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If a, b, and c represent three numbers where b=a+3 and c=b+6, waht is the result when the median of the three numbers is subtracted from the avg. (Arithmetic mean) of the numbers?

A- 0
B-1
C-1.5
d-2
e-2.5

By Jason817 (Jason817) on Thursday, July 24, 2003 - 01:33 pm: Edit

Plug in numbers. Lets say:
a=1
then b=4
then c=10
average of a, b, and c is 5
median is 4
5-4=1
Thus, B is the answer.

By Akaflex (Akaflex) on Thursday, July 24, 2003 - 02:08 pm: Edit

i know that way, i was asking for the "math" way, i know how to do the pluggin numbers i just liek to learn the concept

By Akaflex (Akaflex) on Thursday, July 24, 2003 - 02:30 pm: Edit

heres another

A 30% solution of barium chloride is mixed with 10 grams of water to form 20% solution. How many grams of the original solution did we start with?

A- 10
B- 15
C- 20
D- 25
D- 30

By Xiggi (Xiggi) on Thursday, July 24, 2003 - 02:34 pm: Edit

Can you express the numbers using only a or b or c?

Try with a =>

First is a
Second is a+3
Third is a+9

Now add up and you get 3a+12; divide by 3 to get average => 3a+12/3 = a + 4

Finally, (a+4)-(a+3) = 4-3 = 1

By Jm405 (Jm405) on Thursday, July 24, 2003 - 02:37 pm: Edit

the answer is B
here's how i got it w/ the "math" way
b = a+3
c = b+6
a = b-3 (got it from manipulating b = a+3)
now, you have a,b,c solved for and lucky for us, they also all have a common variable, b, and this enables us to compare the three.
as aresult, we know that a or (b-3) is the least, b or (a+3) is the median, and c, (b+6) is the greatest.
thus, b is the median.
now, to find the average, just add up a,b,c and divide by 3.
(a + b+ c )/3
(b-3)+b+(b+6) / 3
(3b+3)/3 = b+1
now the difference is: b+1 - b = 1

By Serene (Serene) on Thursday, July 24, 2003 - 02:38 pm: Edit

Original solution be x grams
amount of BaCl2 is 0.3x
New 20% solution = 0.3x/20% = 1.5x
New solution is 10 grams greater than original solution:
1.5x-x=10

x=20

By Jm405 (Jm405) on Thursday, July 24, 2003 - 02:51 pm: Edit

the other one:
if water is added, work with percentages of water:
if original is 3/10 solute, then its 7/10 solvent
thus we have the equation:
0.7x + 10 = 0.8(x+10)
0.7X +10 = 0.8x+8
2 = 0.1X
X = 20
buti like serene's way more

By Quarky (Quarky) on Thursday, July 24, 2003 - 03:32 pm: Edit

Hey, Serene, what college will u be attending?

By Xiggi (Xiggi) on Thursday, July 24, 2003 - 03:39 pm: Edit

The math solution works great and is elegant but you could also TRY the "visual" method.

This question uses round percentages (20% and 30%) and round numbers (increase of 10g).

If you look at the numbers of solution, the numbers are simple as well.

If you recognize that the proportion of 20 % yields a 1 to 4 ratio for the final mix. You may want to plug in quick numbers like this (using the 30% original ratio) and simply adding 10 to second number.

Original........Add 10 water
Try 10 = 3/7.....3/17 ======== silly proportion
Try 20 = 6/14....6/24 ======== bingo 1 to 4
Try 30 = 9/21....9/31 ======== silly proportion

Try 15 = 4.5/10.5 ==== silly numbers check later if needed
Try 25 = 7.5/17.5 ==== same as 15.

For this to work, one needs to assume that ETS tends to use very simple numbers when testing a more difficult concept such rate differences and proportions. They do not seek to test your ability to plug the numbers in your calculator but see if you can reason and find a PATTERN.

This could help if you are unsure about writing a math equation.

By Serene (Serene) on Thursday, July 24, 2003 - 03:54 pm: Edit

quarky: hv.

By Yoyo123 (Yoyo123) on Thursday, July 24, 2003 - 04:40 pm: Edit

x=the amount of the barium in the solution
y=the total solution

30/100=x/y
30y=100x

20/100=x/y+10
20y+200=100x Lets now substitute 100x with 30y and simplify to get:
10y=200
y=20
The answer is C

By Pat57575 (Pat57575) on Thursday, July 24, 2003 - 05:14 pm: Edit

hv? Harvard?

By Serene (Serene) on Thursday, July 24, 2003 - 05:39 pm: Edit

indeed harvard the crimson. =)

By Pat57575 (Pat57575) on Thursday, July 24, 2003 - 07:42 pm: Edit

Wow, congrats! Many people have told me Harvard was ultra-selective this year. Would you mind posting your scores and a couple of your more notable accomlishments, just for curiosity's sake? Thanks.

By Serene (Serene) on Thursday, July 24, 2003 - 07:50 pm: Edit

True that this year a lot of people applied to Harvard.

score:
1600/800/800/760/790
rank 2/~680
five AP 5's when i applied

'notable' accomplishments
RSI (*sigh* I know I am lucky)
AMC perfect score
We the People (team) 1st place in state
State math contest 1st place
Other math/science competitions

By Aoe2guy (Aoe2guy) on Friday, July 25, 2003 - 12:53 pm: Edit

Serene what school is your valedictorian attending? and what are his/her stats / accomplishments

btw, what is RSI?

By Serene (Serene) on Friday, July 25, 2003 - 01:01 pm: Edit

She's attending University of Arizona. She was on the We the People team with me. Editor-in-chief for school newspaper. No spectacular scores though.

RSI: Research Science Institute, elite summer camp w/ strong ties to MIT and Harvard (although less so than MIT).

By Aoe2guy (Aoe2guy) on Friday, July 25, 2003 - 01:06 pm: Edit

o ok thanks...by the way, to get into RSI, what is needed and what is asked for on the application? also during what summer/school grade did u attend it?

By Serene (Serene) on Friday, July 25, 2003 - 01:07 pm: Edit

http://www.cee.org/rsi
the summer between jr and sr years

By Quarky (Quarky) on Sunday, July 27, 2003 - 03:31 pm: Edit

Cool. I have a friend, who's attending U of AZ... I think he is a Compt Eng major.

By Ecismyhome (Ecismyhome) on Wednesday, November 19, 2003 - 09:27 pm: Edit

actually, RSI has no official ties to harvard

By Memememe (Memememe) on Wednesday, November 19, 2003 - 11:32 pm: Edit

Yeah, because nobody from RSI is at Harvard.