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# Again me back with some more questions: Q1: A certain

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Manager
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Again me back with some more questions: Q1: A certain [#permalink]  25 Oct 2006, 00:53
Again me back with some more questions:

Q1: A certain baseball league has decided to increase the diameter of the baseballs it uses from 2.9 inches to 3.2 inches. If baseballs are spherical, by approximately what percent will the volume of these baseballs increase? (Volume of a sphere is r3)

a) 15% b)25% c)35% d)45% e)55%

Guys any shortcuts to do this sort of question......

Q2:
If a and b are positive integers, what is the value of a+ b?

(1) a^2 - 2ab + b^2 = 25

(2) a^2 - b^2 = -25

Q3: Refer Fig: A: If point R (not shown) represents the third vertex of triangle PQR in the figure above, is triangle PQR a right triangle?

(1) The x coordinate of point R is not a prime number.

(2) The x coordinate of point R is not a multiple of three.
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Fig-A Q 10-Math 5-6 Adv Drill.JPG [ 3.91 KiB | Viewed 262 times ]

VP
Joined: 15 Jul 2004
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On Q3 -

The first condition rules out the values for x coord - 11, 13, 17, 19
The second condition rules out the values - 9, 12, 15, 18

Still you are left with a infinite values for x and infinite values for Y.

Hence both choices are insufficient.

Let me know the OA on this one as I am not really sure if there's a trick to solving this.
Manager
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Q2. C
Bloody tricky
from I, |a-b| = 5 (difference between a and b is 5)
from II, a+b = -25/(a-b)

We have been informed that a,b are both +ve integer, and from I we knew that their difference is 5. SO , it is either a>b or b>a, we don't know which yet.

Assuming case a>b
from II, a+b = -25/5 = -5 ,
contradiction with the given info that both a,b are +ve integer. So the assumption of a>b is wrong

Assuming case a>b
from II, a+b = -25/-5 = 5
SOLVED.

At first glance, there seems to be multiple solutions, but thanks to the given condition (a,b +ve), only one viable solution left.

Q3. E
Imagine the line PQ is a diameter of a circle. In order to form a right triangle, R can be anywhere in the circumference of the circle.
Quite a trivial question, unless the we are given the condition that coordinate of R is an integer, then it will be tougher.
VP
Joined: 15 Jul 2004
Posts: 1481
Schools: Wharton (R2 - submitted); HBS (R2 - submitted); IIMA (admitted for 1 year PGPX)
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Kudos [?]: 59 [0], given: 13

Viperace wrote:
Q2. C
Bloody tricky
from I, |a-b| = 5 (difference between a and b is 5)
from II, a+b = -25/(a-b)

We have been informed that a,b are both +ve integer, and from I we knew that their difference is 5. SO , it is either a>b or b>a, we don't know which yet.

Assuming case a>b
from II, a+b = -25/5 = -5 ,
contradiction with the given info that both a,b are +ve integer. So the assumption of a>b is wrong

Assuming case a>b
from II, a+b = -25/-5 = 5
SOLVED.

At first glance, there seems to be multiple solutions, but thanks to the given condition (a,b +ve), only one viable solution left.

Q3. E
Imagine the line PQ is a diameter of a circle. In order to form a right triangle, R can be anywhere in the circumference of the circle.
Quite a trivial question, unless the we are given the condition that coordinate of R is an integer, then it will be tougher.

Thanks viper i missed the point of a and b being positive.
Manager
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My answer to Q 2 is B

from statement (2)
(a+b)(a-b)=-25

factors of -25= 1, -25 or 5, -5

since we know a and b are both positive integers, we know that they cannot be 5 and -5, therefore i can conclude that a=12, b=13, which gives me (a+b)=25 and (a-b)=-1, together -25
Manager
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forgot to mention for question 3, why isn't it C

in order to be a right triangle, the x coordinate must be equal to either 9 or 19, since combining both statements, we know that it can't be 9 nor 19, so it is sufficient to conclude it is not a right triangle

what is the OA by the way?
Intern
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Q1:
Volume of the sphere is ( pi*4r^3 )/3

The volume increase:
( 3.2^3 - 2.9^3 ) / ( 2.9 )^3 which equals to

( ( 1 + 0.3 /2.9 )^3 - 1

0.3 / 2.9 is approx 0.1 therefore we have
1.1^3-1 = ( 1.1 - 1 )( 1.1^2 + 1.1 + 1) = 0.1 ( 1.21 + 1.1 + 1 ) ~ 0.33
_________________

-al

Manager
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Thanks alot guys

For Q2, the ans is B,keeeeeekse u nailed it

The Ans to Q3 is E. keeeeeekse, I also fell for the same trap assuming it to be either 9 0r 19 and coming up with C. dwivedys nd viperace have explained it quite nicely and it does seem a trivial problem once I noted as viperace mentioned to consider this as the diameter. and yes...we need to remember that theyve not mentioned R point to be composed of integers.

al1234, u made Q1 question look quite easy....i really need to improve in math...theres way more room for me to improve. I am still confused at what explanation princeton gave which is as follows:

The question asks you to find the approximate percent, did you Ballpark? The radius of the baseball increases by just over 10%, which means the volume increases by just over 3 Ã— 10%.

I wanted to know, if any one can shed light on it...why did we multiply 10% by 3...whats the rule behind this step?
Manager
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keeeeeekse wrote:
My answer to Q 2 is B

from statement (2)
(a+b)(a-b)=-25

factors of -25= 1, -25 or 5, -5

since we know a and b are both positive integers, we know that they cannot be 5 and -5, therefore i can conclude that a=12, b=13, which gives me (a+b)=25 and (a-b)=-1, together -25

Good job!

Guess I need to pay more attention when dealing with INTEGER. Straight algebra won't usually work
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