Need help on some numerical problems (images attached)

[p1nkm4n]

Hi everyone! New member here. I am preparing for taking the GRE sometime in December or January 2019 and been out of touch from mathematics for a long while now. I was taking an online questionnaire where I came across some questions I couldn't solve. I will be attaching the screenshots here, would be glad if anyone can help! Also the moderators please kindly let me know if this is the wrong section or if I should post the questions seperately. Thanks! Attaching the screenshots here:

I could solve #5 and #16 but need to confirm if I got it correct. I'll describe how I got to the solutions below:

#5:
I used speed = distance/time and took distance = 115 miles and time = 59 minutes. Converted the answer in mph and got 117 mph as the average speed. Not sure if I should use 59 minutes as the time here.

#16:
Multiplied 39 x 3 = 117 to get the number of exams Division A staff have to take to get back to their current levels of people.

The rest I have no clue on how to approach the problems. I would be glad if anyone can help with anything among these and will be highly appreciated. Thank you for your time!

Have a nice day.

 

[JeffM]

Hi. We greatly prefer 1 problem per thread. And please read

https://www.freemathhelp.com/forum/threads/112086-Guidelines-Summary?p=436773#post436773

With respect to question #5, it is very badly written. If it takes 65 minutes to go 115 miles, the average speed for the overall trip must be

\(\displaystyle 60 * \dfrac{115}{65} \approx 106 \text { miles per hour.}\)

If what is meant is the average speed of the train between stations, the answer is

\(\displaystyle 60 * \dfrac{115}{59} \approx 117 \text { miles per hour.}\)

Because they offer both answers, who can be sure what is meant. I'd probably go with 106, with the extra information thrown in there to confuse matters, because what we normally care about is the overall distance and the overall time. But this has nothing to do with math. It really is about interpreting English. (What makes it worse is that the answers given are not exact.) Terrible problem.

Very big city. Very fast train.

 

[JeffM]

Again, this is not a well written problem.

One way to attack it is to say that 39 people must pass the Class III exam, which means that at least 39 must take it. Moreover, if 39 pass, those 39 move out of Class II.

Of course, there are not originally 35 people in Class II in Division A. So that means at least 4 must pass both the Class II and Class III exams, but that does not affect how many must pass the Class III test. A total of 39 must pass the Class III test so at least 39 must take the Class III test.

Given all that, how many must pass the Class II test? Well 39 moved out of Class II when they passed the Class III test so 39 must move in. That requires 39 to pass the Class II test. (Again, there are not 39 in Class I initially so at least 12 must pass both the Class I and II tests, but that does not affect how many must pass the Class II test.) For 39 to pass, at least 39 must take the test. And if 39 pass the Class Ii test, 39 leave Class I.

If 39 leave Class I, the ranks must be relenished by 39. So 39 must pass the test for Class I, which entails that at least 39 must take it.

So the least number of tests that must be taken is

39 + 39 + 39 = 3 * 39 = 117.

Now it is possible to attack this a different way.

35 people can take and pass just the Class III exam. 35 passed tests.

4 people can take and pass both the Class II and Class III exams. 2 * 4 = 8 passed tests.

27 - 4 = 23 people can take and pass just the Class II exam. 23 passed tests.

35 - 23 = 12 people can take and pass both the Class I and Class II exams. 2 * 12 = 24 passed tests.

27 people can take and pass just the Class I exam. 27 passed tests.

35 + 8 + 23 + 24 + 27 = 117 passed tests so at least 117 tests taken.

Based on the information given, we cannot determine how many tests need to be taken. We can determine how many tests must pass. So we can determine the minimum number of tests taken. Anothe badly worded problem.

 

[p1nkm4n]

Hi. We greatly prefer 1 problem per thread. And please read

https://www.freemathhelp.com/forum/threads/112086-Guidelines-Summary?p=436773#post436773

With respect to question #5, it is very badly written. If it takes 65 minutes to go 115 miles, the average speed for the overall trip must be

\(\displaystyle 60 * \dfrac{115}{65} \approx 106 \text { miles per hour.}\)

If what is meant is the average speed of the train between stations, the answer is

\(\displaystyle 60 * \dfrac{115}{59} \approx 117 \text { miles per hour.}\)

Because they offer both answers, who can be sure what is meant. I'd probably go with 106, with the extra information thrown in there to confuse matters, because what we normally care about is the overall distance and the overall time. But this has nothing to do with math. It really is about interpreting English. (What makes it worse is that the answers given are not exact.) Terrible problem.

Very big city. Very fast train.

Thank you for the reply, JeffM. Will post the rest of the problems in a seperate thread each.

You're right it's a badly written problem and that's where I was confused. Now that you've pointed it out, I think I'll go with the first one (106mph) since the question says average speed of the train only.

 

[p1nkm4n]

Hi. We greatly prefer 1 problem per thread. And please read

https://www.freemathhelp.com/forum/threads/112086-Guidelines-Summary?p=436773#post436773

With respect to question #5, it is very badly written. If it takes 65 minutes to go 115 miles, the average speed for the overall trip must be

\(\displaystyle 60 * \dfrac{115}{65} \approx 106 \text { miles per hour.}\)

If what is meant is the average speed of the train between stations, the answer is

\(\displaystyle 60 * \dfrac{115}{59} \approx 117 \text { miles per hour.}\)

Because they offer both answers, who can be sure what is meant. I'd probably go with 106, with the extra information thrown in there to confuse matters, because what we normally care about is the overall distance and the overall time. But this has nothing to do with math. It really is about interpreting English. (What makes it worse is that the answers given are not exact.) Terrible problem.

Very big city. Very fast train.

Thank you for the reply, JeffM. Will post the rest of the problems in a seperate thread each.

You're right it's a badly written problem and that's where I was confused. Now that you've pointed it out, I think I'll go with the first one (106mph) since the question says average speed of the train only. Cheers!

 

[p1nkm4n]

Thanks JeffM. I think I'll go with 106 mph since the question says average speed of train and didn't mention anything about finding the average speed between stations. Cheers!