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5 Math Questions: Please Help [#permalink]
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27 Jan 2008, 13:16
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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]
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27 Jan 2008, 13:25
Please, post the problems separately... leizermike wrote: 1. What is the greatest prime factor of 4^17 – 2^28? The correct answer is 7.
\(4^{17}2^{28}=2^{34}2^{28}=2^{28}*(2^61)=2^{28}*63=2^{28}*3^2*7\)
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Re: 5 Math Questions: Please Help [#permalink]
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27 Jan 2008, 14:49
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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=(1007TB)/9 <= 8 <=> TB >= 4
So machine b will operate for minimum 4 hours



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Re: 5 Math Questions: Please Help [#permalink]
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27 Jan 2008, 13:28
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]
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27 Jan 2008, 13:34
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]
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27 Jan 2008, 13:36
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
7t28169
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Re: 5 Math Questions: Please Help [#permalink]
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27 Jan 2008, 13:40
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. 7t57640And, 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]
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27 Feb 2008, 23:15
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. 7t57640And, 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]
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28 Feb 2008, 02:33
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]
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28 Feb 2008, 03:23
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: (56)2 = 5(62) 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: (56) = (65) 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: (20) = 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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