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Be Careful!!

by logitech » Sun Dec 07, 2008 11:34 am
1) If m > 0, y > 0, and x is m percent of 2y, then, in terms of y, m is what percent of x?



2) A certain NYC taxi driver has decided to start charging a rate of r cents per person per mile. How much, in dollars, would it cost 3 people to travel x miles if he decides to give them a 50% discount?


3)What is the ratio of the surface area of a cube to the surface area of a rectangular solid identical to the cube in all ways except that its length has been doubled?

4)A certain square is to be drawn on a coordinate plane. One of the vertices must be on the origin, and the square is to have an area of 100. If all coordinates of the vertices must be integers, how many different ways can this square be drawn?

5) Is z even?

(1) z/2 is even.

(2) 3z is even.
Last edited by logitech on Sun Dec 07, 2008 3:50 pm, edited 3 times in total.
LGTCH
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by niraj_a » Sun Dec 07, 2008 11:54 am
for these two i would pick numbers and match from the answer choices rather than try the algebraic method
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by kris610 » Sun Dec 07, 2008 1:30 pm
Edit: Adding answers one by one!


1. (10^4)/2y ?

2. 1.5rx/100 ?

3. 3/5?

4. I'm guessing 8, but I also feel I may be way off..:)
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Re: Be Careful!!

by muzali » Mon Dec 08, 2008 1:31 pm
1) If m > 0, y > 0, and x is m percent of 2y, then, in terms of y, m is what percent of x?
x=(m/100)*2y=2ym/100=ym/50
m=Z percent of x, we need to find Z
Z=m*100/x=m*100/(ym/50)=5000/y
2) A certain NYC taxi driver has decided to start charging a rate of r cents per person per mile. How much, in dollars, would it cost 3 people to travel x miles if he decides to give them a 50% discount?
r cents per person per mile
=>(r/100) $ per person per mile
=> (3r/100) $ for 3 people per mile
=> (3xr/100) $ for 3 people for x miles
=> (3xr/200) $ for 3 people for x miles with 50% discount
3)What is the ratio of the surface area of a cube to the surface area of a rectangular solid identical to the cube in all ways except that its length has been doubled?
Surface area of cube with side a= 6a*a
Surface area of cuboid with one side 2a= 2(a*a+a*2a+a*2a)=10a*a
Desired ratio=6/10=3/5
4)A certain square is to be drawn on a coordinate plane. One of the vertices must be on the origin, and the square is to have an area of 100. If all coordinates of the vertices must be integers, how many different ways can this square be drawn?
4 squares can be drawn using the +x,+y; +x,-y; -x,-y and -x,+y where the absolute values of x and y are 10 to have area of 10*10 =100
4 other squares can be drwn by using the diagonals between the axes.

Total number = 4+4 =8
5) Is z even?

(1) z/2 is even.

(2) 3z is even.
(1) z/2 is even => z=even*2 = even =>sufficient
(2) 3z is even
odd*even =even, 3 is odd , so z has ro be even =>sufficient

Answer = D[/quote]
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by kris610 » Mon Dec 08, 2008 2:24 pm
Yeah, for the squares, I thought of the four that can be drawn in the 4 quadrants and then I rotated each of them 45 deg to get 8. So, it was a guesswork and am not sure if I missed anything.
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Re: Be Careful!!

by logitech » Mon Dec 08, 2008 10:12 pm
muzali wrote:
1) If m > 0, y > 0, and x is m percent of 2y, then, in terms of y, m is what percent of x?
x=(m/100)*2y=2ym/100=ym/50

m=Z percent of x, we need to find Z

Z=m*100/x=m*100/(ym/50)=5000/y

Good! People usually forget the % ( 100)

muzali wrote:
2) A certain NYC taxi driver has decided to start charging a rate of r cents per person per mile. How much, in dollars, would it cost 3 people to travel x miles if he decides to give them a 50% discount?
r cents per person per mile
=>(r/100) $ per person per mile
=> (3r/100) $ for 3 people per mile
=> (3xr/100) $ for 3 people for x miles
=> (3xr/200) $ for 3 people for x miles with 50% discount

Good! 1dolar=100 cents - you can miss this detail in hurry!
muzali wrote:
3)What is the ratio of the surface area of a cube to the surface area of a rectangular solid identical to the cube in all ways except that its length has been doubled?
Surface area of cube with side a= 6a*a
Surface area of cuboid with one side 2a= 2(a*a+a*2a+a*2a)=10a*a
Desired ratio=6/10=3/5

Well done
muzali wrote:
4)A certain square is to be drawn on a coordinate plane. One of the vertices must be on the origin, and the square is to have an area of 100. If all coordinates of the vertices must be integers, how many different ways can this square be drawn?
4 squares can be drawn using the +x,+y; +x,-y; -x,-y and -x,+y where the absolute values of x and y are 10 to have area of 10*10 =100
4 other squares can be drwn by using the diagonals between the axes.

Total number = 4+4 =8

In Quarter 1: You can have (0,10), (6,8), (8,6) and (10,0)

For the 4 Quarters : 4x4 = 16

4 will be overlap. So 16-4 = 12

This one was trick!! BE CAREFUL

muzali wrote:


5) Is z even?

(1) z/2 is even.

(2) 3z is even.
(1) z/2 is even => z=even*2 = even =>sufficient
(2) 3z is even
odd*even =even, 3 is odd , so z has ro be even =>sufficient

Answer = D

3z = EVEN but nothing in question stems says Z is an integer so Statement two is INSUF.

Hence , A

BE CAREFUL! B-)
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by msd_2008 » Tue Dec 09, 2008 1:34 am
Logitech,

I am somehow not convinced with the 5th answer i.e Is Z even?
You mentioned that it should be A and not D because it is nowhere given that Z is an integer.
Well, if 3Z is even then Z has to be even because 3 is odd. And why do we need the information about Z being an integer here? Can you illustrate any fraction which when mutliplied by 3 gives u an even product?

Regards
MSD
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by logitech » Tue Dec 09, 2008 1:55 am
msd_2008 wrote:Logitech,

I am somehow not convinced with the 5th answer i.e Is Z even?
You mentioned that it should be A and not D because it is nowhere given that Z is an integer.
Well, if 3Z is even then Z has to be even because 3 is odd. And why do we need the information about Z being an integer here? Can you illustrate any fraction which when mutliplied by 3 gives u an even product?

Regards
MSD
3z=2

z=2/3

Is 2/3 even ?

https://en.wikipedia.org/wiki/Even_and_odd_numbers

In mathematics, the parity of an object states whether it is even or odd.

This concept begins with integers. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without remainder; an odd number is an integer that is not evenly divisible by 2. (The old-fashioned term "evenly divisible" is now almost always shortened to "divisible".) A formal definition of an odd number is that it is an integer of the form n = 2k + 1, where k is an integer. An even number has the form n = 2k where k is an integer.

Examples of even numbers are −4, 8, 0, and 42. Examples of odd numbers are −3, 9, 1, and 5. A fractional number like 1/2 or 3.141 is neither even nor odd.

The set of even numbers can be written:

{Evens} = 2Z = {..., −6, −4, −2, 0, 2, 4, 6, ...},

where Z is the set of all integers. The set of odd numbers can be shown like this:

{Odds} = 2Z + 1 = {..., −5, −3, −1, 1, 3, 5, ...}.
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by shafeek » Thu Dec 11, 2008 3:50 pm
regarding the number of squares that can be drawn. It will only be 4.
you can draw the squares with 45 degrees from x axis because then the vertex of the square on X axis will be 10 root 2 which is not an integer.

Question says the points needs to be integers..
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