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Intern
Joined: 22 Jan 2008
Posts: 2
Followers: 0

Kudos [?]: 1 [1] , given: 0

1
KUDOS
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.
CEO
Joined: 17 Nov 2007
Posts: 3574
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 414

Kudos [?]: 2244 [2] , given: 359

2
KUDOS
Expert's post
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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Intern
Joined: 23 Jan 2008
Posts: 1
Followers: 0

Kudos [?]: 1 [1] , given: 0

1
KUDOS
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
CEO
Joined: 17 Nov 2007
Posts: 3574
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 414

Kudos [?]: 2244 [0], given: 359

Expert's post
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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CEO
Joined: 17 Nov 2007
Posts: 3574
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 414

Kudos [?]: 2244 [0], given: 359

Expert's post
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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CEO
Joined: 17 Nov 2007
Posts: 3574
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 414

Kudos [?]: 2244 [0], given: 359

Expert's post
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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CEO
Joined: 17 Nov 2007
Posts: 3574
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 414

Kudos [?]: 2244 [0], given: 359

Expert's post
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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CEO
Joined: 21 Jan 2007
Posts: 2760
Location: New York City
Followers: 9

Kudos [?]: 389 [0], given: 4

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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SVP
Joined: 29 Aug 2007
Posts: 2493
Followers: 59

Kudos [?]: 577 [0], given: 19

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.
_________________
CEO
Joined: 17 Nov 2007
Posts: 3574
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 414

Kudos [?]: 2244 [0], given: 359

Expert's post
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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