While some of you have read my first post, there are still some problems that give me confusion:
1. If n is an integer such that 101< n <118 , for how many distinct values of n is the expression 11(16n )−1 a prime?
I know the answer is 0 from the answer key, but I would like an explanation. Originally I thought thatt it was 0 because of multiplication (then I found the -1). What logic would one use to check (since my calculator results in overflow error).
2. Let N be a three-digit number (with a non-zero hundreds digit) such that the sum of the digits of N is eight. If N2 is divided by 9, the remainder is 1. How many distinct possibilities exist for the value of N ?
I've gotten so far as to see 8 possible digits (0-7) and then was lost.
3. An ordinary clock with a minute hand and hour hand now indicates it is 12:00 P. M. Noon. The minute and hour hands are together at the usual dial positions, but the clock is actually running slow. When the minute and hour hands are first together after 3:00 pm, the clock has actually been running for 210 minutes. Find the number of true minutes lost by the clock during the time from 12:00 P. M. Noon on the clock to the first time after 3:00 P. M. that the minute and hour hands came together. Express your answer as an improper fraction reduced to lowest terms.
(answer is 150/11)
4. Emily travels at a rate of 4k mph. for 4 miles, 5k mph. for 5 miles, etc., and finally at the rate of wk mph. for w miles. For what value of w will the total distance traveled divided by the total time it took (average rate) be 12 times her starting rate?
Also
5. If √(x)=√(600+√(600+√(600+√(600+...)))) (an infinitely nested radical), find the value of x.
Ok if the x wasn't in a radical I see how one could solve it. You could square both sides (x2=600+x (the last x is from substitution)). The answer would be 25 (the -24 wouldn't work) if x had not been a radicand. I see that in the answer key it says 625...
1. If n is an integer such that 101< n <118 , for how many distinct values of n is the expression 11(16n )−1 a prime?
I know the answer is 0 from the answer key, but I would like an explanation. Originally I thought thatt it was 0 because of multiplication (then I found the -1). What logic would one use to check (since my calculator results in overflow error).
2. Let N be a three-digit number (with a non-zero hundreds digit) such that the sum of the digits of N is eight. If N2 is divided by 9, the remainder is 1. How many distinct possibilities exist for the value of N ?
I've gotten so far as to see 8 possible digits (0-7) and then was lost.
3. An ordinary clock with a minute hand and hour hand now indicates it is 12:00 P. M. Noon. The minute and hour hands are together at the usual dial positions, but the clock is actually running slow. When the minute and hour hands are first together after 3:00 pm, the clock has actually been running for 210 minutes. Find the number of true minutes lost by the clock during the time from 12:00 P. M. Noon on the clock to the first time after 3:00 P. M. that the minute and hour hands came together. Express your answer as an improper fraction reduced to lowest terms.
(answer is 150/11)4. Emily travels at a rate of 4k mph. for 4 miles, 5k mph. for 5 miles, etc., and finally at the rate of wk mph. for w miles. For what value of w will the total distance traveled divided by the total time it took (average rate) be 12 times her starting rate?
Also
5. If √(x)=√(600+√(600+√(600+√(600+...)))) (an infinitely nested radical), find the value of x.
Ok if the x wasn't in a radical I see how one could solve it. You could square both sides (x2=600+x (the last x is from substitution)). The answer would be 25 (the -24 wouldn't work) if x had not been a radicand. I see that in the answer key it says 625...
