A 2 min read

The difference 942 − 249 is a positive multiple of 7. If a, b, and c are nonzero digits, how many 3-digit numbers abc are possible such that the difference abc − cba is a positive multiple of 7?

Does the bolded part of this hard official question help you answer the question, or does it make it harder?

If you were to ask me, this information helps you – since it helps you visualize the given scenario.  Now is it required information? Absolutely not; but is it there to scare you – absolutely not again!

Here is why I say so:

We can solve this question by drawing the following inferences step by step and we do not really need the shaded information for the solution: 

1. Translation –> “abc-cba is + multiple of 7” à (100a + 10b + c) – (100c + 10b + a) is a multiple of 7.
   1. This leads to à 99 (a-c) is a multiple of 7.
2. Inference –> a – c is a multiple of 7.
3. Processing
   1. Since a and c are single digits, possible values are (9,2), (8,1), (1,8), (2,9).
   2. But since a – c is a positive multiple, only (9,2), (8,1) are possible values.
4. Final Calculation
   1. b can take any of the 9 values
   2. For a and c only 2 combinations are possible.
   3. So total 9 x 2 = 18 sets.

As you can see, in the entire solution, we did not use the bolded “The difference 942 − 249 is a positive multiple of 7” part at all. 

Now while some may say that this part adds to the difficulty level, I say that it actually helps since it helps you visualize the expression “abc – cba”.  Observe that it shows a case in which a = 9, b = 4, and c = 2 so that you do not need to do that explicit step yourself to understand the expression abc – cba.

What is the takeaway?

So, whenever you see some information that may seem confusing, think a bit deeper – TRUST your skills and TRUST the test maker.  Process information one bit at a time.  Think about every bit of information in the question to have a purpose.  Sometimes that purpose may be to help you visualize information or puts things in context.