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# What is the greatest common divisor of positive integers m

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What is the greatest common divisor of positive integers m [#permalink]

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25 Oct 2006, 19:29
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Hi,

I'm having trouble with DS, and would like an explanation for the following questions:

1. What is the greatest common divisor of positive integers m and n?
1) m is a prime number
2) m and n are consecutive integers

2. Is number A more close to 10^(-2) or 10^(-3)?
(1) A is more close to 10^(-1) than to 10(-4)
(2) A is more close to 10^(-2) than to 10(-4)

3. How many different prime factors does N have?
(1) 2N has 4 different prime factors.
(2) N ^2 has 4 different prime factors.
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26 Oct 2006, 03:50
Q1, B

(1) is INSUFF because we don't know the value of N
(2) SUFF, used picking numbers

Q2, A
(1) is SUFF because if A is closer to 10^-1 than it should be close to 10^-2
(2) is INSUFF because it can be either way

Q3, B

(1) is INSUFF because we don't know if 2 is already a prime factor of N
(2) is SUFF because N^2 has the same prime factors as N but twice as many
Director
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Re: DS - explanation requested. [#permalink]

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26 Oct 2006, 04:54
dancer wrote:
1. What is the greatest common divisor of positive integers m and n?
1) m is a prime number
2) m and n are consecutive integers

C

Statement 1:
Unless n is a multiple of m, there is no common divisor except 1. INSUFF

Statement 2:
Unless m and n are 1 and 2, there are no common divisors. INSUFF

Together, if m is prime and n is the next integer, there can be no common divisors. (I assume that m and n are in that order, because I believe that is what statement 2 means. If I cannot assume that, then it is E.)

Quote:
2. Is number A more close to 10^(-2) or 10^(-3)?
(1) A is more close to 10^(-1) than to 10(-4)
(2) A is more close to 10^(-2) than to 10(-4)

E

Q: Is A less than average of 1/100 and 1/1000?
A< 9/2000 ?

Statement 1:
A is less than average of 1/10 and 1/10000.
A<99.9/2000. INSUFF

Statement 2:
A is less than average of 1/100 and 1/10000
A< 9.9/2000 INSUFF

Together still INSUFF.

Quote:
3. How many different prime factors does N have?
(1) 2N has 4 different prime factors.
(2) N ^2 has 4 different prime factors.

B
Statement 1:
2 may or may not be a factor of N as well. INSUFF

Statement 2:
Prime factors should be the same for both N and N^2. SUFF
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Re: DS - explanation requested. [#permalink]

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26 Oct 2006, 14:02
anandsebastin wrote:
dancer wrote:
1. What is the greatest common divisor of positive integers m and n?
1) m is a prime number
2) m and n are consecutive integers

C

Statement 1:
Unless n is a multiple of m, there is no common divisor except 1. INSUFF

Statement 2:
Unless m and n are 1 and 2, there are no common divisors. INSUFF

Together, if m is prime and n is the next integer, there can be no common divisors. (I assume that m and n are in that order, because I believe that is what statement 2 means. If I cannot assume that, then it is E.)

Quote:
2. Is number A more close to 10^(-2) or 10^(-3)?
(1) A is more close to 10^(-1) than to 10(-4)
(2) A is more close to 10^(-2) than to 10(-4)

E

Q: Is A less than average of 1/100 and 1/1000?
A< 9/2000 ?

Statement 1:
A is less than average of 1/10 and 1/10000.
A<99.9/2000. INSUFF

Statement 2:
A is less than average of 1/100 and 1/10000
A< 9.9/2000 INSUFF

Together still INSUFF.

Quote:
3. How many different prime factors does N have?
(1) 2N has 4 different prime factors.
(2) N ^2 has 4 different prime factors.

