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problem solving,

by siddhartha123 » Thu Dec 15, 2011 11:48 am
Hai,

1.)There are 15 slate rocks ,20 pumice rocks ,10 granite rocks ,randomly distributed
in a certain field . If two rocks are to be choosen random, what is the propability that
rocks will be slate rocks?

[spoiler]Ans: 1/66[/spoiler]

2.) A rectangular frame with length 18 inc and 15 inc wide,The frame encloses a rectanglar picture
that has the same area as the frame itself .If the length and width of the picture have the same ratio as the lenghth and width of the frame, what is the length of the picture in inches?

a) 9 squareroot 2 b) 3/2 c) 9/squareroot 2 d)15(1-1/sqaureroot 2) e)9/2
[spoiler]ans:a[/spoiler]

3.) 6 identical machines ,working at equal rates can ,finish a work in 12 days , How many additional
machines are required to do the same work in 8 days?

[spoiler]Ans: 3[/spoiler]

4.) A group of 8 friends want to play doubles in tennis.In how many different ways can the group be divided into 4 teams of 2 people?

[spoiler]ans: 105[/spoiler]

5.) A certain culture of bacteria quadraples every hour .If a container with these bacteria was half full at 10:00 am , at what time was it 1/8 full.

[spoiler]Ans:9:00 am.[/spoiler]

6.)Peter invested a certain sum of money in a simple interest bond whose value grew $300 at the end
of 3 rd year, and $400 at the end of another 5 yrs . what was the rate of interest at which he invested.?

[spoiler]ans: 8.33 % [/spoiler]
M.siddhartha
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by shankar.ashwin » Thu Dec 15, 2011 10:41 pm
siddhartha123 wrote:Hai,

1.)There are 15 slate rocks ,20 pumice rocks ,10 granite rocks ,randomly distributed
in a certain field . If two rocks are to be choosen random, what is the propability that
rocks will be slate rocks?

[spoiler]Ans: 1/66[/spoiler]
15 slates out in a total of 45.

= 15C2/45C2

(15/45) * (14/44) = 7/66
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by shankar.ashwin » Thu Dec 15, 2011 10:45 pm
siddhartha123 wrote:Hai,



4.) A group of 8 friends want to play doubles in tennis.In how many different ways can the group be divided into 4 teams of 2 people?

[spoiler]ans: 105[/spoiler]
4 teams of 2 each can be formed in 8C2 * 6C2 * 4C2 * 2C2 ways

= 28 * 15 * 6 * 1

Ordering of the 4 teams do not matter, so divide the number by 4!

= (28*15*6) / (4*3*2) = 7*15 = 105
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by neelgandham » Fri Dec 16, 2011 6:11 am
3.) 6 identical machines ,working at equal rates can ,finish a work in 12 days , How many additional
machines are required to do the same work in 8 days?

6 Machines can finish the work in 12 days
1 Machine can finish the work in 12*6 days
x Machines can finish the work in 8 days

machine days, the product of # of machines and the number of days they can complete the work in, are equal. i.e x*8 = 12*6*1
x = 9
So,(9-6) 3 additional machines are required to do the same work in 8 days
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by neelgandham » Fri Dec 16, 2011 6:30 am
5.) A certain culture of bacteria quadraples every hour .If a container with these bacteria was half full at 10:00 am , at what time was it 1/8 full.

At 10:00 am - The container is 1/2 full
At 09:00 am - The container is 1/8((1/2)/4) full
At 08:00 am - The container is 1/32((1/8)/4) full.

The answer is 'at 09:00 am'
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by siddhartha123 » Fri Dec 16, 2011 10:22 am
neelgandham wrote:5.) A certain culture of bacteria quadraples every hour .If a container with these bacteria was half full at 10:00 am , at what time was it 1/8 full.

At 10:00 am - The container is 1/2 full
At 09:00 am - The container is 1/8((1/2)/4) full
At 08:00 am - The container is 1/32((1/8)/4) full.

