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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]  29 Apr 2006, 22:08
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68% (02:08) correct 31% (00:48) wrong based on 3 sessions
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
[Reveal] Spoiler: OA
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E for me 2
t1 > t2 gives us nothing))
p1t1 > p2t2 only tells us about tax amount in dollars
so E it is
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Agree with E
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E
which one is greater???

p1 + p1t1/100 OR p2+p2t2/100

St1: No info about p1 and p2:Clearly INSUFF

St2: no individual info about p1 and p2.: INSUFF

Together: Still INSUFF
Less for state A if p1 = 20 , t1=10, p2= 199, t2=1
Higher for state A if p1 = 20, t1=10, p2 = 15, t2 = 5
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p1 is the total cost in state A. thus this will include tax t1 in it. thus p1 + p1t1/100 does not mean anything.

p1 = Cost of PC(1+t1/100).

similarly for p2.

Combining statement 1 and 2, we can see that
so the stmt p1t1 > p2t2, will hold if p1 = p2, p1 > p2 and p1>p2t2/t1
here t2/t1 will be a fraction less than 1.
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E as well
The cost of the computers are not known, only the sales tax
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OA is E .. Great job people !
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Re: Leo computer - DS [#permalink]  23 Aug 2006, 22:31
gmatornot 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
.

Qstem: p1+P1*t1/100 > p2+P2*t2/100
Qstem: p1(1+*t1/100) > p2(1+t2/100)

(1) t1> t2
BCE

(2) p1t1>p2t2
dont know abt p1,p2
CE

(1)&(2)
E

Heman
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(E) for me

The final prices are definied by:
o p1*(t1 + 1)
o p2*(t2 + 1)

Stat1

o If p1=p2,
t1 > t2
=> t1 + 1 > t2 + 1
=> p1(t1+1) > p1(t2+1) = p2(t2+1) >>> The final price of A i superior to the final price of B

o If p2 = 100*p1 and t1 = 100*t2 (t1 > t2), we have
p2*(t2+1)
= p2*t2 + p2
= 100*p1*t1/100 + 100*p1
= p1*t1 + 100*p1 > p1*(t1 + 1) >>> The final price of B i superior to the final price of A

INSUFF.

Stat2
p1*t1 > p2*t2 brings nothing more alone.

o If p1 = p2, we have the same case as above. The final price of A is superior to the finale price of B.

o If t2 = 0,01 and t1 = 1 and p1 = 10 and p2 = 100, then we have:
- p1*t1 = 10 > p2*t2 = 0,01*100 = 1
- p1*(t1+1) = 20 < p2*(t2+1) = 101 .....The final price of B is superior to the finale price of A.

INSUFF.

Both (1) and (2)
The 2 cases just above remain right.

Last edited by Fig on 28 Jan 2007, 23:52, edited 2 times in total.
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Re: DS - Percents (Tough one) [#permalink]  28 Jan 2007, 17:36

Last edited by devilmirror on 28 Jan 2007, 20:23, edited 1 time in total.
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Re: DS - Percents (Tough one) [#permalink]  28 Jan 2007, 19:52
TOUGH GUY 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.

One more for E.

Q is P1 + (P1T1/100 ) > P2 + (P2T2/100)

Stmt 1) we cant say about P1 and P2

Stmt2 ) P1T1 > P2T2 from this also we cant say about P1 and P2.

Combining together also we can not say about P1 and P2 values

SO E.
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E ?

Cost in state A is P1 + P1t1/100
Cost in state B is P2 + P2t2/100

stat 1 t1 > t2

P1 <<P2>> P2 will give different results

stat2 P1t1 > P2t2

it is possible to find sets of t1, t2 & P1,P2 such that this condition is satisfied and cost A > Cost B or otherwise

P1 = 100
t1 = 50

P2 = 300
t2 = 1

p1t1 = 50, p2t2 = 30

but cost A = 150, cost B = 303
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Without knowing p1 and p2 (or the relation between them) it is not possible to see which is greater.
So E.
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Re: DS - S26 q20 [#permalink]  12 Jun 2008, 06:54
mrwaxy 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

Detailed explanation will be appreciated.

