Official Guide DS#120

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Official Guide DS#120

#120 on the OG

This one provides information that is “%” and “%”….and then the question is asking about “%”. So in this case, it’s not about %’s and #’s. This one is entirely about %s. The above framework doesn’t let you speed through this one. Here is the question and a few pointers to speed thru:

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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 1998 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

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GMATPill Explanation
Recognize this question is asking you whether it’s possible to compare 1999 to 1997. Let’s see if we can by figuring out what they gave us first.

1998 = 1997(1+x/100)
1999 = 1998(1-y/100)

Be careful in laying this information out. You may have an inclination to say 1998= 1997 (1+x) but you need the divide by 100 because if you read the question carefully, it’s saying x percent. To convert to algebra terms you need the divide by 100. If you don’t, then the expression (1+x) might read (1+5)..and that would translate to 600% rather than the 1+5% = 1.05 that you are trying to use. So this is an important point. Divide by 100 in your expressions.

By substituting 1998 into the second equation we can get:
1999 = 1997(1+x/100)*(1-y/100)

So at least we know from the information they gave us, that we can compare 1997 to 1999. The problem is that it’s not yet solvable because it’s one equation with 2 unknowns.

Let’s check (1). We have x>y. Well, our equation above will become:
1999 = 1997 * (1+x/100-y/100-xy/10000)
Since x>y, we know that x-y>0…which is the same as x/100 – y/100 > 0. Great. That means:
1999 = 1997 * (1 + something positive – xy/10000). Still not enough info to solve since the unknown “xy” is still remaining.

Now we look at (2).
Going back to 1999 = 1997 *(1+x/100-y/100-xy/10000)
Using (2), we can get 0 This looks almost similar, but we can manipulate it. Since the left side is 0, just divide both sides by 100.

You get: 0/100 < x/100 – y/100 – xy/10000
or 0 < x/100 – y/100 – xy/10000
Going back to 1999 = 1997 *(1+x/100-y/100-xy/10000)
we can see that this is 1999 = 1997 * (1+ something greater than 0).
The equation is solved. (2) gets the answer so it’s B.

GMATPill vs Official Guide Explanation

Now, if you were to get an explanation from the Official Guide book itself, notice the difference in explanation depth and attack strategy compared to GMATPill’s explanation above. According to most students, the official guide explanations don’t really give them a good enough thought process to attack the question. And sometimes, it’s just difficult to follow.

For many students, the GMATPill explanation works a lot better.

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1. dhimaan
  
  [1] is not sufficient because for example if x is 20 percent and y is 18 percent then 1997>1999, however if x is 20 percent and y is 10 percent then 1999>1997, thus you get conflicting answers. [2] shows that for the expression to be true x must always be greater than y by a margin of 3.4 or greater if that margin is less than 3.4 than the expression doesn’t hold true. And for x-y margins 3.4 and greater (such as x is 20 percent and y is 16.6 percent) 1999>1997 always.