OG #79

[Reft]

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 great in State A than in State B?

(1) t1 > t2

(2) p1t1 > p2t2

OA: E


I approached this problem by substituting easy to work with numbers, and seemed to come up with the wrong answer. Apparently, even though substituting numbers works for one of the statements, the actual answer is found by trying to determine if p1(1+t1/0) is greater than p2(1 +t2/100)

What do those equations even mean? I'm so lost.

[Rahul@gurome]

We need to find whether p1(1 + t1/100) > p2(1 + t2/100) or p1(100 + t1) > p2(100 + t2)?
or 100.p1 + p1.t1 > 100.p2 + p2.t2 implies 100(p1 - p2) + (p1.t1 - p2.t2) > 0 ?

(1) t1 > t2 does not imply if 100(p1 - p2) + (p1.t1 - p2.t2) > 0 or not.
So, (1) is NOT SUFFICIENT.

(2) p1.t1 > p2.t2 implies (p1.t1 - p2.t2) will be a positive value. But again we don't know whether (p1 - p2) is positive or negative.
So, (2) is NOT SUFFICIENT.

Combining (1) and (2) also we cannot determine whether 100(p1 - p2) + (p1.t1 - p2.t2) > 0 or not.

[spoiler]The correct answer is (E).[/spoiler]

[barcebal]

I understand why you could get lost here. It's important to look at the question they ask in order to solve ALL DS questions.

They want to know, is the TOTAL cost greater in state A than in state B. Let's write that as an equation.

Before we do that, let's understand the following:

The total cost of a computer is it's pre-tax cost + it's pre-tax cost*tax rate.

For example a computer that costs $100 pre-tax at a 6% tax rate will cost $100 + .06*100=$106.

An easier way to think of that equation is as follows

Total cost with tax of a computer= (pre-tax cost)(1+tax rate).

With our example above, we would find that the total cost with tax = 100*(1+.06) = 100*(1.06) = $106

So with that in mind let's write the equation to the question posed, is the total cost of the computer greater in A or B?

Total Cost of A= p1(1+t1/100)
Total Cost of B= p2(1+t2/100)

So is p1(1+t1/100) > p2(1+t2/100)? This is the expression that is equivalent to the question.

Now let's go through the problem:

If t1>t2 is the total cost of the computer great in State A than in State B?

This cannot be determined. If the tax rate (t1) for State A is 10% and the tax rate (t2) for State B is 0% and the computers pre-tax cost is the same, then State A > B. But let's say that pre-tax A costs (p1) $100 and B costs (p2) $200, then the tax rate of State A isn't high enough to make A > B. Thus, Statement (1) is not sufficient.

Statement (2)
We have the same problem as statement one. Just because pre-tax cost of A is > than pre-tax cost of B doesn't mean that the total cost will be more. If the tax rate is 0% in both states A>B but let's say the computer in State A has a pre-tax of 100 and State B has a pre-tax cost of 99. If State A has no sales tax and B has a 50% tax rate, then B>A. The statement isn't strong enough to answer the question.

TAKEN TOGETHER:

If the pre-tax cost of the computer in A AND its tax rate are greater than BOTH the pre-tax cost and the tax rate of B then it's impossible to have B>A. For example if A is $100 and 10% tax rate and B is $99 and a 9% tax rate then 100(1.1)>99*(1.09) so A must be greater than B at all times which answers the question is A>B.

Together we can solve. Answer is C.

Hope this helps.