Quant Review Q 70. Word Problem Statistics

[AnupritaM283]

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[PetriF258]

What about smart numbers? Make the even numbers 2-10, avg is (2+10)/2 = 6. The odd numbers will be 9 (2+7) to 27 (9 + (10-1)x2), avg is 18 ((9+27)/2). The difference is 12. I think it is a bit easier.

Just remeber, when I calculated the 27, I had to multply the 2 by 9, although there are 10 numbers, we need to multiply by n-1. The same principle applies to the first 5 even numbers: 2,4,6,8,10. Test it: last number (2+(4(n-1)x2)).

In the begining I was afraid, I was petrified, to use smart numbers. But I have noticed that you can answer a lot of the questions a lot quicker by using smart numbers, and now it is raining solutions in less than 2 minutes :-) Ok not really raining solutions but it helped a lot!

Regards

[AnupritaM283]

Wow that made it so simple. Thanks a ton for responding. That really helped.

[RonPurewal]

hi,
please read the forum rules--we don't allow problems from this source on the forum.

[RonPurewal]

In the begining I was afraid, I was petrified, to use smart numbers.

^^ this is ... interesting.
is there any particular reason (that you can identify) why you felt this way?

i'm asking because i genuinely don't understand this mentality -- don't understand it at all. (if there's any way to avoid doing work, believe me, i'm on it.)

do you think it's just a residual form of "my grade-school teacher would have marked me off for that"?
... or is it something else?

please let me know if you have any insights. thanks.

[RonPurewal]

here's a thought experiment:
• let's say they gave you the gmat WITHOUT answer choices on the quant section.
• let's say they gave everyone else the answer choices.

ok, you'd probably be screaming "unfair", right?

... but now, think about why.
the ONLY advantage the other people would have = their ability to backsolve, use smart numbers, etc.

this thought experiment might change the way you think about non-algebraic methods entirely.

[NL]

Nice thought experiment, Ron!
It's similar to the phenomenon that non-native English speakers seem good at quant than verbal, not because they are innately good at math, but because they (or at least me) are bad at verbal. So studying math is more fun.

please let me know if you have any insights. thanks.

I have an "insight", hi, not about using smart numbers, but about your lazy-typing style. It's cool, but it causes some feeling below:

1. If you don't use capitalization and I do use it in written conversations, it seems like you are sitting and I am standing when we are talking to each other. Cool, but humm.
2. Sometimes it takes extra energy to get points since I am not sure a line is a new sentence or a continuing sentence.

(A tip: studies show that typing capital letters is good for exercising your thumbs)

[tim]

I would say Ron definitely managed to get his point across in his post, and with less effort than if he'd wasted time with the shift key. After all, remember he's the one who said "if there's any way to avoid doing work, believe me, i'm on it." Perhaps there's a lesson here about how to approach the GMAT; Ron must have been doing something right to get that 800!

[NL]

After all, remember he's the one who said "if there's any way to avoid doing work, believe me, i'm on it."

How nice you are, Tim!
I can see how much love you give to Ron though your words.
But I’ve learned the lesson: I want to have less effort in reading while he wants to have less effort in typing.

Perhaps there's a lesson here about how to approach the GMAT;

Approaching the GMAT & Typing capital letters? Ah, interesting analogy. It likes I say “I find it difficult to eat this mango because it’s still green”. And you say “Dozen of studies show that there are lots of vitamins in a mango, so there’s nothing to complain about mangos”

Ron must have been doing something right to get that 800!

Ron got an 800 in GMAT? I knew. He’s my Big Guru. As a student, I know another thing (maybe you don’t) is that he changed my life: he changed my attitude toward difficulties, helping me survive in real-life tough situations.

But we should stop discussing the “topic” here. I am afraid he will suddenly jump out from somewhere and scream: you guys are digressing too far away from the original post (I love digressing, hehe). See you in Southwest airlines. I‘ll take the seat 21b.

[PetriF258]

I definitely agree that smart numbers is the way. It was just strange to get used to it. You asked why it was difficult for me to accept it? I think it relates to my background. In my previous courses most of the marks were allocated in the workings, and the answer in itself counted very little.

