#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:
(2) xy/100 < x-y
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
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.