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OAT quantitative reasoning questions!


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Hello all,


I was wondering if you could share how to solve these questions.

This is from official OAT website


A tank can be filled by a pipe in a 30 minutes and emptied by another pipe in 50 minutes. How many minutes will it take to fill the tank if both pipes are open?


Answer is 75 min ( what's the easiest method to get to this answer? :confused:)


Optometry school applicants decreased by 25% during 4 year period. During the same time, the number of first-year opening in optometry school increased by 12%. If the ratio of applicants to first year openings had been 3 to 1, then which of the following would be the approximate ratio at the end of 4 year period?


Answer is 2:1 (how????)



When each of the sides of a squqre is increased by 1 yard, the area of the new square is 53 square yards more than that of the original square. what is the length of the sides of the original square?

Answer is 26 (how????)


Calculate variance of following set of numbers (3,6,9,18)

The answer is 27.5 (how do you calculate variance in hand?)

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These are answers that I figured out when I read your post - I think they're correct (I got the right answer anyways)



(minutes passed)/(minutes required to fill or empty the tank) = how much tank is filled



(minutes passed)/30 minutes = amount of tank full

(minutes passed)/(-50 minutes) = amount of tank empty


The amount of tank full/empty are as fractions


Let's say t= minutes passed


t/30 - t/50 = 1


it equals 1 because the tank is full


solve for t




A1 = Applicants at year 1

A4 = Applicants at year 4


O1 = Optometry student opening at year 1

O4 = Optometry student opening at year 4


0.75 A1 = A4

1.12 O1 = O4


A1:O1 = 3:1

So, A4:O4 = 0.75(3) : (1.12)(1) = 2:1


*there is a calculator given to you so this will be easy to calculate using that .. the actual ratio is 2.0089:1, but you can also see that 2.25:1.12 is approximately 2:1*




x=original length in yards


So in the original square

x^2 = Area


With the increase of 1 yard, new length is x+1


So, (x+1)^2 = new area


In the question it says the area increased by 53 yards so, x^2+53 is the new area


(x+1)^2 = x^2 + 53

Solve for x




Use the variance formula to calculate it.. you have a basic calculator

It could be time consuming, but you can calculate in your head quickly (it would be faster than clicking on a calculator)


I can't teach you that, you just have to practice and recognize multiples easily



Good luck

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  • 4 weeks later...

Question 1 could also been done this way

Let X be the size of the pool

Rate of actual pool filling=rate in-rate out= x/30 - x50=2x/150=x/75


And well... There you have it... Already...

But if you want the whole thing...

Fill volume=rate*time

Let t be time...


We want to fill the whole pool, thus...

x=x/75 * t


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