1. a total of 120 numbers can be formed using all 5 digits 1, 2, 3, 4, and 5. If these numbers are arranged in increasing order 12 345, 12 453, up to 54, 321, which one is the 75th number in this order?
*can someone tell me how to do this problem???^)
2. Jane cycles to work alongside a railroad track at 6km/h. every day she arrives at a crossing at the same time that a train does. One day she was 50 minutes late and was overtaken by the train 4 kilometers from the crossing. In how many minutes will the train reach the crossing?
3. my grandfather's age at his death was one-thirtieth of the year of his birth. How old was my grandfather in 1980?
thanks! your help is greatly appreciate :]
Ok, here is how I did number 1. I hope someone can check my thinking.
We know first n in the sequence will start with a 1. And there are 24 ways to arrange 2,3,4,5. So n=24.
So, the first 48 must start with a 1 or a 2, and the first 72 must start with a 1,2,or 3. So
73rd must be 4, 1,2,3,5
74th must be 4, 1,2,5,3
75th must be 4, 1,3,2,5
for number 3, if was alive on Jan 1, 1980, he was 66 years old, and died in 1980.
I did this by guess and check. If age 65, he must have died in 1950, if 67 he must have died in 2010.
for number 2)
It will take Jane 40 minutes to travel the 4 kms. So, in 40 minutes, she will be 50 minutes late. So, the train should take more 10 minutes to reach the crossing.
Check my thinking. plz.
For question 1, you have correctly determined that there are 24 ways to arrange the digits 2, 3, 4, and 5 after the fixed digit 1. This means that each set of five consecutive numbers in the increasing order will have 24 permutations.
To find the 75th number in this order, you need to determine which set of five consecutive numbers it belongs to. Since 75 is in between the numbers 72 and 73, it belongs to the set starting with the digit 4, followed by 1, 3, 2, and 5. Therefore, the 75th number in this order is 41325.
For question 3, if your grandfather's age at his death was one-thirtieth of the year of his birth, it means that he lived for 30 years. So, if he died in 1980, he was born in 1950. Since you mentioned that he was alive on January 1, 1980, he would have turned 66 years old on that day.
Regarding question 2, your thinking is correct. Since Jane travels at a speed of 6 km/h and arrives 50 minutes late while being overtaken by the train 4 kilometers from the crossing, we can calculate her travel time to be 40 minutes (4 kilometers divided by 6 km/h). Since she arrived at the crossing 50 minutes late, it means that the train will take an additional 10 minutes to reach the crossing after overtaking her. Therefore, the train will reach the crossing in 50 minutes.