Quantitative reasoning for my Law Aptitude test..

Identity · 2007-11-29 01:37:38

http://mathcounts.saab.org/mc.cgi/

Just found this site today, it is aaaaaaaawesome!

Last edited by Identity (2007-11-29 14:46:44)

mathsyperson · 2007-11-29 07:53:08

That is a most excellent site. I just did a test and got 9/10, missing an evil question with two hexagons and a bunch of triangles.

The given answer used the formula to get the area of a regular hexagon from its side length (which I didn't know), so my method took the longer way round and I must have slipped up somewhere.

I'm also slightly annoyed that it told me to round to the nearest tenth, and then claimed I was wrong when I put 93.0 as the answer (when it said it was 93).

Overall though, very fun site. Challenging enough to get you thinking, but still easy enough that no question should take much more than 5 or 10 minutes.

roel · 2007-11-29 17:17:02

this one's for

DAY 4

1.

(all x here means multiply. How do you make the multiplication sign?)

2.

(what does "|" mean?)

3.

4. Jorge started smoking 4 cigarettes a day when he was 18 years old. Each year thereafter, he increased his consumption by 2 cigarettes a day. When he died of lung cancer, he was smoking 2 packs a day (40 cigarettes). How old was he when he died?
(i already have an answer here, but it took me too much time to solve this problem. So if there is an easier way, ......)

5. A thief steals a number of rare plants from a nursery. On his way out, the thief meets 3 security guards, one after another. To each security guard, the thief is forced to give one-half of the plants that he still has, plus 2 more. finally, the thief leaves the nursery with 1 lone palm. How many rare plants were originally stolen?

thanks again mates...

roel · 2007-11-29 17:21:28

about the math problems you gave me, I am working on it.. All i can do is to smile everytime i see those problems.. those are really hard for me.. ahaha

mathsyperson · 2007-11-29 23:29:55

To get

instead of , write "\times" wherever you want the x to be.

1. Your expression is

If you see any common terms on the numerator and denominator, you can get rid of them. Doing this for a while reduces the expression to

But if you write 6² as (2x3)², then you can simplify it further to 3²x7.
Evaluating that directly shows that the expression is equal to 63.

2. Putting something between two "|" signs means you should knock off the minus sign if there is one. For example, |5| = 5, |-3| = 3, |0| = 0, etc.

So, after doing that, the expression becomes

From there it's fairly easy to work out what the value is.

3.

4. Here we want a formula that relates Age (A) to Number of cigarettes (C).

We're told that for every year he smokes two more cigarattes a day, so we know that A = C/2 + ?
We're also told that he smoked 4 a day when he was 18, so plugging that in gets 18 = 4/2+?.
From that, we can work out that ?=16.

So the formula is A=C/2+16.
We want to know when he died, so we use C=40, which gives A = 40/2+16 = 20+16=36.

5. For this one, it's easier to work backwards.
When he meets the third guard, he gives him half his plants and two more, ending up with just one left. So if we say that he had x plants upon meeting the third guard, then the guard would get x/2+2 plants and he would keep 1.

So, (x/2+2)+1 = x, and so x/2=3, and so x=6.

The same equation can be used to work out how many the thief had when he met the second guard, except that he kept 6 plants at the end.

(x/2+2)+6 = x --> x/2=8 --> x = 16.

Do that one more time to find out how many plants the thief originally stole.

roel · 2007-12-01 14:29:30

mathsyperson wrote:

To get
instead of
, write "\times" wherever you want the x to be.
1. Your expression is
If you see any common terms on the numerator and denominator, you can get rid of them. Doing this for a while reduces the expression to
But if you write 6² as (2x3)², then you can simplify it further to 3²x7.
Evaluating that directly shows that the expression is equal to 63.

Uhm, if it's ok, I'm still confused with this problem... Is there another way of solving this? sorry...

