ASTB Math Skills

total number of degrees in a polygon (triangle, rectangle, pentagon, hexagon, etc)

(# of sides - 2)*180 = total # of degrees ex. A triangle has 3 sides. (3-2)*180 = 1*180 = 180 degrees in a triangle. ex. A pentagon has 5 sides. (5-2)*180 = 3*180 = 540

a bridge crosses a river that is 1520 feet wide. one bank of the river holds 1/5 of the bridge, and the other holds 1/6 of the bridge. how long is the bridge?

(1/6)*x + (1/5)*x + 1520 = x common denominator: 5x + 6x + 45600 = 30x; solve for x = 2,400 feet long

How much pure acid must be added to 12 ounces of a 40% acid solution to produce a 60% acid solution?

.4(12) + 1(x) = .6(12+x) 4.8 + x = 7.2 + .6x .4x = 24 x= 6

A tank that holds 450 gallons of water can be filled by 1 pipe in 15 minutes, and emptied by another in 30 minutes. How long would it take to fill the tank if both pipes are open?

450/15 = 30 gallons per minute fill rate 450/30 = 15 gallons per minute empty rate 30 gpm - 15gpm = 15 gpm with both pipes open so 450 gpm/15 gpm = 30 minutes

A field can be plowed by 9 machines in 5 hours. If 3 machines are broken and cannot be used, how many hours will it take to plow the field?

9*5 = 45 total machine hours to finish job 3 broken, so 6 will be used 45/6 = 7.5 hours

In a 3 hour examination of 320 questions, there are 40 mathematics problems. If twice as much time should be allowed for each mathematics problem as each of the other questions, how many minutes should be spent on the mathematics problems?

Let x = minutes to be spent on each problem 40*x + 1/2*x*280 = 180. solve for x, x = 1 minute plug back in to initial, 40*1=40 minutes

A naval detachment has enough rations to feed 16 people for 10 days. If 4 more people join the detachment, for how many fewer days will the rations last?

First, get the total rations, 16*10=160 4 more people = 20 people; so divide 160/20 = 8 days. 8 is 2 less days.

Questions about discount price

amount of discount/original price = % of reduction

A can complete a project in 20 days and B can complete the same project in 30 days. if A and B start working on the project together and A quits 10 days before the project is completed, in how many days will the project be completed?

remember: time needed/time alone + time needed/time alone = 1. so A doesn't do last ten days, so: (x-10)/20 + x/30 = 1; solving for x, we get x=18

If a driver completes a trip of 120 miles at a rate of 30 mph, at what rate would the driver have to travel on the return trip in order to average 40mph for the round trip?

round trip = 240 miles. 240 miles @ 40mph would take 6 hours. So used 4 hours. 2 hours left for 120 miles. so 60mph.

total miles traveled =

take the gallons of gas used * miles per gallon

hours traveled =

takes miles traveled/average speed

Questions about how fast people can do a job together

time actually needed/time needed to do the job alone = 1 (example: one recruiter can complete a certain assignment in 40 minutes; another can complete the same assignment in one hour; how long would it take to complete the assignment if they worked together? x/40 + x/60 = 1, x = 24 minutes)

A purchaser paid 17.16 for an article that had recently been increased in price by 4%. What was the price before the increase?

x/100 = 17.16/104 x=16.5