IMAT 2011 Q40 [Rats and People]

Consider the following statements:

  1. There are fewer rats than people.
  2. There are not more people than rats.
  3. There are at least as many rats as people.
  4. There are not more rats than people.

Which two of the above statements are equivalent?

A. 1 and 3

B. 1 and 4

C. 2 and 3

D. 2 and 4

E. 3 and 4

This is a unique type of problem solving. The best approach is to make each into a simplified statement using variables and then seeing which are equivalent.

Let p be for people and r for rats. Keep an eye out for answers that are greater to or equal. We can distinguish these apart because it says “at least as many” or “not more”, so there can be just as many or less/more.

  1. r < p

  2. p ≤ r

  3. r ≥ p

  4. r ≤ p

\fcolorbox{red}{grey!30}{Now we can easily see that statement 2 and 3 are the same, therefore C is the answer.}