Let’s say you’re faced with the following quantitative comparison problem:
Column A: 20 / sqrt(10)
Column B: 10 / sqrt(5)
The first thing to note here is that since there aren’t any variables in this situation, you can eliminate D right off the bat. You can be sure that one of these numbers is always bigger than the other, and if you had infinite time you could figure out which. But you don’t have infinite time. What are you going to do?
You probably don’t know what the square root of 5 or 10 is off the top of your head, even approximately. And you won’t have a calculator to figure it out with. You could probably ballpark these, but that would take time. What are you going to do?
Think about it: if the number in A is bigger than the number in B, squaring the number in A will give a result larger than squaring the number in B. 3 is bigger than two, and 3 squared = 9 is bigger than 2 squared = 4. So if you square the numbers in both columns, then compare the squares, you’ll be able to infer which column is bigger. Let’s try it.
Column A: ( 20 / sqrt(10) ) squared = 400 / 10 = 40.
Column B: ( 10 / sqrt(5) ) squared = 100 / 5 = 20.
Since Column A squared turns out to be bigger than column B squared, Column A must have been bigger than Column B. So the answer is A.
There are many quantitative comparison questions where the quickest way to solve the problem is by doing the same thing to both sides. Be careful, though: If you’re working with negative numbers, you may run into trouble. Multiplying both columns by a negative number will reverse their relationship. For example, we know that
4 < 5
But if we multiply both 4 and 5 by -2, we get:
-8 > -10. The inequality has reversed. So this technique is best used when you’re sure you’re working with positive numbers.
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