rekhabishop wrote:
Carcass wrote:
Which one of the following is closest to 1?
A. \(\frac{3}{3+0.3}\)
B. \(\frac{3}{3+0.3^2}\)
C. \(\frac{3}{3-0.3}\)
D. \(\frac{3}{3-0.3^2}\)
E. \(\frac{3}{3+0.33}\)
This came out to be a 4th decimal place thriller. I know we can do it with a calculator but how to do it manually? I could eliminate all others except B and D.
We shouldn't need a calculator here, though it goes quick if you use it. Since all the numerators are 3, we want the denominator that is closest to 3. This eliminates A, C, and E, as you've done. Now let's look at the denominators of B and D:
B: 3.09
D: 2.91
The trick here is to realize that they are both 0.09 away from 3, but 0.09 is a greater percentage of 2.91 than it is of 3.09. 0.09 is exactly 3% of 3. 0.09 is less than 3% of 3.09, though, and more than 3% of 2.91. Proportionally speaking, then, it's easier for 3.09 to move down to 3 than it is for 2.91 to move up to 3.
The better way to think about this, though, is to use easier examples. Say instead of adding or subtracting 0.09, we added or subtracted 2. So:
B = \(\frac{3}{3+2} = \frac{3}{5}\)
D = \(\frac{3}{3-2} = \frac{3}{1}\)
Now B is only 0.4 away from 1, while D is a full 2.0 away from 1. This is because the denominator, 1, in D, has to triple itself to reach the numerator, 3. The denominator of B, though, 5, doesn't even have to halve itself to get to the numerator, 3. So that shows the same concept on a bit larger scale. This kind of reasoning by analogy can be extremely helpful when dealing with GRE problems you aren't quite sure about.