My last MATH Qs

[airvent]

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Ok, I?ve been studying for the math section (as you can tell), I?m moving on to Orgo now, but I need an assist on these last few MATH problems:

1)The circumference of a circle is increased by 20%. Find the % of increase in the area.

A 40%
B) 44%
C) 10%

2)If the diameter of a cylinder is increased by 20%, and the Height is decreased by16&2/3%. What % is the volume changed?

A) +10%
B) +20%
C) +24%

The length of a rectangle is twice the width. If the perimeter of a square equals the perimeter of the rectangle, what is the ratio of the area of the rectangle to the area of the square?
A 1:1
B) 4:1
C) 8:9

Paris Hilton has a total of $34 in nickels, dimes, and quarters. If she has 3 times as many dimes as quarters and 2 times as many nickels as dimes, how many dimes does she have?
A 12
B) 40
C) 120

Thanks again to all the math pros. These are from the Kaplan final. So I don?t have explanations for these problems. I would buy the Kaplan GRE math, but its time for me to move on to Chemistry(my last section to study). My DAT is scheduled for AUG 2(about a week)

 

[dane4695]

I also have a qusetion about math that puzzles me (I don't want to look @ those Q's yet cuz i haven't taken the final).

What is the probability of flipping tails 5 of 8 times? I can't figure out how to do this for some reason...

 

[coodoo]

Ok, I?ve been studying for the math section (as you can tell), I?m moving on to Orgo now, but I need an assist on these last few MATH problems:

1)The circumference of a circle is increased by 20%. Find the % of increase in the area.

A 40%
B) 44%
C) 10%

Ill take the first one

C = 2piR A=piR^2

R = C/2pi

A = pi(1.2C/2pi)^2 I got the 1.2 from 1*1/5=1/5 = .2 and .2+1 =1.2
the pi's cancel and you get 1.44C/4 = A2 and C/4 =A1
so you see that 44% of 1 is .44 and hence a 44% increase from 1 to 1.44

 

[CJMPre-Med]

The length of a rectangle is twice the width. If the perimeter of a square equals the perimeter of the rectangle, what is the ratio of the area of the rectangle to the area of the square?

A 1:1
B) 4:1
C) 8:9

Assume a rectangle with length 2x and width x. Therefore, the perimeter of the rectangle will be 6x (2x+2x+x+x). The perimeter of the square is also 6x, but each side of the square will then be 1.5x, as all 4 sides must be equal (6x/4 = 1.5x).

Now, the area of the rectangle is given by length x width, or (2x)x(x) = 2x^2

The area of the square will be (1.5x)x(1.5x) = 2.25x^2


Since they ask for the ratio between the area of the rectangle and the area of the square, you need to find the common factor, which is (.25x^2). Divide each area by .25x^2, and you get (2x^2)/(.25x^2) = 8 for the rectangle, and for the square, you have (2.25x^2)/(.25x^2) = 9.


Thus, the ratio of the area of the rectangle to the area of the square is choice C) 8:9.

Paris Hilton has a total of $34 in nickels, dimes, and quarters. If she has 3 times as many dimes as quarters and 2 times as many nickels as dimes, how many dimes does she have?

A 12
B) 40
C) 120

For this, I feel the easiest (and for me the quickest, since I can do multiplication in my head very rapidly) way to proceed is to just plug in the #'s from the choices given. 120 dimes assumes 240 nickels (120x2) assumes 40 quarters (120/3). These relationships are given in the question. So you have $12 in dimes, $12 in nickels, and $10 in quarters (by simple multiplication by their respective monetary values). $12+12+10 = $34.


To do this algebraically, I believe you'd have to proceed like so:

Find the coin denomination with the fewest # of individual coins. This would be quarters, and should be obvious from the way the question is phrased, as there are TWICE as many nickels as dimes, yet THREE TIMES as many dimes as quarters. So among the coins, there will be the fewest quarters. You then set quarters to be x, and the other values follow as 3x (dimes) and 6x (nickels); this is given by the expressed relationships, though it may be hard to pick out from the text.