2. Putting something between two "|" signs means you should knock off the minus sign if there is one. For example, |5| = 5, |-3| = 3, |0| = 0, etc.
So, after doing that, the expression becomes

From there it's fairly easy to work out what the value is.

i see.. I got it.. So it's 60

3.
4. Here we want a formula that relates Age (A) to Number of cigarettes (C).
We're told that for every year he smokes two more cigarattes a day, so we know that A = C/2 + ?
We're also told that he smoked 4 a day when he was 18, so plugging that in gets 18 = 4/2+?.
From that, we can work out that ?=16.
So the formula is A=C/2+16.
We want to know when he died, so we use C=40, which gives A = 40/2+16 = 20+16=36.
5. For this one, it's easier to work backwards.
When he meets the third guard, he gives him half his plants and two more, ending up with just one left. So if we say that he had x plants upon meeting the third guard, then the guard would get x/2+2 plants and he would keep 1.
So, (x/2+2)+1 = x, and so x/2=3, and so x=6.
The same equation can be used to work out how many the thief had when he met the second guard, except that he kept 6 plants at the end.
(x/2+2)+6 = x --> x/2=8 --> x = 16.
Do that one more time to find out how many plants the thief originally stole.

So, it's 36.. right?

Thanks for that.. Sorry I was not able to go online yesterday.. Everything is now clear.. Except that I am a bit confused with number 1. Thanks again..

roel · 2007-12-01 15:22:28

Here's for

DAY 5

1. Sol was offered two different jobs. The first job offers a starting salary of 9000 with a monthly increase of 100, while the second job offers an initial salary of 8400 and a monthly increase of 110. After how many years will the jobs pay equally?
(I tried to answer this.. But I'm not sure if it's right.. I'm still having a hard time interpreting/converting words into math ________...)

x - number of months

9000 + 100 x = 8400 + 110 x
600 = 10x
60 = x
(number of months in which the jobs will pay equally)

60/12 = 5 - number of years...

not sure about that.. nice try... ahaha

2. An airplane flew 360 miles in 3 hours against a headwind. The airplane made the return trip in 2 hours with a tailwind of the same velocity as the headwind. what was the airspeed of the plane without wind?

3. On a game show, a contestant is given four digits to arrange in a proper order to win a car. What is the probability of winning if the contestant guesses the position of each digit?

(I think it's

)

4. The average of a set of numbers is 78. If 32 is included in the set, the new average becomes 76. How many numbers are there in the original set?

I tried to answer this also.. But I'm not sure if my answer is right..

The average of a set of numbers is 78.

If 32 is included in the set, the new average becomes 76.

so

76y+44=78y
44=2y
22=y

(Is this right?)

5. Joan asked Jona to pick a card from a deck of cards. Find the probability of getting a black card or a number 6.

thanks again...

Identity · 2007-12-01 17:47:08

1 Well done, it looks like you're right.

2

Let x be the speed of the plane, and let y be the speed of the headwind (and tailwind).

On the first trip, as speed = distance/time, we have

(the headwind is buffeting the plan e and slowing it down, so you subtract its speed from the plane's)

On the return journey, we still cover the same distance - 360 miles, but in 2 hours. The tailwind this time is helping the plane along, so you add it's speed to the plane's speed.

So

We now have two simultaneous equations:

By adding them up,

So the plane's speed by itself is 150 mph.

3

Ok, this is a variation of the simple counting principle.

How many ways can you arrange four different objects in a row?

Well, for the first position, you can have a choice of 4 objects, for the second you have a choice of 3 objects, for the third, there are 2 objects remaining and for the last position you can only have 1 object.

So the number of ways of arranging 4 different digits is

We denote this also as .

He must pick 1 arrangement out of these 24, so the probability is indeed

and you are correct!

4 You are most certainly correct. Just remember to give more explanation when doing the problem.

5

Use the Addition Principle for Probability. It is a realy nifty formula.

Or if you prefer:

(make sure you understand why, try drawing ven diagrams to convince yourself)

Ok, so Pr(Black card) = 1/2 and Pr(Number 6) = 4/52 = 1/13. The probability of Pr(Black card AND Number 6) = 2/52 = 1/26, because there is only two cards in the entire deck which are black and 6 (Six of spades, Six of Clubs).

Using the formula,

Last edited by Identity (2007-12-01 17:52:48)

mathsyperson · 2007-12-02 00:53:39

roel wrote:

mathsyperson wrote:
To get
instead of
, write "\times" wherever you want the x to be.
1. Your expression is
If you see any common terms on the numerator and denominator, you can get rid of them. Doing this for a while reduces the expression to
But if you write 6² as (2x3)², then you can simplify it further to 3²x7.
Evaluating that directly shows that the expression is equal to 63.
Uhm, if it's ok, I'm still confused with this problem... Is there another way of solving this? sorry...

