Re: decimal arithmetics--gre


"Randy Poe" <poespam-trap@xxxxxxxxx> wrote in message
news:1166716480.482013.69860@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

john wrote:
Thanks to those who have posted helpful informatin.

And, yes, GRE is for entry into graduate school and this is from
exercise section of general GRE which is required for all grad school.


In my case, I haven't done that level of arithematics since I was 12.

NIck asked what other type of arithmetics are seen, and a few examples
are as follows:

1. What is the greatest positive integer n such that 2^n is a factor of
12^ 10
a. 19 b. 12 c. 16 d. 20 e. 60

(this question triggers some vague memories of my youth... not what it
is)

Did you ever see numbers written as prime factorizations?
For instance, 72 = 9*8 = 2^3 * 3^2

That's what you need here. Write out 12^10 in terms of
prime factors and see how many times 2 occurs.

12^10 = (4*3)^10 = 2^20 * 3^10

So the answer is 20. The factor 3^10 is not divisible by 2.

2.which of the following is divisible by 8?
a. 312 b. 98 c. 112 d. 144

I can't think of an approach other than brute force.
Start dividing by 2. If you can divide by 2 three times,
the original number was divisible by 8.

312/2 = 156, 156/2 = 78, 78 is even. So 312 is divisible by 8.
98/2 = 49. Not divisible by 2, so 98 is not divisible by 8.
112/2 = 56. 56/2 = 28. 28 is even. So 112 is divisible by 8.
144/2 = 72. 72/8 = 36. 36 is even. So 144 is divisible by 8.

All but 98 are divisible by 8. Was the question perhaps
which is NOT divisible by 8?

(how does one do this without having to do it one at a time?)

Well, I did one at a time. Dividing by 2 is pretty quick,
once you get a little practice at it. You can do it
left to right in your head with only a little bit of thought.

Example: 312/2. First digit. 3/2 is 1, with remainder 1. Write
down "1" for first digit of answer and look at 11/2 for
the next digit.

11/2 = 5 with remainder 1. Write down "5" and look at
12/2 for the next digit.

12/6 = 6, no remainder. Write down "6".

312 = 156.

Doing single-digit division by any other value 3-9 is
almost as easy to do in your head from left to right.

My undergraduate major was in Biochemistry which is a physical sciences
and I did quite well. It's just that I haven't seen or had the need to
do this level of of math since I was like 12- 14. I do have more
experiences writing programs for simulations though. I'm stil baffled
at the level of arithmetics expected for acceptance into grad school.
Knowing thi shelps me very little in running simulations for
Biochemical reactions... I don't do the math--comupter does.

Mine was in physics. We were taught back of the envelope
estimation right from the start. I guess they figured a
lot of physics is done on cocktail napkins, which is true.

When I did my A Level Physics ie school-leaving exam at age 18 in the UK,
there was a 3-hour Practical exam.

We were given a number of expts to do - some of them are standard textbook,
but one is not a textbook expt - but is totally original and is designed to
test one's ability to carry out an expt, follow instructions, take readings
etc.

On the original expt which was an expt to do with light involving lenses,
rulers etc I had been working on it for about 45 minutes, when my teacher
came by and gave some loud coughs. I realised something was up and I checked
what I was doing and found that I had made a mistake in the way that I had
set up the expt.

I adjusted the set-up but I knew that I didn't have time to again take 3
readings for every position of the lens. Instead I took one reading and made
up the other two - and then plotted my graph.

Nick


.

Quantcast