IMO - E
Price in state A = p1+(p1t1)/100
Price in state B = p2+(p2t2)/100

(1) alone is not sufficient, since we do not know p1 and p2
(2) alone is not sufficient again since we do not know about p1 and p2 or t1 and t2 individually. Pick -

p1 = 100
t1=10%
p2=110
t2=1%
In this case -> p1t1 >p2t1 but cost in state B is more where as in below example cost in state A is more -

p1 = 100
t1=20%
p2 = 110
t2 = 1%

Combining both - still does not give the answer.

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Re: DS - S26 q20 [#permalink]  12 Jun 2008, 08:49
mrwaxy 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

Detailed explanation will be appreciated.

statement 1 does not define what is p1 and p2 hence we cannot solve it further to derive the conclusion whether the total cost of the computer greater in State A than in State B
so statement 1 is insufficent

statement 2 tells us that p1t1 > p2t2, therefore we can conclude that the total cost of the computer is greater in State A than in State B
try plugging in some numbers to confirm
let us say p1 and p2 is 100 and 200
and t1 =10% and t2=9 %
since it is given p1t1 > p2t2

therefore we can conclude that price is given by 110<218

combining both statements dont help

what is the OA for this one

HTH
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Re: DS - S26 q20 [#permalink]  17 Jul 2008, 01:16
OA : E

I was looking on how to solve this question. Thanks for the input
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Re: GMAT Set 27 - 20 [#permalink]  23 Nov 2008, 07:00
I would say E
1) is insuff because the tax itself does not define the total cost.
2) is insuff because p1t1 and p2t2 are the actual taxes applicable, but do not gve suficient info about p1 and p2.
together insuff as well, e.g.
t1=10, t2=5, p1t1=100, p2t2=50 => p1=1000 , p2 =1000 => p1=p2
t1=4, t2=3, p1t1= 80, p2t2=30 => p1=2000, p2=1000 => p1 > p2
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Re: GMAT Set 27 - 20 [#permalink]  23 Nov 2008, 08:30
Yep, OA E. Thank you sapnaprakash!
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Re: Leo's case from OG problems [#permalink]  02 Nov 2009, 13:07
Hi fellows,

Found a problem in OG but did not accept the ans or the solution either. Here it is:
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 rate is t2 percent. Is the total cost of the computer greater in State A than in state B?
1. t1 > t2
2. p1t1 > p2t2

Now let me tell u my problem, if the question is about the total cost of the same computer with in states, and p1 and p2 is post sales tax amounts, shouldn't we assume the basic cost to be the same?

No we can not assume that.
Let
p1=100 and t1=33% then pre-tax amount of p1 is 75
p2=90 and t2=12,5% then pre-tax amount of p2 is 80
You can see that we can not assume anything.

Then lets come to the question.
1) insuff.
As you see t1 and t2 comparison gives us nothing.
2)insuff.
p1t1 and p2t2 shows us the approximate tax amounts. But unfortunately it does not give us something.
p1=100, t1=20; p2=90, t2=15 or
p1=80, t1=20; p2=90, t2=15

Together insuff
let
t1=20
t2=15
there can be 2 types possibilities that makes the comparison true.
p1=100 p2=80 p1>p2
p1=89 p2=90 p2>p1
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Re: Leo's case from OG problems [#permalink]  02 Nov 2009, 18:27
Hi fellows,

Found a problem in OG but did not accept the ans or the solution either. Here it is:
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 rate is t2 percent. Is the total cost of the computer greater in State A than in state B?
1. t1 > t2
2. p1t1 > p2t2

Now let me tell u my problem, if the question is about the total cost of the same computer with in states, and p1 and p2 is post sales tax amounts, shouldn't we assume the basic cost to be the same?

No, one should not assume the basic cost is the same (at least not for the GMAT) unless it says so. In reality, the prices of items do differ between two states (before tax). The question just states the computers are the same, but not necessarily the price.
Re: Leo's case from OG problems   [#permalink] 02 Nov 2009, 18:27
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