Not really, although it might be clearer if you tidied the fraction up a bit before starting to cancel things. For example, the 3^-1 on the bottom can become a 3 on the top.
The 9/2 can be written as 9x2^-1, and then the 2^-1 becomes a 2 on the top, etc.

This is how to get it as tidy as you can before cancelling:

(Alternatively, you could use a calculator and evaluate it directly without doing anything to it, but I'm guessing that's not the exercise)

roel · 2007-12-04 14:51:09

hey... thanks for the replies..

here's for our

DAY 6

1. Numerico's age is twice trixie's age. frezel is 2 years more than twice trixie's age. if the sum of numerico and trixie's age 2 years ago si equal to the age of Frezel 4 years from now, find the present age of Numerico.
(I tried to answer this.. But again, i don't know if i'm right)

N = 2T
F = 2+2T
T = ?

(N-2)+(T-2) = F + 4

so,

2T - 2 + T - 2 = 2 + 2T + 4
3T - 4 = 6 + 2T
T = 10 (is this the present age of Trixie? or her age 2 years ago?)

So

N=2(10) = 20?

2. A coffee brand that sells for P120 per kilo is mixed with another grade that sells 180 per kilo. If the amounts of two grades of coffee are 4 and 8 kilograms respectively, what should be the final selling price to even up the capital?

120 4 (120 x 4) / 12 = 40
180 8 (180 x 8) / 12 = 120
12 160

Is it 160? (did i do the right thing?)

3. The two legs of a triangle are 14 cm and 28 cm. what could be the length of the third side?
(i really don't know this.. except if it is a right triangle.. can you please give me all the formulas of a triangle? thanks)

4. every choice has a corresponding point. A is worth 5 points, B is 4 points, C is 3 points, and D is 2 points. Michelle got a total of 100 points. If she had 3 more B's than A's, 5 C's more than twice the number of A's and 6 D's less than thrice the number of A's, find the number of C's she got.

A - 5
B - 4
C - 3
D - 2

Michelle's
A = ?
B = 3 + A
C = 5 + 2A
D = 3A - 6

so,
what's next? ahaha...

5. A chemist wants to mix a 3-liter solution that is 30% acid to a solution that is 20% acid. How much of the 20% acid solution must he use to obtain a 26 % acid solution?

thanks again mates.. I wish i can have your mind...

Identity · 2007-12-04 17:54:12

1.
Make sure to define your pronumerals clearly in the beginning, so you won't run into problems like wondering whether you have the age 2 years ago or not. "Let N, F, and T be Numerico, Frezel, and Trixie's present ages respectively."

But your answer is correct, Bravo!

2. Correct - at least I can't spot anything wrong with it.

3.
A very important fact about triangles, is that one side must be less than the sum of the other two. A special case is when the third side equals the sum of the other two. In this case, the triangle is a straight line, called a degenerate triangle (experiment with this yourself). I will assume here, that the triangle is not degenerate.

Let c be the third side.

Then the following requirements must be satisfied:
c < 14+28
28 < c+14
14 < c+ 28

They give, respectively, the following restrictions on c:
c < 42
c > 14
c > -14
This can be summed up succinctly by 14 < c < 42.

4.

5.

Let x be the amount of 20% acid solution that must be added in litres.

0.3(3)+0.2(x) = 0.26(3+x)

0.9 + 0.2x = 0.78 + 0.26x

0.06x = 0.12

x = 2

So he ought to add 2 litres of 20% acid solution.

These problems are really nice, lots of fun to do

Last edited by Identity (2007-12-05 16:43:51)

NullRoot · 2007-12-04 21:48:09

roel wrote:

4. every choice has a corresponding point. A is worth 5 points, B is 4 points, C is 3 points, and D is 2 points. Michelle got a total of 100 points. If she had 3 more B's than A's, 5 C's more than twice the number of A's and 6 D's less than thrice the number of A's, find the number of C's she got.
A - 5
B - 4
C - 3
D - 2
Michelle's
A = ?
B = 3 + A
C = 5 + 2A
D = 3A - 6

Here's how I went about it.
The A, B, C, and D are misleading, Roel. They give you the values for these so they aren't actually variables. They're what I would call a placeholder.

