1 )At a bottling company,machine A fills a bottle with spring water and machine B accepts the bottle only if the number of fluid ounces is between 11 7/8 and 12 1/8. if machine B accepts a bottle containing n fluid ounces which of the following describes all possible values of n?
A) (n-12) = 1/8
B ) (n+12)= 1 /8
c) (n-12) < 1/8
D)(n-12)>1/8
e ) (n+12)<1/8
Do i solve these kind of questions by plugging in a number?
2)Dwayne has a newspaper route for which he collects k dollars each day. From his amount he pays out k/3 dollars per day for the cost of papersand he saves the rest of the money. in terms if k how many days will it take dwayne to save 1000$?
A) k/1500
B )k/1000
c)1000/k
d)1500/k
e)1500k
esther drove to work in the morning at an average speed of 45 miles per hour. she returned home in the evening along the same route and averaged 30 miles per hour. if esther spent a total of one hour commuting to and from work, how many miles did esther drive to work in the morning?
4)carlos delivered n packages on monday,4 times many packages on tuesday as on monday and 3 more packages on wednesday than on monday. what is the average(arithmetic mean) number of packages he delivered per day over the three days?
A) 2n-3
b) 2n-1
c)2n+1
d)2n+3
e)6n+1
You could...in this case plugging in n = 12 eliminates all choices except C. A better way (e.g. if you don't have answer choices) is to notice that the interval (11 7/8, 12 1/8) contains all numbers within 1/8 distance of 12 and your desired interval is |n-12| < 1/8.
He keeps 2k/3 dollars each day, the number of days required is 1000/(2k/3) = 3000/2k = 1500/k. You can also solve by plugging in a number for k, e.g. k = 3.
Assume Esther took 2t hours driving to work, then she took 3t time driving home (using D = rt). Then 2t+3t = 1 (hour) --> t = 1/5 hr. So 2t = 2/5 hr, and she drove (45 mph)(2/5 hr) = 18 mi to work.
n packages on Mon., 4n packages on Tues., n+3 packages on Wed.
A girl rides her bicycle to school at an average speed of 8 mph. She returns to her house using the same route at an average speed of 12 mph. If the round trip took 1 hour, how many miles is the round trip.
A. 8
B. 9 3/5
C. 10
D. 11 1/5
E. 12
PR offers this solution: First the problem is a hard problem (level 5). TCB assumes that the common student will not attempt to solve the problem and pick the trick answer of 10 since it represents the average of 8 and 12. The common student second choice will be to pick a value that is stated in the problem: 8 or 12. PR provides the strategy to eliminate those Joe Blogg answers. Again, the conclusion of PR is to end up with two choices and pick between B and D. In their words, the student will be in great shape!
What’s my issue with this? In my eyes, a 50-50 chance is really not good enough. When you consider how this problem can be solved, the recommendation to guess becomes highly questionable.
What could a student have done? Use a simple formula for average rates -an opportunity that PR strangely forgets to mention. Is this formula really complicated? I could detail the way I developed it while working through similar problems, but the reality is that millions of people have seen it before. Im absolutely convinced that many good tutors teach it, but you wont find it in the typical help book. Here it is:
[2Speed1Speed2] / [speed1 + Speed2] or in this case:
2* 8 * 12 / 8 + 12.
Most everyone will notice that the answer is 2*96/20 or simply 96/10. This yields 9.6 or 9 3/5. The total time to do this, probably 20-45 seconds. Not a bad method to know!
It does get better. How would I solve it?
Check the problem to make sure we have a ONE hour unit. Most often, the SAT writers will use a one hour limit and not a different number of hours.
As soon as I verify that the unit is 1 hour, I will mark B because I know that the answer is ALWAYS a number slightly BELOW the straight average. It takes only a few problems OF THAT TYPE to realize that it ALWAYS works.
My total time including reading the problem: about 10 seconds!
Here you have it: two methods that are faster and are bound to yield the correct answer and a healthy dose of self-confidence!
You can derive it by generalizing the problem – suppose the distance to work is D, and your rates going there and back are r1 and r2, with corresponding times t1 and t2 (e.g. D = r1t1 = r2t2). You are also given what t1+t2 is. Then you can solve for t1 or t2 and then find D.
Humm, I think I have done this a few times. There is really not much to learn from seeing how this very effective SAT tool is derived directly from the well-known formula … d = rt.
As we know the total average speed = Total distance/Total time
This is s = d/t. For the people who prefer the d=rt, simply substitute r for speed.
A. Let’s establish that
d = distance traveled in each direction
The total distance traveled is d+d or 2d
B. Let’s establish that
t1 = time spent on first leg
t2 = time spent on return leg
Total Time = t1+t2
C. By formula, speed = distance/time but also time = distance/speed
S1= d/t1 and t1 = d/S1
S2 = d/t2 and t2 = d/S2
Now, let’s start (following A and B above)
Total average speed = Total Distance/Total time or
Total average speed = d + d / t1+t2
Total average speed = 2d / t1+t2
Substituting according to C yields
Total average speed = 2d / (d/S1) + (d/S2)
Getting rid of the common “d” gives
2 / (1/S1) + (1/S2) or
2 / (1.S2/S1S2) + (1.S1/S1S2) or
2 / (S1+S2 / S1S2) or
2 * S1S2 / S1 +S2
And here we have it
Total average speed = 2 * S1*S2 / S1 +S2
++++++++++++
Piece of cake for my friend MITer94, but helpful to understand that there is no voodoo involved in the harmonic rate formula. It remains a very simple and elegant tool for the SAT.
@MITer94 thanksssssssssssssssssss allooooooottttttttttttttttttttttttttt = ))))))))))))
@xiggi thanks alot i really appreciate this detailed explanation but i have one small question in the question i wrote why we did 3045/30+45 not 2(3045)/30+45 as in the rule? i mean why we didnt multiply it by 2? because it asked about the distance of the morning only?
^ Yes, it is important to remember to read the problem carefully. You are correct that I did not multiply by 2 and then divided by 2 because the question was about the morning distance only. Note that the formula would give you the average speed for 1 hour (36 mph) and that my answer was about the distance of the one-way (18 miles)
the ratio for 45 is 3 not 3…