine. Thanks again.
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Re: Total cost of computer [#permalink] New post 17 Feb 2011, 18:11
Bunuel wrote:
Orange08 wrote:
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 think number plugging is better this time.

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

(1) t_1>t_2 --> no info about the prices. Not sufficient.

(2) p_1*t_1>p_2*t_2 --> amount of tax in $ is more in A than in B. Now if t_1>0% and t_2=0% then given statement works for any prices of computers (any positive p_1 and p_2). So not sufficient, to answer whether total cost of the computer greater in State A than in State B.

(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 from this we can not establish relationship between total cost of the computer in State A and in State B. For example if p_1=p_2, then total cost in A would be higher than in B (because total cost in B would be just p_2, as t_2=0% and in A would be higher than p_2=p_1 as t_1>0%), but if p_1=1 and p_2=100 then total cost in A would be lower than in B (because total cost in B would be p_2=100, as t_2=0% and in A would be p_1*1.1=1.1 as t_1=10%). Not sufficient.

Answer: E.


Any tips on how to effectively pick numbers to test? Or are there any rules that I can use to come to a conclusion? My gut instinct was E, but there was a part of me that kept thinking "what if (1)+(2) presents a concept whereby A > B?" I tried picking numbers, but it was pretty cumbersome as I had zero logic when picking numbers to plug in.
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Re: Total cost of computer [#permalink] New post 28 May 2011, 10:22
Some how Im not comfortable with this question at all and more over the OG explanation is rubbish !!
Can some one explain me;
p1t1>p2t2

P1 1000 t1 = 5%
P2 1200 t2= 4%
50>48 and never 5000>4800 ( thats rubbish for me )

can someone explain this?
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Re: Total cost of computer [#permalink] New post 09 Sep 2011, 12:28
Answer is E. Had they said, p1t1+p1 > p2t2 + p2, that stmt would've been sufficient.
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Re: Numbers Question [#permalink] New post 17 Sep 2012, 20:04
dineesha wrote:
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

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.


We actually have to figure out that => p1 + (p1t1/100) > p2 + (p2t2/100)
from both options we know we can't conclude that above equation is valid or not. Hence, E is the answer.

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Re: Numbers Question [#permalink] New post 17 Sep 2012, 20:18
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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Re: Numbers Question [#permalink] New post 17 Sep 2012, 21:29
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dineesha wrote:
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!
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Re: Numbers Question [#permalink] New post 20 Jan 2013, 09:54
Bunuel wrote:
dineesha wrote:
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

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.


Merging similar topics. Please refer to the solutions above.


Hello Bunuel,

Ans is E for sure.
I would like to share my approach. Please let me know if this is correct.

St 1 Not sufficient but tells us t1>t2 ----> t1/t2 >1 or t2/t1<1 but greater than zero 0< t2/t1<1

St2 we get p1t1>p2t2 ----> p1/p2> t2/t1...Not sufficient alone.

Combining we get p1/p2 may be > or < 1 and therefore will give 2 solutions and hence will have to be E.

Ex let us say t1=20 and t2 =10, t2/t1 =0.5 < 1
and p1=600,p2 =1000 therefore p1/p2 > t2/t1 but Total price in each case will be

600+600*0.2 < 1000+1000*0.1 ----> 720< 1100

Second case,keeping same rate of t1 and t2 but taking p1 1100 and p2 1000, we get

1100+1100*0.2> 1000+1000*0.1.

We do get 2 different answers and hence E

Thanks
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Re: Leo can buy a certain computer for p1 dollars in State A [#permalink] New post 19 Nov 2013, 04:45
Hi All,
Am new to GMAT , so forgive me if my question sounds very basic.

I think A should be correct Answer.

Why can't we assume P1 as the base price of computer + tax on it. As the question says "Leo can buy a certain computer for P1 dollars in state A, where the sales tax is t1 percent". So it does sounds like P1 is the final cost.

If this is right than same goes for P2.

So,

Total price of computer = Base price of computer + tax incurred on it.

As Leo is buying same computer in state A and State B we can assume , that Base price of computer will remain same. So the differentiating factor will be whether the tax incurred is higher in state A or State B.

Following this line of thought i think A should be correct Answer . As it says t1 > t2 . We can easily say that total price in state A will be higher than State B.
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Re: Leo can buy a certain computer for p1 dollars in State A [#permalink] New post 19 Nov 2013, 04:50
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prabhakarsharma wrote:
Hi All,
Am new to GMAT , so forgive me if my question sounds very basic.

I think A should be correct Answer.

Why can't we assume P1 as the base price of computer + tax on it. As the question says "Leo can buy a certain computer for P1 dollars in state A, where the sales tax is t1 percent". So it does sounds like P1 is the final cost.

If this is right than same goes for P2.

So,

Total price of computer = Base price of computer + tax incurred on it.

As Leo is buying same computer in state A and State B we can assume , that Base price of computer will remain same. So the differentiating factor will be whether the tax incurred is higher in state A or State B.

Following this line of thought i think A should be correct Answer . As it says t1 > t2 . We can easily say that total price in state A will be higher than State B.


Note that this is a GMAT Prep question and the correct answer is E.

Also, note that that the prices p1 and p2 are NOT the same.
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Re: Leo can buy a certain computer for p1 dollars in State A [#permalink] New post 08 Apr 2014, 21:45
I also approached the problem in a manner similar to how prabhakarsharma (above) did. Since the problem states - Leo can buy a certain computer for p1 dollars in State A - I thought p1 was inclusive of taxes (price Leo has to pay for the computer) and since the computer is same, base price is same in both state A and state B.

Base price = C
Price in state A -> p1 = C(1 + t1/100)
Price in state B -> p2 = C(1 + t2/100)

Question -> Is p1 > p2
or p1- p2 > 0 ?
or (C+ Ct1/100 ) - (C + Ct2/100) > 0
or (t1 -t2) > 0

A) t1> t2
A is sufficient

B) p1t1 > p2t2
Insufficient.

How did people who get this correct, figure out that p1 and p2 are not inclusive of taxes?
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Re: Leo can buy a certain computer for p1 dollars in State A [#permalink] New post 14 Apr 2014, 07:45
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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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Re: Leo can buy a certain computer for p1 dollars in State A   [#permalink] 14 Apr 2014, 07:45
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