Leo can buy a certain computer for p1 dollars in State A : GMAT Data Sufficiency (DS)
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# Leo can buy a certain computer for p1 dollars in State A

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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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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. _________________ Intern Joined: 06 Jun 2009 Posts: 24 Followers: 1 Kudos [?]: 7 [2] , given: 4 Re: Total cost of computer [#permalink] ### Show Tags 05 Sep 2010, 08:22 2 This post received KUDOS 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 _________________ If you like my post, consider giving me a kudos. THANKS! CEO Status: Nothing comes easy: neither do I want. Joined: 12 Oct 2009 Posts: 2795 Location: Malaysia Concentration: Technology, Entrepreneurship Schools: ISB '15 (M) GMAT 1: 670 Q49 V31 GMAT 2: 710 Q50 V35 Followers: 224 Kudos [?]: 1595 [0], given: 235 Re: Total cost of computer [#permalink] ### Show Tags 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. _________________ Fight for your dreams :For all those who fear from Verbal- lets give it a fight Money Saved is the Money Earned Jo Bole So Nihaal , Sat Shri Akaal Support GMAT Club by putting a GMAT Club badge on your blog/Facebook GMAT Club Premium Membership - big benefits and savings Gmat test review : http://gmatclub.com/forum/670-to-710-a-long-journey-without-destination-still-happy-141642.html Math Expert Joined: 02 Sep 2009 Posts: 35867 Followers: 6840 Kudos [?]: 89958 [0], given: 10384 Re: Total cost of computer [#permalink] ### Show Tags 21 Oct 2010, 15:27 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. _________________ Intern Joined: 01 Nov 2010 Posts: 7 Location: NJ Schools: Rutgers MQF WE 1: 2 years IT Followers: 0 Kudos [?]: 1 [0], given: 0 Total Cost [#permalink] ### Show Tags 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? _________________ WE ARE! "Believe deep down in your heart that you're destined to do great things." - Joe Paterno You must learn to walk before you can run. Intern Joined: 01 Nov 2010 Posts: 7 Location: NJ Schools: Rutgers MQF WE 1: 2 years IT Followers: 0 Kudos [?]: 1 [0], given: 0 Re: Total cost of computer [#permalink] ### Show Tags 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. _________________ WE ARE! "Believe deep down in your heart that you're destined to do great things." - Joe Paterno You must learn to walk before you can run. Intern Joined: 29 Jan 2011 Posts: 24 Followers: 0 Kudos [?]: 4 [0], given: 2 Re: Total cost of computer [#permalink] ### Show Tags 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.

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]

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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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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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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.

Cheers!
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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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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!
P.S. - Always try to substitute few values and test in these kind of scenario based questions.
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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
Mridul
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Re: Leo can buy a certain computer for p1 dollars in State A [#permalink]

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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]

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19 Nov 2013, 04:50
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]

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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]

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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]

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25 Nov 2014, 16:44
dipsy001 wrote:
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?

In your explanation the base price C seem to be equal in both states, but the problem doesn't say whether the base price is the same or not
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