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1 ) For every positive interger n, function h(n) is defined [#permalink]
06 May 2006, 04:40

1 ) For every positive interger n, function h(n) is defined as the product of all even integers from 2 to n inclusive. If p is the smallest prime factor of h(100)+1, then p is -

between 2 and 10
between 10 and 20
between 20 and 30
between 30 and 40
greater than 40

2) Last month 15 homes were sold in town X. The average sale price was 150,000 and the median sale price was 130,000. Which of teh following must be true -

I Atleast one of the homes was sold for 165,000
II Atleast one of the homes was sold for more that 130,000 and less than 150,000
III Atleast one of the homes was sold for less than 130,000

I Atleast one of the homes was sold for 165,000 --> not necessary
II Atleast one of the homes was sold for more that 130,000 and less than 150,000 ---not necessary, could be more and still average to 150,000
III Atleast one of the homes was sold for less than 130,000 --true since the median is 130,000

Hi,
I took both CATS of GMATprep, but never encountered these questions
Are you sure they are from gmatprep?

1) I think the answer is E - greater than 40
h(100)+1=2*4*6*...*100 +1 = 2^50*50! + 1.
50! can be evenly divided by any number from 1 to 50. Consequently 50! +1 cannot not be divided by any of these integers.
Thus it has to be greater that 47(lgreatest prime) and greater than 50.

What is OA?

2)
I think this one contains an error. beause each choice is unnecessary.
But if we assume that choice 1 is NOT "for 165k" BUT "for more than 165k" then the answer should be A:

1+2+...+15 = 2250k
7 of the houses cost less than or equal to 130k

1 Yes:
assume that first 8 houses cost 130k(the greatest possible cost).
8*130k + 7X= 2250k, X=~172k. So one of these house should cost more than 165k.

2 No: assume the same numbers: first eight 8 houses sold for 130k, all remainnig houses could have been sold for ~172k.

3 No: first eight wesre sold for 130k, other for more

Can someone elaborate on the answer to Question 1. I'm still confused at how to arrive at the right anwer.

1) I think the answer is E - greater than 40

h(100)+1=2*4*6*...*100 +1 = 2^50*50! + 1.
***how did you get to this?

50! can be evenly divided by any number from 1 to 50.
***I understand this part

Consequently 50! +1 cannot not be divided by any of these integers.
Thus it has to be greater that 47(lgreatest prime) and greater than 50.
***Not clear on why this is true

I'm taking the gmats in a month and I want to make sure I'm understanding these questions correctly. Thanks!

Re: GMAT Prep Killers! [#permalink]
11 May 2006, 18:03

Loner wrote:

1 ) For every positive interger n, function h(n) is defined as the product of all even integers from 2 to n inclusive. If p is the smallest prime factor of h(100)+1, then p is -

between 2 and 10 between 10 and 20 between 20 and 30 between 30 and 40 greater than 40

I Atleast one of the homes was sold for 165,000 --> not necessary II Atleast one of the homes was sold for more that 130,000 and less than 150,000 ---not necessary, could be more and still average to 150,000 III Atleast one of the homes was sold for less than 130,000 --true since the median is 130,000