What was extremely difficult was to recognize when to use smart numbers. But, the more I practiced, the easier it got to identify which questions should be solved using smart numbers. Also, I guess I was afraid that I did not understand the underlying concepts if I used smart numbers, which I now know is not true.

On a side note, I think the advanced GMAT strategy guide is a totally underrated book. That book really helps you to think "GMAT".

So bottom line: The mentality probably originated through my previous studies and myself being a person who wants (now wanted) to get every thing 100% correct 100% of the time.

[RonPurewal]

He’s my Big Guru. As a student, I know another thing (maybe you don’t) is that he changed my life: he changed my attitude toward difficulties, helping me survive in real-life tough situations.

i didn't actually know that i've influenced you so strongly.

thanks for writing this. these are the kinds of things that keep this job from just being "work".

[RonPurewal]

oh, and, about the capital letters, you guys are both wrong. my main laptop has a broken left-hand shift key (and i've failed to acclimate to using the right-hand one); hence typing capitals involves considerable extra effort.
... but that was a fun exchange.
(:

(ironically, i have a much harder time reading writing without capital letters, as an extension of the problems of dyslexia.)

i also like the standing/sitting analogy.
when i take questions from students after live classes, i'm usually sitting down (having just been standing for 3 hours). some students stand—even though there are chairs in the vicinity—while others pull up one of the chairs.
i've noticed that the students who pull up the chairs tend to speak to me more as an equal, rather than as "sensei" / "authority figure" (the latter of which i just find awkward). so, there's definitely something to what you're saying.

[RonPurewal]

by the way—you might want to try writing without capitals from time to time, just to see how it affects your writing.
you know how your hearing and proprioception improve when you close your eyes? in the same way, you might find that you write more varied or higher-quality sentences if you don't use caps.
i.e., if the sentences without caps are harder for you to read, you might (perhaps subconsciously) work harder to improve the quality of your sentences so that they become easy to read again.
try it!

in any case, we've now completely abandoned any semblance of discussing the GMAT exam in this thread, so, time for me to stop.

[RonPurewal]

Petri:

I definitely agree that smart numbers is the way. It was just strange to get used to it. You asked why it was difficult for me to accept it? I think it relates to my background. In my previous courses most of the marks were allocated in the workings, and the answer in itself counted very little.

this makes sense, but you just have to realize that this test doesn't work that way.
if you get a problem right with smart numbers, someone else gets it with textbook-type methods, and i get it by poking voodoo dolls in the right places, guess who wins? all of us.

oh, and, the good news: you know what else doesn't work that way?
real life.

see, in real life, we have a word for people who solve problems by non-traditional methods. we call them "innovators".
the real world likes innovators.

[RonPurewal]

What was extremely difficult was to recognize when to use smart numbers. But, the more I practiced, the easier it got to identify which questions should be solved using smart numbers.

in my opinion, there's still too much of a burden on your shoulders.

here are the major ways of addressing multiple-choice problems:
• textbook-style methods
• smart numbers
• backsolving
• estimation
• brute-force methods (making lists, performing long-hand arithmetic, etc.)

just put these in some sensible order, and then, when a problem proves stubborn, just move down the line.
zero patience.
zero perseverance.
if something isn't giving results VERY readily... don't keep doing it. (many gmat problems are hard, but ALL gmat problems are short.)

this is hardly genius, but note what it does for you: it takes away the necessity of "recognizing" problems on which a given method will apply. instead, if method number N doesn't work, you just ask yourself whether method number N+1 will work. if there's any opportunity there, just try it.

if you have a possible solution method in mind, DO NOT EVER decide against using it on the basis of "oh, i think that will take too long."
(unless your goal is to get a lower score on this exam, in which case that's easily the best way to accomplish your goal)

don't make yourself reconnoiter the problem too much, and don't give yourself a whole flowchart/decision tree BEFORE starting something.

just throw stuff at the problem, and see whether it sticks. if it doesn't stick, just throw something else at it.