math tricks and shortcuts

[Timbo]

So you're given a set of numbers. What's the best and fastest way of finding the mean, median, and mode? What's the fastest way of finding the standard deviation? These types of questions often frequent the quantitative section. Of course it all sounds like child's play, until I try to do it under 1 min with no scratch paper other than the tiny space I get in between text on the question booklet.

---

Members don't see this ad.

 

[pharmschooler]

So you're given a set of numbers. What's the best and fastest way of finding the mean, median, and mode? What's the fastest way of finding the standard deviation? These types of questions often frequent the quantitative section. Of course it all sounds like child's play, until I try to do it under 1 min with no scratch paper other than the tiny space I get in between text on the question booklet.

I wouldn't actually find the exact number; it would take too long. Get a rough estimate in your head, then look to see what you can immediately rule out. You can usually plow through these faster when you don't solve the whole problem.

 

[chemguy79]

I wouldn't actually find the exact number; it would take too long. Get a rough estimate in your head, then look to see what you can immediately rule out. You can usually plow through these faster when you don't solve the whole problem.

That's what I did on the PCAT as well. They give you problems where you can frequently perform that calculation and be successful. When I tutor students for AP Chemistry or for the SAT Chemistry II examination, I give them the same advice. It's been an massive time saver for all parties involved. If you're OCD about seeing the exact number before choosing your answer, you will run out of time.

 

[pharmschooler]

That's what I did on the PCAT as well. They give you problems where you can frequently perform that calculation and be successful. When I tutor students for AP Chemistry or for the SAT Chemistry II examination, I give them the same advice. It's been an massive time saver for all parties involved. If you're OCD about seeing the exact number before choosing your answer, you will run out of time.

TRUE FACT! Make sure to answer all problems in all sections. If that means you have to make some educated guesses, you'd better do it. I'm really OCD; I had to train myself to work this way (painful!).

 

[Timbo]

That's what I did on the PCAT as well. They give you problems where you can frequently perform that calculation and be successful. When I tutor students for AP Chemistry or for the SAT Chemistry II examination, I give them the same advice. It's been an massive time saver for all parties involved. If you're OCD about seeing the exact number before choosing your answer, you will run out of time.

I guess that makes sense. Any specific tips on estimating? I remember on the test, they gave us something like 97.8, 95.6, 95.8, 93.5, 95.6, 94.2, 96.1, 95.6, 93.5 (i'm just making up numbers, but it was similar) and asked for the mean, median, and mode. Also seems like the only way to find the median and mode would be to neatly rewrite the list of numbers in order. Sounds very time consuming to me.

 

[Swishers]

I would look at the answer choices first. For instance, let's say you look over them and notice that each choice has a different value for the median. That means you can get away with finding only the median in the whole problem.

 

[dudecoolname]

One that I thought of:


Instead of doing factorials completely in your head just memorize the values for

1!, 2!, 3!,...all the way to 10!

Im assuming none will go higher than 10! Right?

 

[chemguy79]

One that I thought of:


Instead of doing factorials completely in your head just memorize the values for

1!, 2!, 3!,...all the way to 10!

Im assuming none will go higher than 10! Right?

Personally, I think that's a massive waste of time. Most probability problems involve cancelling out factorials so you won't need to know the actual numbers. If you're going to memorize things, memorize vocabulary words, not factorials.

 

[Timbo]

Ok geniuses, someone solve this problem in under a minute and tell me how you did it.

I'm having the most trouble with doing these types of problems fast.

 

[moose pharm]

Ok geniuses, someone solve this problem in under a minute and tell me how you did it.

I'm having the most trouble with doing these types of problems fast.

Bahaha.. I saw this question for the first time today while doing a practice test. It took me at least 3 minutes.

 

[mbpuffer]

Ok geniuses, someone solve this problem in under a minute and tell me how you did it.

I'm having the most trouble with doing these types of problems fast.

Surprisingly I got this problem right when I took the practice exam. I forgot how long I spent on this but what I did was rounded the numbers. For example, August was 1300 and 50, September was 1000 and 40, etc...If you always round up, you know your actual answer will be lower than the number you get.

 

[dudecoolname]

Ok geniuses, someone solve this problem in under a minute and tell me how you did it.

I'm having the most trouble with doing these types of problems fast.

Hmm

Well you can rather easily see that October is better than August and September...However, December is pretty damn close to October...

I'd be interested if anyone knew a trick for this as well

 

[liebht90]

When I did these problems I did a quick glance to see if some were obviously lower than others to skip it, then I got it down to 2-3 of them to compare. Every time I come across these problems I do it that way and it works rather quickly, but that is for me. Everyone might have their own little tricks and things that work better for them.

 

[pharmschooler]

Bahaha.. I saw this question for the first time today while doing a practice test. It took me at least 3 minutes.

The key is just knowing that this problem will take too long to solve and you're better off narrowing it down to two choices, then guessing and moving on to a quicker problem. At least that's what I would do.

