Problem Solving

Hello,

Could someone help me to solve these problems? They are fairly simple, but they seem to stump me everytime I see them.

Thanks!

1) If the ratio of TAs to students must be 3/80, what is the maximum number of students if there are 5 TAs.
a) 130
b) 131
c) 132
d) 133
e) 134
Answer is(d)

2) A small water pump takes 2 hours to fill an empty tank. The larger pump fills the tank in half an hour. How many hours would it take both pumps at their rates to empty the tank if they being at the same time?
1) 1/4
b) 1/3
c) 2/5
d) 5/4
e) 32
Answer is (c)

3) 999/100 + 1/999
a) 10
b) -1
c) .1
d) .01
e) .001
Answer is (a)

THANKS!

1) If the ratio of TAs to students must be 3/80, what is the maximum number of students if there are 5 TAs.
a) 130
b) 131
c) 132
d) 133
e) 134

Your first problem becomes a lot easier if you set up two ratios--the current TA to students ratio and the TA to student ratio if there are 5 TAs. To determine the maximum number of students, we just set those ratios equal to each other:

3/80 = 5/x

where x the number of students when we have 5 TAs.

Then, we can solve this by simple algebra:

x = (5 * 80) / 3 = 400 / 3 = (4/3) * 100 = 133.3

Thus, the maximum number of students is 133, which answer (d).

To help you with other ratio problems, I'd suggest trying the ratio practice problems on these websites:

https://www.platinumgmat.com/about_gmat/ ... e_question
https://www.800score.com/guidec7view1f.html
https://www.platinumgmat.com/gmat_study_guide/fractions
https://www.syvum.com/gmat/math_review/index.htm

For question C, the way I solved is is by process of estimation.

(999/100) = 9.99

Since it is (999/100) PLUS a positive number (1/999), the answer clearly has to be larger than 9.99 and the only option is 10.

Indeed, if you approximated (1/999) to become (1/1000), it becomes 0.001.

9.99+0.001 = 9.991 which again is close to 10.

I'd be interested to see if anyone could find a shortcut to get an exact answer though.

For rate questions, you generally solve them by determining rate1, rate 2 and then you can just add them to find the new rate and solve.

If the question asks how many hours it takes, then you need to have a rate per hour.
If the question asks how many tanks are filled, you need rate per tank.

So for this question, we need to determine the two rates by tanks per hour.
Smaller hose: 0.5 tank / hr
Larger hose: 2 tanks / hr
Combined rate: (0.5 + 2) tanks / hr = (5/2) tanks / hr

So you know that (5/2) = 2.5 tanks are filled in one hour. But you want to know how long it takes to fill 1 tank.

Simply divide the combined rate by 5/2. This gives you:
[ (5/2) / (5/2) ] tanks per [ 1/ (5/2) ] hours
= 1 tank per (2/5) hours

Answer: it takes (2/5) hours to fill one tank.