This is what I interpret her score to be:
100 = wA + xB + yC + zD
From the word problem we know:
x = 3+w
y = 5+2w
z = 3w-6

Substituting, including for the values of A,B,C,D:
100 = w5 + (3+w)4 + (5+2w)3 + (3w-6)2
100 = 5w + 12 + 4w + 15 + 6w + 6w - 12
100 = 21w + 15
85 = 21w
4.0476 ≈ w

So I think there may have been an error in copying somewhere? I'd expect only whole numbers given the context of the problem.

mathsyperson · 2007-12-05 01:50:35

For questions like 1, it's easy to check for yourself whether your answer is right - you just check to make sure the given facts aren't contradicted.

You think that Trixie is 10, Numerico is 20 and Frezel is 22.

Check 1:Numerico's age is twice trixie's age.
20 = 2 x 10, so that's true.

Check 2:Frezel is 2 years more than twice trixie's age.
22 = 2 x 10 + 2, so that's true.

Check 3:The sum of numerico and trixie's age 2 years ago is equal to the age of Frezel 4 years from now.
(20-2)+(10-2) = 18+8 = 26 = (22+4), so that's true.

All conditions are met, so your answer works.

For 2, you're perfectly right, but the way I'd do it is to find the total cost of the 12kg of coffee, and then divide that by 12 at the end. It's just slightly less work.

roel · 2007-12-07 12:30:17

Identity wrote:

5.
Let x be the amount of 20% acid solution that must be added in litres.
0.3(3)+0.2(x) = 0.26(3+x)
0.9 + 0.2x = 0.78 + 0.26x
0.06x = 0.12
x = 2
So he ought to add 2 litres of 20% acid solution.
These problems are really nice, lots of fun to do

How did you get the (3+x) in 0.3(3)+0.2(x) = 0.26(3+x)?

thanks identity. you're right.. lots of fun.. lots of headache, too...

Last edited by roel (2007-12-07 12:59:00)

roel · 2007-12-07 12:37:16

NullRoot wrote:

roel wrote:
4. every choice has a corresponding point. A is worth 5 points, B is 4 points, C is 3 points, and D is 2 points. Michelle got a total of 100 points. If she had 3 more B's than A's, 5 C's more than twice the number of A's and 6 D's less than thrice the number of A's, find the number of C's she got.
A - 5
B - 4
C - 3
D - 2
Michelle's
A = ?
B = 3 + A
C = 5 + 2A
D = 3A - 6
Here's how I went about it.
The A, B, C, and D are misleading, Roel. They give you the values for these so they aren't actually variables. They're what I would call a placeholder.
This is what I interpret her score to be:
100 = wA + xB + yC + zD
From the word problem we know:
x = 3+w
y = 5+2w
z = 3w-6
Substituting, including for the values of A,B,C,D:
100 = w5 + (3+w)4 + (5+2w)3 + (3w-6)2
100 = 5w + 12 + 4w + 15 + 6w + 6w - 12
100 = 21w + 15
85 = 21w
4.0476 ≈ w
So I think there may have been an error in copying somewhere? I'd expect only whole numbers given the context of the problem.

Thanks.. I checked the questionnaire, and I copied it right. Anyway, I trust you more here. So, i think It is the questionnaire itself that has the problem.. It's ok.. thanks again..

roel · 2007-12-07 12:41:43

mathsyperson wrote:

For questions like 1, it's easy to check for yourself whether your answer is right - you just check to make sure the given facts aren't contradicted.
You think that Trixie is 10, Numerico is 20 and Frezel is 22.
Check 1:Numerico's age is twice trixie's age.
20 = 2 x 10, so that's true.
Check 2:Frezel is 2 years more than twice trixie's age.
22 = 2 x 10 + 2, so that's true.
Check 3:The sum of numerico and trixie's age 2 years ago is equal to the age of Frezel 4 years from now.
(20-2)+(10-2) = 18+8 = 26 = (22+4), so that's true.
All conditions are met, so your answer works.

For 2, you're perfectly right, but the way I'd do it is to find the total cost of the 12kg of coffee, and then divide that by 12 at the end. It's just slightly less work.

thanks.. now I know..

roel · 2007-12-07 13:44:39

Here's for
DAY 7

1. Increasing the original saline solution by 12% and then increaseing the new solution by 25% is equivalent to increasing the original saline solution by how many percent?

2. Dr. A wishes to have 15 gallons of an 80% formaldehyde solution. In her inventory, she has a pure fomaldehyde and some 50% formaldehyde solution. How many gallons of pure formaldehyde should she mix to obtain the desired solution?

3.the total travel time for a family to reach a campsite is 2 hours. THey drive for 81km and hike for 2 km. If they drive 50kph faster than they hinke, what is their average driving speed?

