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

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10 Jun 2007, 17:44

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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

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.

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?

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.

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

(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

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

gmatclubot

Re: Number property
[#permalink]
14 Jun 2007, 09:09