SAT Math question
Some of you guys may have seen this already if you got the practice booklet for the PSAT/NMSQT. I can get the answer to this question through a long process, but is there any quick way to do this?
How many positive integers less than 1,000 do NOT have 7 as any digit?
The answer is 728.
September 20, 2011
2 Comments • Newest first
Thanks a ton!
The answer is 728 because it's (9^3) - 1. The way I solved it was by thinking of the 3 digits as separate. In each digit there are 9 different options (usually 10, but 7 isn't allowed). It becomes 9 x 9 x 9 for all the different numbers, but because it has to be a positive integer we have to exclude 0, therefore there would be (9X9X9) - 1 different options, AKA 728.