4. Ryan travels in his car from north E to east E at a rate of 30kph and returns along the same route at a rate of 50kph. what is his average speed for the whole trip?

5. working alone, it takes twice as long for a helper to do a welding job as it would take for an experienced welder. If it takes a total of 8 hours for the two welders to complete the job working togeteher, how long does it take the helper to finish alone?

In these set, I don't really have an idea on how i should start answering it.

NullRoot · 2007-12-07 14:54:24

1. Original Saline Volume = S
S*1.12 = S2, Saline Volume #2
S2*1.25 = S3, Saline Vol #3

Substituting in for S2:
(S*1.12)*1.25 = S3
S*1.12*1.25 = S3
S*1.4 = S3

So it's the same as a 40% increase.

2.
In 15 gallons of 80% solution, the amount of fermaldehyde is:
15*0.80 = 12 gallons

The amount of Fermaldehyde per gallon of pure fermaldehyde is 1 gallon.
The amount of Fermaldehyde per gallon of 50% fermaldehyde is 0.5 gallons.
So, we're looking for the answer to these equations:
x + y = 15
x + 0.5y = 12
Where x is gallons of pure solution, and y is gallons of half solution. There should be 15 gallons of fluid between them, but 12 gallons of fermaldehyde.
If we use substitution, we can see:
x = 15 - y
so: (15 - y) + 0.5y = 12
-y + 0.5 y = -3
-0.5y = -3
y = 6
Then x = 9.
So 9 Pure gallons and 6 half gallons.

Identity · 2007-12-07 14:57:05

roel wrote:

How did you get the (3+x) in 0.3(3)+0.2(x) = 0.26(3+x)?
thanks identity. you're right.. lots of fun.. lots of headache, too...

Sorry, I didnt' make it very clear

0.3 is the percentage of acid in (3) litres of solution.
0.2 is the percentage of acid in (x) litres of solution.
0.26 is the percentage of acid in (3+x) litres of solution. (As you're adding x litres to 3 litres the total becomes 3+x litres).

That's kinda how it works... it took me a while to understand it when I first saw the solution.

Last edited by Identity (2007-12-07 14:57:59)

mathsyperson · 2007-12-08 02:56:37

3.

Let's say the family hikes with an average speed of x km/h.
Then, because time = distance/speed, it would take them 2/x hours to hike 2 km.

Similarly, if they drive for 81km at a speed of (50+x), it would take them 81/(50+x) hours to do that.

We're told that it take 2 hours to do both, so now we can make an equation.
2/x + 81/(50+x) = 2.

Multiply by stuff until there aren't any denominators:
2(50+x) + 81x = 2x(50+x)

Expand:
100+2x + 81x = 100x + 2x²

Simplify:
2x² + 17x - 100 = 0

Solve by quadratic equation: x = [-17 ± (17² - 4x2x(-100))]/2x2

x = [-17± 33]/4 = -12.5 or 4.
Since a negative x wouldn't make sense in this case, that means that x=4.

Therefore, the family hikes at 4 km/h and drives at 54 km/h.

Check: 2/4 + 81/54 = 1/2 + 3/2 = 2.

roel · 2007-12-20 04:12:28

hi... i'm back.. ahaha... sorry, i was not able to check this for a long time... I've been busy with my feasibility study..

But then, let's keep it going.. haha..

here's for

DAY 8

1. The average speed of a train is 20kph faster than that of a car. In 20 hours, the train covers the same distance that the car covers in 30 hours. what is the average speed of the train?

2. A can finish a job in 6 hours. After working for an hour, J helped him and together they finished the job in 2 more hours. How many hours will it take Joseph to finish the job if he will work alone?

3. Anthropologists can approximate the height of a primate by the size of the humerus by using the equation H = 1.2L + 27.8, where L is the length of the humerus and H is the height of the primate. Dr. A, an anthropologist, measured the height of a primate to be 66 inches, what is the approximate length of the humerus of his primate?
(I'm really having a hard time dividing when there is a decimal. especially when there is a decimal in both the divisor and dividend.)

4. If 5 workers can complete 9 chairs in 4 days, how long will it take for 8 workers to complete 18 chairs.

(there are some problems here that i already solved. I just don't know the reason why when i tried to solve it again, i didn't arrive at any answer.. ahaha.. any tip?)

we'll just have 4items.. so we can start with the new set of problems tomorrow...

thanks again...

