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5 Math Questions: Please Help

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5 Math Questions: Please Help [#permalink] New post 27 Jan 2008, 12:16
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Hello, can somebody please help me solve the following 5 questions. Thank you very much.

1. What is the greatest prime factor of 4^17 – 2^28?
The correct answer is 7.


2. If K is a positive integer, is K the square of an integer?
i) K is divisible by 4
ii) K is divisible exactly by 4 different prime numbers.
The correct answer is e, statement i and ii together are NOT sufficient.


3. The symbol * represents one of four arithmetic options, plus, minus, divide, or multiply. Is (5*6)*2 = 5*(6*2)?
i) 5*6 = 6*6
ii) 2*0 = 2
The correct answer is a, statement i alone is sufficient.


4. Five pieces of wood have an average length of 124 cm and a median length of 140cm. what is the maximum possible length of the shortest piece of wood?
The correct answer is 100cm

5. Machine A produces pencils at a constant rate of 9000/hour. Machine B produces pencils at a constant rate of 7000/hour. If the two machines together must produce 100,000 pencils, and if each machine can operate for at most 8 hours, what is the least amount of time that machine B must operate.
The correct answer is 4 hours.
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Re: 5 Math Questions: Please Help [#permalink] New post 27 Jan 2008, 12:25
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Please, post the problems separately...

leizermike wrote:
1. What is the greatest prime factor of 4^17 – 2^28?
The correct answer is 7.


4^{17}-2^{28}=2^{34}-2^{28}=2^{28}*(2^6-1)=2^{28}*63=2^{28}*3^2*7
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Re: 5 Math Questions: Please Help [#permalink] New post 27 Jan 2008, 13:49
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No 5.

Asume machine A takes Ta time and machine b takes TB.

then 7000*TB+9000*TA=100,000
AND TA <=8 , TB <= 8

So TA=(100-7TB)/9 <= 8 <=> TB >= 4

So machine b will operate for minimum 4 hours
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Re: 5 Math Questions: Please Help [#permalink] New post 27 Jan 2008, 12:28
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leizermike wrote:
2. If K is a positive integer, is K the square of an integer?
i) K is divisible by 4
ii) K is divisible exactly by 4 different prime numbers.
The correct answer is e, statement i and ii together are NOT sufficient.


K=2^2*3^2*5^2*7 and K=2^2*3^2*5^2*7^2 are satisfy both conditions but only one is the square of an integer. E
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Re: 5 Math Questions: Please Help [#permalink] New post 27 Jan 2008, 12:34
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leizermike wrote:
3. The symbol * represents one of four arithmetic options, plus, minus, divide, or multiply. Is (5*6)*2 = 5*(6*2)?
i) 5*6 = 6*6
ii) 2*0 = 2
The correct answer is a, statement i alone is sufficient.


I think It have to be 5*6=6*5.

(5*6)*2 = 5*(6*2) is true for "+", "*" and is false for "-", "/"

1. 5*6=6*5 is true for "+", "*". sufficient.

2. 2*0=2 is true for "+", "-".insufficient.
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Re: 5 Math Questions: Please Help [#permalink] New post 27 Jan 2008, 12:36
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leizermike wrote:
4. Five pieces of wood have an average length of 124 cm and a median length of 140cm. what is the maximum possible length of the shortest piece of wood?
The correct answer is 100cm


7-t28169
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Re: 5 Math Questions: Please Help [#permalink] New post 27 Jan 2008, 12:40
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leizermike wrote:
5. Machine A produces pencils at a constant rate of 9000/hour. Machine B produces pencils at a constant rate of 7000/hour. If the two machines together must produce 100,000 pencils, and if each machine can operate for at most 8 hours, what is the least amount of time that machine B must operate.
The correct answer is 4 hours.


7-t57640

And, please, post OA after discussion. It will be more useful for you to see not only right ways but also wrong ones... :)
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Re: 5 Math Questions: Please Help [#permalink] New post 27 Feb 2008, 22:15
walker wrote:
leizermike wrote:
5. Machine A produces pencils at a constant rate of 9000/hour. Machine B produces pencils at a constant rate of 7000/hour. If the two machines together must produce 100,000 pencils, and if each machine can operate for at most 8 hours, what is the least amount of time that machine B must operate.
The correct answer is 4 hours.


7-t57640

And, please, post OA after discussion. It will be more useful for you to see not only right ways but also wrong ones... :)

We want to maximize A so that we can minimize B.
9,000*8 = 72,000

This implies we have 100,000 – 72,000= 28,000 remaining

Work/Rate = Time
28,000/7,000 = 4 hours
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Re: 5 Math Questions: Please Help [#permalink] New post 28 Feb 2008, 01:33
walker wrote:
leizermike wrote:
3. The symbol * represents one of four arithmetic options, plus, minus, divide, or multiply. Is (5*6)*2 = 5*(6*2)?
i) 5*6 = 6*6
ii) 2*0 = 2
The correct answer is a, statement i alone is sufficient.


I think It have to be 5*6=6*5.

(5*6)*2 = 5*(6*2) is true for "+", "*" and is false for "-", "/"

1. 5*6=6*5 is true for "+", "*". sufficient.
2. 2*0=2 is true for "+", "-".insufficient.


walker, 5*6=6*5 is true for "+", "x" but how is that suff?

if * is "x", suff.
if * is "+", insuff.
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Re: 5 Math Questions: Please Help [#permalink] New post 28 Feb 2008, 02:23
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GMAT TIGER wrote:
walker, 5*6=6*5 is true for "+", "x" but how is that suff?

if * is "x", suff.
if * is "+", insuff.


plus: (5+6)+2 = 5+(6+2) true
multiply: (5x6)x2 = 5x(6x2) true
minus: (5-6)-2 = 5-(6-2) false
divide: (5/6)/2 = 5/(6/2) false


1. 5*6=6*5:
plus: (5+6) = (6+5) true
multiply: (5x6) = (6x5) true
minus: (5-6) = (6-5) false
divide: (5/6) = (6/5) false
Therefore, condition 1 points that * could be + or x. For both operations (5*6)*2 = 5*(6*2) is true. So, information is sufficient to answer the question.

2. 2*0=2:
plus: (2+0) = 2 true
multiply: (2x0) = 2 false
minus: (2-0) = 2 true
divide: (2/0) = 2 false

Therefore, condition 2 points that * could be + or -. For each operations (5*6)*2 = 5*(6*2) can be true (+) or false (-). So, information is not sufficient to answer the question.
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Re: 5 Math Questions: Please Help   [#permalink] 28 Feb 2008, 02:23
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