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Issues with mcat calculations

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I'm having some issues with not being able to use a calculator. I find it difficult to work with decimals and large numbers with lots of digits. For example, the chapter in BR gen chem on gas laws has a lot of long calculations that I spend too much time on.
"What is the speed of a gas particle at 125 C, if it has a speed of 100 m/s at 25 C?"

Okay, so I go to use the equation v2/v1 = square root of T2/T1


I set up V2/100 = square root of 398/298.
Hm let me make that fraction nicer

v2/100 = square root of 400 over square root of 300

Square root of 400 is 20. But what is square root of 300? I realize it's between 15 and 20, so I spend a minute or two writing calculations on the side until I realize that 17 is probably the best estimate.

V2/100 = 20/17 Let me flip that
100/V2 = 17/20

What is 17/20? Takes me a second to make it into 85/100.

Alright, so now I have 100=.85V2

I hate decimals. Let me make that 10,000 = 85V2

Then I have to figure out what 10,000 / 85 is. So I go to long division, and that takes a while.
Finally, I get 117, which seems close to 114, answer D, which is correct.


That whole calculation probably took me 4, 5, maybe 6 minutes. Is there a quicker way to do these? I know that BR has tips, but a lot of the explanations just assume quick calculations that I cannot do in my head. For example, in this question, it says, "The temperature increase is from 298 to 398, which means the temperature is 1.33 times greater."
I wouldn't see something like that, especially in a testing situation. I always do laborious calculations. Also, I have to make a lot of rounding estimations, and sometimes the rounding error builds up so much that the final answer I get is wrong, and all that time I spent figuring it out was wasted.



Also, this is really, really embarrassing, but I still count on my fingers sometimes for some reason. I never seemed to learn how to do quick arithmetic in my head haha. Like 13+6 takes me longer than it should to know.........Or even if I think I know it, I count to make sure I'm not wrong
 
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Jay.bee

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There are multiple ways to do this, and the one which is "best/fastest" will partially depend on the answer choices given. Blindly going in without looking at the answers, here is how I would approach this question:
Notice the relevant equation is V2/V1 = sqrt (T2/T1)
See that we can use proportions here, which are often integer fractions and easy to use in these problems: T1 ~= 300, T2 ~= 400
Using these facts and rearranging: V2 = V1 * sqrt (T2 / T1) (I would probably skip this step, and move directly to the next)
We know T2 and T1, so V2 = V1 * sqrt (400/300) = V1 * sqrt (4/3)
If this is too hard to estimate you can simplify to V1 * 2/sqrt3

Hopefully this gets you to a point where you can estimate the answer without actually doing the exact math. Proportions are your friend for MCAT questions that require math. Try to find what is known, and realize what can be restated in proportion to what is known (thereby eliminating numbers, if you're lucky)
 

jwilliams1993

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I want to say that on the actual mcat, they round a lot in their calculations. for example, they 10 instead of 9.8 m/s^2. that could be something I misremembered, but it's worth a google.
 
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