I believe you'd then have to multiply each by its denomination's monetary value in cents. So x quarters would become 25x, 3x dimes would become 30x, and 6x nickels would also become 30x. This gives you 85x, which you then set equal to $34 (it's easier to view this as 3400 cents for our present purposes).

We then have 85x = 3400 (in cents); you then divide 3400 by 85 to get x = 40.

Then just plug x = 40 in to the original values of the numbers of coins you had. If you'll recall, you had x quarters, so there are 40 quarters; you had 3x dimes, so there are 120 dimes; you had 6x nickels, so there are 240 nickels. All of these values are in agreement with the quicker, more intuitive method shown previously.

As you can see, the algebraic method is, in this case, much more cumbersome to use than simple intuition and multiplication in my opinion. 🙂 But it may be useful for you to try to do as many of these algebraically as you can, as it's a skill that is often necessary for these types of questions; it just so happens that we didn't need it in this case. 🙂


Perhaps I'll do some more in a bit, but I have to get ready to head out for some drinks. Hope this helped. 🙂

 

[CJMPre-Med]

I also have a qusetion about math that puzzles me (I don't want to look @ those Q's yet cuz i haven't taken the final).

What is the probability of flipping tails 5 of 8 times? I can't figure out how to do this for some reason...

I think it would be the probability value for each separate event (which is 1/2, because you have a one out of two chance of flipping tails for each toss) multiplied 5 times. So it would be (1/2)^5, which is 1/32. This should be one of your choices. 🙂


But I may very well be mistaken-- I haven't done any sort of probability or permutations since freshman year of HS, which was over a decade ago. 😛 So take this with a dollop of salt until someone more learned pops up. 😀

 

[Sprgrover]

CJM - You've sure been hanging around the dental forums a lot! You are of course welcome here. So when are you going to see the light and take that exciting step into dentistry?

 

[CJMPre-Med]

CJM - You've sure been hanging around the dental forums a lot! You are of course welcome here. So when are you going to see the light and take that exciting step into dentistry?

Probably when they socialize medicine. 😉 😛

Nah, but seriously, I was just scrolling down the main forum listing page, and saw that this topic was posted by airvent; I had helped him out with a math question in a topic a couple of days ago, so I figured I'd see what he was having trouble with now. 🙂


Glad to know I'm welcome, though. 🙂

 

[dane4695]

Yeah... that wasn't one of the answers. It's not a 1/2 probability question -- it's different. That's what I was thinking also, but because it can happen at any part of the flipping process, it's not 1/2 prob. I still don't know how to do it though 🙂

 

[simonlee]

This probability question is quite tricky. I got a similar question in Topscore("6 tails our of 9 tosses"). I cannot figure out when I was taking the exam. Then while I was "sleeping", I remembered how I did it in my old class.
First of all, if you got 5 tails out of 8 tosses, it means you got 3 heads, and T T T T T .
Look at the 5 tails I drew above, there are 3 possible situations to put 3 heads in the empty space between the tails.
(1) 3 heads together. Then there are 6 positions to put the 3 heads between "T", so 1C6.
(2) 2 heads together and 1 heads between 2 "T". Then there are 6 positions and 2 heads occupy one of them and 1 head occupies another. So it is 2C6. However, these two positions are interchangable. So it is 2*2C6.
(3) Finally, each of the 3 heads is separated by "T". So it is 3C6.
The probability is (1C6+2*2C6+3C6)/(2^8)=7/32.
Hope this makes sense to you.

 

[CJMPre-Med]

Yeah, I think the "problem" I "solved" was the easier (and unasked 😛) one of "what is the probability of flipping tails 5 times in a row?"-- which I believe would be 1/32. Now that I read the question again, it's clearly asking something different. My advice would be to listen to the above poster. 😀