Some Xs are Ys

Just occasionally you get a question like the following:

Some bings are bangs. All bangs are bongs. Which of the following can we conclude?

  1. All bings are bongs.
  2. All bongs are bings.
  3. Some bings are bongs.
  4. No bongs are bings.
  5. No bongs are bangs.

Each statement in the question can be rewritten in some form so that it points the other way. For instance, stating Some bings are bangs can be rewritten as Some bangs are bings but not necessarily all. Similarly, the statement All bangs are bongs can be rewritten as There are some bongs which are bangs (in fact, that statement does not take into account the fact that being a bang automatically makes you a bong, but that is already encoded in the original statement).

Since we have been told "Some bings are bangs", we can also add the statement It is possible to be a bing without being a bang. Adding these statements to our repertoire gives the following set of statements.

Some bings are bangs. All bangs are bongs. Some bangs are bings but not necessarily all. There are some bongs which are bangs. It is possible to be bing without being a bang.

We will compare each statement in turn with this repertoire. If we find a statement that is in direct contradiction with these, then we know that statement cannot be true. If we find a statement that essentially duplicates one the statements in the repertoire, then that statement must be true (i.e. that will be the answer to the question)

If you do this you will see that the only that works entirely is (C) - "Some bings are bongs." Since being a bang automatically qualifies you as a bong, and since some bings are bangs, then those particular bings must be bongs.

An alternative method - visualise!

An alternative is to visualise these made up things using words that you already know. Try replacing "bings" with "men", "bangs" with "police officers" and "bongs" with "working people" gives the following:

Some men are police officers. All police officers are working people

Does this make sense? Yes, there are no inconsistencies there - it agrees with what we know about the world. Let's rewrite the possible answers in the same form:

  1. All men are working people - No, not true.
  2. All working people are men - Clearly not, women work as well!
  3. Some men are working people - Yes, this seems reasonable.
  4. No working people are men - No!
  5. No working people are police officers - Again, not true!

We can see again that the correct answer must be (C). Of course, you have to be careful when assigning the unknown objects to things you already know. You couldn't replace "bings" with "humans" and "bangs" with "mammals" as the first statement would become "Some humans are mammals." Well, clearly, all humans are mammals!

Of course, this method doesn't always work - no analogy may present itself, and you shouldn't take time hunting around for one (in GMAT exams, time is the perpetual enemy!) However, if an every-day analogy immediately becomes obvious, don't hesitate to use it.