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# I. If p is a prime number greater than 2, what is the value

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I. If p is a prime number greater than 2, what is the value [#permalink]  10 Jun 2007, 17:44
I. If p is a prime number greater than 2, what is the value of p?
(1) There are a total of 100 prime numbers between 1 and p+1
(2) There are a total of p prime numbers between 1 and 3,912

Could anyone suggest the best way to solve this problem?

II) [ x, 3, 1, 12, 8 ]
If x is an integer, is the median of the 5 numbers shown greater than the average (arithmetic mean) of the 5 numbers?

1) x > 6
2) x is greater than the median of the 5 numbers

IMO E
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Re: Number property [#permalink]  10 Jun 2007, 17:59
priyankur_saha@ml.com wrote:
I. If p is a prime number greater than 2, what is the value of p?
(1) There are a total of 100 prime numbers between 1 and p+1
(2) There are a total of p prime numbers between 1 and 3,912

Could anyone suggest the best way to solve this problem?

II) [ x, 3, 1, 12, 8 ]
If x is an integer, is the median of the 5 numbers shown greater than the average (arithmetic mean) of the 5 numbers?

1) x > 6
2) x is greater than the median of the 5 numbers

IMO E

Question 1: Remember we only need to know whether we're able to solve the problem. Both of those statements give enough information to do so, but figuring the answer is beyond the scope of the problem. The answer is D because if we had enough time, we could find p from both statements.
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[#permalink]  10 Jun 2007, 18:49
Exactly.

First question is a classic example of problems requiring some out of the box thinking! Answer is D

I think E is the correct asnwer for second question
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[#permalink]  10 Jun 2007, 19:03
Qn1:

St1:
Sufficient. I'm too lazy to count, but you could list them if you like, though DS wouldn't require you to do that.

St2:
Sufficient. Same as above.

Ans D
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[#permalink]  10 Jun 2007, 19:07
Qn2:

From the set, we can derive that:
x<=5, median <mean>6 median > mean

St1:
Sufficient. We can asnwer the question.

St2:
Sufficient. We can answer that too.

Ans D
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[#permalink]  10 Jun 2007, 22:23
go with E for 2nd

st1, consider x=7 , median is greater than mean
consider x = 10,000000000 , median is lesser than mean

st2, max median for the given set of 5#s = 8

consider x=9, median > mean
consider x = 10^234654, median <mean>8 same as st2

hence E
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[#permalink]  11 Jun 2007, 01:48
I. If p is a prime number greater than 2, what is the value of p?
(1) There are a total of 100 prime numbers between 1 and p+1
(2) There are a total of p prime numbers between 1 and 3,912

Could anyone suggest the best way to solve this problem?

----------------------------------------------------------------------------

Well your approach should be:

1. To identify p you need to know a unique identifier for it. Lets consider the fisrt option"There are a total of 100 prime numbers between 1 and p+1 "

Since p is prime(given), then p+1 cannot be prime. So p is the 100th prime number --> hence unique

So we can find out p using statement 1 only.
Note that you dont really need to calculate the value of p...just think of a way of identifying it

2.Now consider option 2:"There are a total of p prime numbers between 1 and 3,912 "

To begin with...I dont know how many prime number are between 1 and 3,912...but do i need to know it for solving this question...The answer is 'NO'

All you need to know is that there is a unique no. (say X) and according to question X = p.

So we can find out p using statement 2 only.

Hence answer is D

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2nd Question [#permalink]  11 Jun 2007, 01:57
II) [ x, 3, 1, 12, 8 ]
If x is an integer, is the median of the 5 numbers shown greater than the average (arithmetic mean) of the 5 numbers?

1) x > 6
2) x is greater than the median of the 5 numbers

------------------------------------------------------------------------------

Lets consider statement 1:
x> 6
Then my possible sets are:
1. [1,3,x,8,12] -->
Median = x = 7
Mean = 6.2

2. [1,3,8,x,12] (x = 8 or 9 or 10 or 11)
Median = 8
Mean = 6.4 to 7
Median > Mean

3. [1,3,8,12,x] ( x>= 12)
Median = 8
Mean >= 7.2
Median > Mean or Median < Mean both possible

Hence, staement 1 alone not sufficient

Consider statement 2:"X is greater than the median of the 5 numbers"

All possible sets are:

A. When x<6> 3

(i)[1,3,x,8,12]

Median = 4, 5, 6
Mean = 5.6 , 5.8, 6
Median < Mean or Mean = Median both possible
x= Median

(ii) [1,x,3,8,12] (x <= 3)
Median = 3
Mean = 5 , 5.2, 5.4
Median < Mean
x <Median> 6

Then my possible sets are:
1. [1,3,x,8,12] -->
Median = x = 7
Mean = 6.2
Median > Mean
X = Median
2. [1,3,8,x,12] (x = 8 or 9 or 10 or 11)
Median = 8
Mean = 6.4 to 7
Median > Mean
x >= Median
3. [1,3,8,12,x] ( x>= 12)
Median = 8
Mean >= 7.2
Median > Mean or Median <Mean> Median

Sets 2 and 3 above are the ones which become applicable for option "Both Statement Together"
But even then we cannot say conclusively whether Median > Mean
Hence answer is E
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[#permalink]  11 Jun 2007, 04:42
For question " I ",

(1) we can count 100 prime numbers starting from 2 and that will lead us to the value of P

statement 1 is sufficient

(2) we can count the number of prime numbers here also. It's possibly, not easy, but the information is sufficient to answer the question

statement 2 is sufficient

ANSWER: D
__________________________________________________________________

For question " II ",

(1) The fact that x>6 doesn't lead us to a median of either X or 8. Each median results in a different relation between the median and the mean.

statement 1 is insufficient

(2) If X is greater than the median, then the median has to be 8. Yet, X can be a really huge integer and thus inflate the mean OR can be 7 which results in a much smaller mean and thus switched the relationship between the median and the mean

statement 2 is insufficient

ANSWER: E
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Re: Number property [#permalink]  14 Jun 2007, 09:09
priyankur_saha@ml.com wrote:
I. If p is a prime number greater than 2, what is the value of p?
(1) There are a total of 100 prime numbers between 1 and p+1
(2) There are a total of p prime numbers between 1 and 3,912

My answer is D
We don't need to count. Sufficient only to know that it's possible to count if needed.

II) [ x, 3, 1, 12, 8 ]
If x is an integer, is the median of the 5 numbers shown greater than the average (arithmetic mean) of the 5 numbers?

1) x > 6
2) x is greater than the median of the 5 numbers

IMO E
My answer is E here as x in both cases can be as small as 7 or 9, and as big as 1000 000 000...

Please provide the OAs
Re: Number property   [#permalink] 14 Jun 2007, 09:09
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# I. If p is a prime number greater than 2, what is the value

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