B
Statement 1:
2 may or may not be a factor of N as well. INSUFF

Statement 2:
Prime factors should be the same for both N and N^2. SUFF

Don't you think that 1 will be a common divisor in all the cases.Hence for Q 1 we have (B)

Also I beleive it should be (D) for Q 2

And for Q 3 my answer is (B)
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Re: DS - explanation requested. [#permalink]

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26 Oct 2006, 14:57
Nice questions Dancer!
My take is:
1)B
2)E
3)B

1)1 is their only common divisor
2)draw the numbers in the # line, and I think you can find the answer, which is none
3)the number multiplied by its own, will still have the same prime factors, try it if not with 7; 49; 5; 25; 125...

Please let me know if I am missing sthg.
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26 Oct 2006, 16:31
1-B
2-A
3-B

QUESTION 1

Statement 1) :
A prime number can be divided, without remainer, by 1 and by itself
As we don't know if n is a multiple or not, of m
Insufficient : eliminate A - D

Statement 2):
No consecutive numbers have common prime factorization (try picking numbers) , so the only possibility for GCD is this case 1
Sufficient

QUESTION 2
The best way to resolve this problem is writting the numbers in an easier way
Multiply everything by 10000

The problem now is:
Is number A more close to 100 or 10?
(1) A is more close to 1000 than to 1
(2) A is more close to 100 than to 1

Statement 1) : Any number that you pick will be closer to 100 than to 10 : SUFFICIENT
Statement 2) : If you pick 51, the number A is closer to 10, but if you pick 80 the number A is closer to 100. INSUFFICIENT

QUESTION 3

Statement 1) :
If N= 3*5*7*11, then 2N will have 5 prime numbers, but
if N= 2*3*5*7. then 2N will have 4 prime numbers
INSUFFICIENT

Statement 2)
If N= 3*5*7*11, then N*N will have 4 prime numbers ALWAYS
SUFFICIENT
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26 Oct 2006, 18:46
3. How many different prime factors does N have?
(1) 2N has 4 different prime factors.
(2) N ^2 has 4 different prime factors.

Statement 1: Insufficient
Can't tell whether 2 is a prime factor.

Statement 2: Insufficient
Can't assume N is an integer (e.g. N = sqrt(2) * 3 * 5 * 7).

Statement 1 + Statement 2:
For N = 2 * 3 * 5 * 7 both statements hold.
For N = sqrt(2) * 3 * 5 * 7 the statements also hold.

Answer: E
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DS - explanation requested [#permalink]

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27 Oct 2006, 07:35
Thanks guys!

However, I'm still battling with question 3. gxgcristea - I don't quite get your explanation. When you say for N = 2*3*5*7.... could you please expound?

PS - I'm not very good at DS and wonder what materials I should use to get more practice - please let me know.
Director
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Re: DS - explanation requested [#permalink]

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27 Oct 2006, 19:04
dancer wrote:
Thanks guys!

However, I'm still battling with question 3. gxgcristea - I don't quite get your explanation. When you say for N = 2*3*5*7.... could you please expound?

PS - I'm not very good at DS and wonder what materials I should use to get more practice - please let me know.

Please post the OA and OE(if available).
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Re: DS - explanation requested. [#permalink]

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29 Oct 2006, 18:57
dancer wrote:
Hi,

I'm having trouble with DS, and would like an explanation for the following questions:

1. What is the greatest common divisor of positive integers m and n?
1) m is a prime number
2) m and n are consecutive integers

2. Is number A more close to 10^(-2) or 10^(-3)?
(1) A is more close to 10^(-1) than to 10(-4)
(2) A is more close to 10^(-2) than to 10(-4)

3. How many different prime factors does N have?
(1) 2N has 4 different prime factors.
(2) N ^2 has 4 different prime factors.

1 . B
1. m is prime ,but n could be 2m . Insuff
2. m(m+1) only 1 is possible . Suff

2. D
This could be rephrased as
Is number A more close to 10 or 1?
(1) A is more close to 1000 than to 1. A has to be >= than 501. Suff
(2) A is more close to 100 than to 1. A has to be >= 51. suff
Re: DS - explanation requested.   [#permalink] 29 Oct 2006, 18:57
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# What is the greatest common divisor of positive integers m

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