Does 3 Equal 11?

It can, if you know how to do a few tricks with algebra. Why point this out? If you aren’t paying attention, you can be tricked into believing all sorts of crazy things, from financial scams like the one that Bernie Madoff pulled to the latest conspiracy theory. In the end however, logic and reason usually prevail. In the meantime, brush up on your high school math skills for a moment and examine the following:

Given that a = b

  1. 3a = 3b and 11a = 11b
  2. Multiply by a on both sides, 3a^2 = 3ab
  3. Multiply by b on both sides, 11ab = 11b^2
  4. Subtract the above equation from the one in step 2, 3a^2 – 11ab = 3ab – 11b^2
  5. Subtract 3ab and add 11ab to both sides, 3a^2 – 3ab = 11ab – 11b^2
  6. Add ab and subtract b^2 from both sides, 3a2 – 3ab + ab – b^2 = 12ab – 12b^2
  7. Factor out common factors, 3a(a-b) + b(a-b) = 12b(a-b)
  8. Divide both sides by a-b, 3a + b = 12b
  9. Subtract b from both sides, 3a = 11b
  10. Substitute a for b, remembering that they are equal, 3b = 11b
  11. Remove common terms and 3 = 11

Did you see that? Three DOES equal eleven? … Ha ha! It really didn’t matter which numbers I used so long as they were different. I could just as easily made $12 equal $300 million. Where does this simple equation go wrong? When we “factor out the common items” in step 7, we’re actually dividing by zero and any one who passed 5th grade math can tell you that dividing by zero is a big mathematical NO-NO.

But it’s easy to get caught up in the moment and overlook that step because the rules violation is hidden. What’s always odd is that sometimes the most important, most common sense rule can get obscured by technical mumbo-jumbo, quickly glossed over, and ignored by someone who should know better.

Such is the case with most scams. They lure us in with an outrageous claim (“make $50,000/yr stuffing envelopes at home!”) just like the 3 = 11 title. Then they convince us that we really can “buy a home with no money down,” or “join this multi-level marketing ‘business’ and become rich in 12 months,” or even “I am a Nigerian prince who needs to hide $700 million in your bank account for a few days.”

But, if you’ll take your time, examine the claims slowly and with a discriminating eye for detail, you will usually find that one fatal flaw. Or you could use the old pessimist’s rule: if it sounds too good to be true, it probably is.

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