GMAT Question of the Day – Problem Solving – Puzzle 2
If the sum of the digits of 10^42 – x is 368. Which of the following could be a value of x?
GMAT Question of the Day Solution
The GMAT scientists love to use powers of 10 because powers of 10 have some specially qualities. Here is one: they always follow the format of a 1 followed by a number of zeroes (depending on the exponent). Also, when you subtract an integer from a power of 10 you get some predictable things happening. See the diagram below.
If you are subtracting a three digit integer then the number of 9’s is x-3. So it’s x minus the number of digits you are subtracting, Of course you could be subtracting a number that would produce 9’s on its own such as 11 in which case you would have an extra 9. So what’s the point of all this? Well, this question is all about the 9’s. 10^42 – a 2 digit integer produces 40 9’s digits. Add those up and you get 360. We know that the digits of our expression sum to 368 so that means that the last two digits must add up to 8. You can try each of the answer choices to test which integer will produce 8 or use a little algebra.
Additional GMAT Units Digit Practice Questions
Here is a units digit question from the GMAT Official Guide: If n = (33)^43 + (43)^33 what is the units digit of n?
Here is a slightly more challenging version of that units digit question from GMAT Question of the Day with an important twist. Make sure you follow through with all of you basic math rules.
Here’s a digits Data Sufficiency Example from GMAT Question of the Day It’s got a bit more going on but also good digits practice.