Last edited by roel (2007-12-20 04:13:47)

TheDude · 2007-12-20 06:55:50

1. Let's call the speed of the car C and the speed of the train T. The train is 20 kph faster than the car, so T = C + 20. We also know that in 20 hours the train will travel as far as the car can in 30 hours, so that gives us 20T = 30C. This gives us a system of 2 simultaneous equations. To solve it we'll use substition.

From the first equation we know what T equals in terms of C, namely T = C + 20. We'll substitute this value in for T in the second equation to give us 20(C + 20) = 30C. From here we get 20C + 400 = 30C -> 10C = 400 -> C = 40. Plug this value of C into the first equation to give us T = 40 + 20 = 60 kph. To check this, the train will travel 60 * 20 = 120 km in 20 hours, while the car will travel 40 * 30 = 120 km in 30 hours, so we have the right answer.

2. Since A finishes the job in 6 hours, after 1 hour he's finished 1/6 of the job, meaning that there is still 5/6 of the job left to go. After 2 more hours A will do another 2/6 of the job for a total of 3/6, or 1/2 of a full job. That means that J did 1/2 of a job in 2 hours, so multiply that by 2 and we find that J can do a whole job in 4 hours.

3. This one's simple if you have a calculator. Just plug 66 in for H to give you 66 = 1.2L + 27.8 -> 1.2L = 66 - 27.8 = 38.2 -> L = 38.2 / 1.2 = 31.833333.... inches = 31 5/6 inches.

When dealing with decimals, don't let them scare you. Just treat them like normal numbers until you have to either add, subtract, mulitply, or divide them. Then just break out a calculator and keep going.

4. We know that 5 workers build 9 chairs in 4 days. That means that 5 workers build 9/4 chairs in 1 day, which we can further simplify to discover that 1 worker builds 9/20 of a chair in 1 day. Now multiply that value by 8 since we have 8 workers and we see that 8 workers build 18/5 chairs in 1 day. From here, divide the number of chairs they need to build by the number of chairs they build per day for your answer. In this case we have to build 18 chairs, at 18/5 chairs per day gives us 18 / (18/5) = 5 days.

If any of these explanations don't make sense just let me know and I or someone else can explain in more detail.

Math Is Fun Forum

#26 2007-11-29 01:37:38

Re: Quantitative reasoning for my Law Aptitude test..

#27 2007-11-29 07:53:08

Re: Quantitative reasoning for my Law Aptitude test..

#28 2007-11-29 17:17:02

Re: Quantitative reasoning for my Law Aptitude test..

#29 2007-11-29 17:21:28

Re: Quantitative reasoning for my Law Aptitude test..

#30 2007-11-29 23:29:55

Re: Quantitative reasoning for my Law Aptitude test..

#31 2007-12-01 14:29:30

Re: Quantitative reasoning for my Law Aptitude test..

#32 2007-12-01 15:22:28

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#33 2007-12-01 17:47:08

Re: Quantitative reasoning for my Law Aptitude test..

#34 2007-12-02 00:53:39

Re: Quantitative reasoning for my Law Aptitude test..

#35 2007-12-04 14:51:09

Re: Quantitative reasoning for my Law Aptitude test..

#36 2007-12-04 17:54:12

Re: Quantitative reasoning for my Law Aptitude test..

#37 2007-12-04 21:48:09

Re: Quantitative reasoning for my Law Aptitude test..

#38 2007-12-05 01:50:35

Re: Quantitative reasoning for my Law Aptitude test..

#39 2007-12-07 12:30:17

Re: Quantitative reasoning for my Law Aptitude test..

#40 2007-12-07 12:37:16

Re: Quantitative reasoning for my Law Aptitude test..

#41 2007-12-07 12:41:43

Re: Quantitative reasoning for my Law Aptitude test..

#42 2007-12-07 13:44:39

Re: Quantitative reasoning for my Law Aptitude test..

#43 2007-12-07 14:54:24

Re: Quantitative reasoning for my Law Aptitude test..

#44 2007-12-07 14:57:05

Re: Quantitative reasoning for my Law Aptitude test..

#45 2007-12-08 02:56:37

Re: Quantitative reasoning for my Law Aptitude test..

#46 2007-12-20 04:12:28

Re: Quantitative reasoning for my Law Aptitude test..

#47 2007-12-20 06:55:50

Re: Quantitative reasoning for my Law Aptitude test..

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