Data Sufficiency

Can an instructor chyme in on this? I cannot understand anyone's answer explanation. I think B is sufficient bc it gives the price and tax rate of both and says that one is greater than the other.

p1,p2 and t1,t2 are unknowns

Statement 1:

Unless you know the exact value of p1 and p2 ,t1 > t2 doesn't conclude anything. INSUFFICIENT

Statement 2:

Unless you know the exact value of p1 and p2 ,p1t1 > p2t2 doesn't conclude anything. INSUFFICIENT

Combining also we can't predict about p1 and p2 individually( Test with Examples)

Rastis wrote:Can an instructor chyme in on this? I cannot understand anyone's answer explanation. I think B is sufficient bc it gives the price and tax rate of both and says that one is greater than the other.

I read the question the same way! The book says "Is the Total Cost of the computer greater in State A than State B. Therefore I would thought it was referring to P and T... since Total cost seems like that would included tax... but the only way I can rationalize OA being E is if this is misinterpreted. Maybe just poorly worded

We cant find the answer until we dont know the value of P1 & P2

E is the correct answer

S1: Definitely not sufficient

100 = p1, t1 = 10 => price = 110
200 = p2, t2 = 5 => price = 210

S2: A: p1*(1+p1t1/100) B: p2*(1+p2t2/100)
If p1t1 > p2t2 does not imply that the expression will also follow the same rule

Comb:
Does not yield anything

(E) is answer

Good One !

Found by substituting values.

Ans E

I did nt get the question rgt.. I presumed total cost includes both cost of computer and the tax..

@ Ganesh

STATEMENT a IS INSUFFICIENT BECAUSE WE DONT HAVE THE EXACT VALUES FOR COST AND TAX

MOVING FORWARD FOR STATEMENT B;

city 1: cost 100, tax 10%
cost*tax= 100x(10/100)=10--------------(i)

city 2:cost 1000, tax 5%
cost*tax=1000x(5/100)=50--------------(ii)

(i) < (ii) as per statement B

so (E) insufficient

E for Answer.

CASE I:

P1=10,t1=1 P2=10,t2=0.5

Here, P1=P2,t1>t2 and (P1)*(t1)>(P2)*(t2) and (total cost in state A) > (total cost in state B)

CASE II:

P1=10,t1=1 P2=20,t2=0.25

Here, P1>P2,t1>t2 and (P1)*(t1)>(P2)*(t2) and (total cost in state A) < (total cost in state B)

Let the base price of computer is x.
Leo can buy a certain computer for p1 dollars in State A, where the sales tax is t1 percent.
p1 = x+x*(t1/100)
simillarly
p2 = x+x*(t2/100)

Now p1/p2 = (100 +t1)/(100 + t2)

1) t1>t2 , then p1 >p2 . SUFFUCIENT
2) p1t1 > p2t2 ==> p1/p2 > t2/t1 . we do not know t2/t1. so INSUFFICIENT

Ans is A.

Can any expert comment on this solution ?

sks74 wrote:Let the base price of computer is x.
Leo can buy a certain computer for p1 dollars in State A, where the sales tax is t1 percent.
p1 = x+x*(t1/100)
simillarly
p2 = x+x*(t2/100)

Now p1/p2 = (100 +t1)/(100 + t2)

1) t1>t2 , then p1 >p2 . SUFFUCIENT
2) p1t1 > p2t2 ==> p1/p2 > t2/t1 . we do not know t2/t1. so INSUFFICIENT

Ans is A.

Can any expert comment on this solution ?

The statement in red is incorrect.
Each state has a DIFFERENT base price.

State A:
Base price = p�.
Tax = (t�/100)p�.
Total cost = p� + (t�/100)p� = p�(1 + t�/100).

State B:
Base price = pâ‚‚.
Tax = (tâ‚‚/100)pâ‚‚.
Total cost = pâ‚‚ + (tâ‚‚/100)pâ‚‚ = pâ‚‚(1 + tâ‚‚/100).

Question: Is p�(1 + t�/100) > p₂(1 + t₂/100)?

For this problem, plugging in values seems easier and faster.
I posted a complete solution here.

https://www.beatthegmat.com/og-12-ds-79-t116694.html

In the question it states Leo can buy certain computer at some price in State A and different price in State B, hence IMO it implies price P1 & P2 are inclusive of taxes T1 & T2. There is some base "price" P of computer which is independent of tax. Thus,
P + P*(T1%/100)= P1 or P + Pt1 = P1
P + P*(T2%/100)= P2 or P + Pt2 = P2

Now, as per statement 1
t1 > t2 this will imply p1 > p2
hence sufficient

Statement 2
p1t1 > p2t2
thus replacing p1 and p2
pt1 + p(t1^2) > pt2 + p(t2^2)
t1 + t1^2 > t2 + t2^2
implies t1 > t2
same as statement 1

thus sufficient!

IMO both are sufficient!

GMATGuruNY wrote:

sks74 wrote:Let the base price of computer is x.
Leo can buy a certain computer for p1 dollars in State A, where the sales tax is t1 percent.
p1 = x+x*(t1/100)
simillarly
p2 = x+x*(t2/100)

Now p1/p2 = (100 +t1)/(100 + t2)

1) t1>t2 , then p1 >p2 . SUFFUCIENT
2) p1t1 > p2t2 ==> p1/p2 > t2/t1 . we do not know t2/t1. so INSUFFICIENT

Ans is A.

Can any expert comment on this solution ?

The statement in red is incorrect.
Each state has a DIFFERENT base price.

State A:
Base price = p�.
Tax = (t�/100)p�.
Total cost = p� + (t�/100)p� = p�(1 + t�/100).

State B:
Base price = pâ‚‚.
Tax = (tâ‚‚/100)pâ‚‚.
Total cost = pâ‚‚ + (tâ‚‚/100)pâ‚‚ = pâ‚‚(1 + tâ‚‚/100).

Question: Is p�(1 + t�/100) > p₂(1 + t₂/100)?

For this problem, plugging in values seems easier and faster.
I posted a complete solution here.

https://www.beatthegmat.com/og-12-ds-79-t116694.html

Hi,
Sorry for the trouble, but I have a query here. In the question it is mentioned that the computer can be bought at P1 & P2 in different states. Thus shouldn't it mean that P1 or P2 is the final price being paid and base price is same (reflected from the phrase "same computer"), only difference being tax?

tarangchhabra wrote:Sorry for the trouble, but I have a query here. In the question it is mentioned that the computer can be bought at P1 & P2 in different states. Thus shouldn't it mean that P1 or P2 is the final price being paid and base price is same (reflected from the phrase "same computer"), only difference being tax?

That's a reasonable objection, but you can't assume that the same computer has the same price in two different states - if I want to buy an iMac in California, it might cost more would than the same iMac in, say, Guangzhou. The fact that the question denotes the prices under separate names is cause to doubt that the price is necessarily the same (though it certainly COULD be).

IMO E.