The answer is 'at 09:00 am'
Thank you neel ;
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by neelgandham » Fri Dec 16, 2011 12:46 pm
No problem ! and All the best for your exam on the 19th !
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by siddhartha123 » Sat Dec 17, 2011 11:02 pm
neelgandham wrote:No problem ! and All the best for your exam on the 19th !
THANKS NEEL; HOPE THIS TIME WILL SCORE
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by shekhar.kataria » Sun Dec 18, 2011 3:22 am
Is the Quoted Question below correct??.. I am not able to understand. To me it seems the picture will have the same size.

2.) A rectangular frame with length 18 inc and 15 inc wide,The frame encloses a rectanglar picture
that has the same area as the frame itself .If the length and width of the picture have the same ratio as the lenghth and width of the frame, what is the length of the picture in inches?

a) 9 squareroot 2 b) 3/2 c) 9/squareroot 2 d)15(1-1/sqaureroot 2) e)9/2
[spoiler]ans:a[/spoiler]
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by GMATGuruNY » Sun Dec 18, 2011 4:29 am
siddhartha123 wrote: 4.) A group of 8 friends want to play doubles in tennis.In how many different ways can the group be divided into 4 teams of 2 people?
I posted two different approaches here:

https://www.beatthegmat.com/forming-teams-t73034.html
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by GMATGuruNY » Sun Dec 18, 2011 4:38 am
siddhartha123 wrote: A certain culture of bacteria quadruples every hour. If a container with these bacteria was half full at 10:00 a.m., at what time was it one-eighth full?
(A) 9:00 a.m.
(B) 7:00 a.m.
(C) 6:00 a.m.
(D) 4:00 a.m.
(E) 2:00 a.m.
Let the container = 16 units.
At 10am, the half-full container = 16/2 = 8 units.
The number of units when the container is 1/8 full = 16/8 = 2.
Since the culture quadruples every hour, it takes 1 hour for the culture to increase from 2 to 8.
Thus, the time when container was 1/8 full (with 2 units) = 10am - 1 = 9am.

The correct answer is A.
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by GMATGuruNY » Sun Dec 18, 2011 4:57 am
siddhartha123 wrote:Peter invested a certain sum of money in a simple interest bond whose value grew to $300 at the end of 3 years and to $400 at the end of another 5 years. What was the rate of interest in which he invested his sum?
(A) 6.25%
(B) 6.67%
(C) 8.33%
(D) 12%
(E) 12.5%
Since the bond grows from 300 to 400 at the end of another 5 years, the amount of interest earned each year = 100/5 = 20.
Since after 3 years the account has 300, the initial investment = 300 - 3(20) = 240.
Since 10% of 240 = 24, the yearly interest rate must be a bit less than 10.

The correct answer is C.
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by GMATGuruNY » Sun Dec 18, 2011 5:14 am
siddhartha123 wrote:
A rectangular frame with length 18 inc and 15 inc wide,The frame encloses a rectangular picture that has the same area as the frame itself. If the length and width of the picture have the same ratio as the length and width of the frame, what is the length of the picture in inches?

a) 9√2 b) 3/2 c) 9/√2 d)15(1 - 1/√2) e)9/2
Since the frame and the picture have equal areas, the area of the picture = 1/2 the total area = (1/2)(18)(15) = 135.
It is given that l:w = 18:15 = 6:5.
If each dimension doubles so that l=12 and w=10, the area = 12*10 = 120.
Since the actual area = 135, the length must be a bit more than 12.
Only answer choice A works:
9√2 ≈ 9(1.4) ≈ 12.6.

The correct answer is A.
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by LalaB » Sun Dec 18, 2011 8:11 am
A certain culture of bacteria quadraples every hour .If a container with these bacteria was half full at 10:00 am , at what time was it 1/8 full.

1/8*(4^t/1)=1/2

(2^-3)*(2^-2t)=(2^-1)
-3+2t=-1
2t=2
t=1

so, now we see that in an hour 1/8 of bacteria became 1/2
since it was 1/2 at 10-00, then it was 1/8 at 10-1 =9.00 am
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