Here's hoping someone can please help explain these to me!

Question 1

**Quote:**

Leo can buy a certain computer for p1 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) \(p_1t_1 > p_2t_2\)

I've seen this posted a few times, but it appears that a lot of people assumed that \(P_1\) and \(P_2\) have the same price and incorrectly approached the question. \(P_1\) and \(P_2\) are different prices, so (2) is not just looking at the taxes. I read the answer and I understand it for the most part. I get that (1) is Insufficient, because we have no idea what \(p_1\) and \(p_2\) are. But when I get to (2) and when I want to try to combine (1) and (2), how do I effectively pick numbers to test? And when combined, Is there some kind of rule that I can use to come to a conclusion?

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Question 2

**Quote:**

The annual rent collected by a corporation from a certain building was x percent more in 1998 than in

1997 and y percent less in 1999 than in 1998. Was the annual rent collected by the corporation from the

building more in 1999 than in 1997?

(1) \(x > y\)

(2) \((xy) / 100 < x - y\)

I tried to read the answer to this one, but I just don't understand this one at all.

Let A be the annual rent collected in 1997. Then the annual rent collected in 1998 is \((1 + (x/100)A\) and the annual rent collected in 1999 is \((1+ (x/100))(1-(y/100)A\). Determine if \(A(1+ (x/100))(1-(y/100) > A\). Okay, I get that, so far... but then they say: or equivalently, if \((1 + x/100)(1 - y/100) > 1\). Huh? Why did the A's disappear, and where did that 1 come from? Can someone please explain this to me? Beyond that, I'm completely lost with (1) and (2). I'd appreciate if someone could really hold my hand on this one. I tried Googling this questions, but I still don't understand the explanations.

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Question 3

**Quote:**

The price per share of Stock X increased by 10 percent over the same time period that the price per share of Stock Y decreased by 10 percent. The reduced price per share of Stock Y was what percent of the original price per share of Stock X ?

(1) The increased price per share of Stock X was equal to the original price per share of Stock Y.

(2) The increase in the price per share of Stock X was \(10/11\) the decrease in the price per share of Stock Y.

I read the answer and kind of understood it. But I thought that with these types of DS problems, solving for either x or y would be sufficient. In this case, I need to find the value of \(y/x\). How do you come to the conclusion that you're solving for \(y/x\) instead of just y or x?

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Question 4

**Quote:**

89. Is the number of members of Club X greater than the number of members of Club Y ?

(1) Of the members of Club X, 20 percent are also members of Club Y.

(2) Of the members of Club Y, 30 percent are also members of Club X.

Couldn't get this one at all, even after reading the answer.