Christian has 13 coins in his pocket. The total value of the change is $1.37. The change may be composed of pennies, nickels, dimes and quarters. How many dimes could be in Christian’s pocket?

A) 0

B) 3

C) 5

D) 7

E) 9

There are several ways to approach this problem. Many of them are wrong. That’s because the core problem (13 coins, $1.37) can be solves several different ways. If you approached this and just decided to solve it you might find two or three solutions before you found one that was in the answer choices. That’s the first important step. When you’re given a problem without a clear, obvious and quick solution look to the answer choices.

Once, we’ve decided that we’re going to work through the answer choices, there is still some uncertainty. Look at answer choice B for instance. Even if we know that we have 3 dimes, that still doesn’t sort out how many pennies, nickels and quarters we have. That brings us to tip number two: when you’re given complex information, look for opportunities to simplify. The best example of that in this case is the pennies. Because our total needs to end in a 7, and all the other coins can only get us multiples of 5, we know that we must have either 2 or 7 pennies in order to make this work. That makes quick work of checking the possibilities for answer choice B. If we have 3 dimes and 2 pennies, can we make $1.05 out of 8 coins? Well, quarters can only get us to multiples of 25, so we must have at least one nickel so we can simplify again. Can we make $1.00 composed of quarters and nickels? Nope. Doesn’t work. Test 3 dimes and 7 pennies and you’ll very quickly see that you can’t make $1.00 out of 3 of the coins we’re given.

The final tip is that challenging problems don’t need to be tough. If you went into this and said I’m not sure how to solve this, but I can work from the answer choices and I can simplify problems, you might have started by testing answer A.

If I don’t have any dimes, I might have exactly 2 pennies. If that’s the case I have 11 coins to make $1.35. I need at least 2 nickels, so now I have 9 coins to make $1.25. 4 quarters and 5 nickels would work. Done. Answer choice A is correct. (You can also make this work with 0 dimes and 7 pennies).

When you don’t know where to start, look at the answer choices and look to simplify.

7 pennies, 1 nickel, 0 dimes, 5 quarters