 

[dudecoolname]

Here's an even better one:


An LCD TV was purchased for $891 including 8% sales tax. What was the original price on the TV?

a)$825 b)$820 c)$810 d)800

 

[Timbo]

Hmm

Well you can rather easily see that October is better than August and September...However, December is pretty damn close to October...

I'd be interested if anyone knew a trick for this as well

Even that wasn't obvious to me when I did it. Yeah you can tell October is better than September because more miles were driven and less gas was consumes. But comparing October to August, more miles were driven but slightly more gas was also used. Having to do multiple long divisions involving 3-4 digit numbers seems a bit much for one question. Not sure what they expect us to do in this case? In the answer explanation they just went ahead and solved for all 6 months without estimating lol.

Here's an even better one:


An LCD TV was purchased for $891 including 8% sales tax. What was the original price on the TV?

a)$825 b)$820 c)$810 d)800

This is easier, it only involves one long division. Start with 1.08x = 891, so the price was 891/1.08 or 89100/108 to get rid of the decimal, then divide. I don't know what's the best way to do this, but in order to find multiples of 108 in my head I just split it into 100+8, so:
108 * 8 = (100 + 8) * 8 = 800+64 = 864
108 * 2 = (100 + 8) * 2 = 200 + 16 = 216
,,,

 

[chemguy79]

Another important thought when taking the PCAT is realizing which problems are time wasters. This problem is a CLASSIC example of one that will take tons of time.

Therefore, you mark those problems, skip them until you go through the entire exam. It is downright PATHETIC the number of people who futilely insist on going through the problems one at a time in numerical order.

*rant head*
Furthermore, after the PCAT, they come onto SDN and say that I didn't have time to finish the last 15 questions. Whenever I read those posts, I want to say ... WHAT IS WRONG WITH YOU?!?!?!?! LOL Maybe I'm over-estimating the amount of common sense that one would have when taking the PCAT, but seriously folks ... Some problems you can't shortcut. HOWEVER, for a vast majority of the problems in the Quantitative section, you can perform shortcuts and they work BEAUTIFULLY.
*rant over*

The problems akin to the one above is the problem which you save for the end so you can get the maximum number of questions on the exam correct.

Chemguy79 (99th Percentile, 499 on Quantitative Section of January 2010 PCAT)

 

[Swishers]

This is easier, it only involves one long division. Start with 1.08x = 891, so the price was 891/1.08 or 89100/108 to get rid of the decimal, then divide. I don't know what's the best way to do this, but in order to find multiples of 108 in my head I just split it into 100+8, so:
108 * 8 = (100 + 8) * 8 = 800+64 = 864
108 * 2 = (100 + 8) * 2 = 200 + 16 = 216
,,,

Solid method, but I think it takes too long. I look at it this way: The purchase amount (891) is an odd number and multiplying any of the choices by 8 gives an even number. The only choice that would makes sense in this case is A since adding an even number (8 times whatever) to an odd number (825) gives an odd number (891). Much quicker.

 

[Timbo]

Here's another tough one:

Knew exactly what to do from the start, but it still took me almost 3 min to solve. I really want to get it down to less than 90 sec. So what should be my thought process here?

I know some here recommend guessing or skipping. I do leave the longer problems for last, but ultimately I'm gonna have to solve some of these because there's quite a few.

 

[chemguy79]

Here's another tough one:

Knew exactly what to do from the start, but it still took me almost 3 min to solve. I really want to get it down to less than 90 sec. So what should be my thought process here?

I know some here recommend guessing or skipping. I do leave the longer problems for last, but ultimately I'm gonna have to solve some of these because there's quite a few.

IMO, there isn't a shortcut to do this problem. Just solve it. FOIL is pretty easy and you should be able to do it quickly. It took me 45 seconds to do it, so it may be that your math skills are quite rusty.

 

[Timbo]

IMO, there isn't a shortcut to do this problem. Just solve it. FOIL is pretty easy and you should be able to do it quickly. It took me 45 seconds to do it, so it may be that your math skills are quite rusty.

I guess i've never been fast at arithmetic. That's what I'm trying to work on - figuring out how to multiply, divide, and add stuff thats beyond single digits in my head...

Anyways I got it into polynomial form pretty quick, but then when writing out the quadratic equation to solve for x, you get [34^2 + 4(73)]^1/2 for the discriminant 😡. BTW this is the type of problem that looks easy at first glance, then I realize this is gonna take a while halfway through it. So I have to work out every multiplication, addition, and division on paper to figure out this square root. Is it wrong to do this? Should I be able to do it all in my head?

 

[rxman10]

Solid method, but I think it takes too long. I look at it this way: The purchase amount (891) is an odd number and multiplying any of the choices by 8 gives an even number. The only choice that would makes sense in this case is A since adding an even number (8 times whatever) to an odd number (825) gives an odd number (891). Much quicker.

i would have never thought about it that way. two thumbs up!