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Question

prep.doc

abhijit_sen · Answer

2 consecutive integers are always relatively prime. E.g 4 & 5, or 9 & 10 etc.
If two numbers are relatively prime, then factor of one number leaving 1 cannot be factor of other number. E.g 9 has factor 3 but 10 does not have it as factor and 10 has factor 5, which is not shared by 9.

This question focuses on the above mentioned concept.

h(100) can be written as = 2.4.8.16...100 = 2*1.2*2.2*3.2*4....2*50 = 2^50(1.2.3....50). 
h(100)+1 will be immediate number to h(100), so it will be relatively prime number to h(100).
As h(100) has all the factors from 1 to 47 (biggest prime number from 1 to 50, I did not consider 48, 49, and 50 as they can be reduced to smaller prime numbers). 
So factor of h(100) + 1 will have factor which is at least greater than 47.

Answer E.

jallenmorris · Answer

This is still a confusing topic. Can someone explain in a different way?

maratikus · Answer

h(n) = 2^(n/2)*(n/2)! 
h(100) = 2^25*(50!)

if k < 50 remainder of h(100) + 1 will be 1: since k is a factor of 50! and h(100) = c*50!
Therefore, k > 50 -> E

jallenmorris · Answer

As for your second question in that .doc, you have one segment that is 90 degrees (perpendicular) to another segment. Each is a radius of the circle. You have to figure the slope of the first which you do know. The point is  (-\sqrt{3},1)  and the center O is at {0,0}.

This means the slope is  \frac{change in y}{change in x} . This is the change from P to 0. Figure Y first. 0 - 1 = -1. Now change in X.  0 - -\sqrt{3} = \sqrt{3} , so the slope of this line is  -\frac{1}{\sqrt{3}} . Because the line segment OQ is perpendicular to segment PO, you need to do the inverse of the slope of PO.

The inverse of  -\frac{1}{\sqrt{3}}  is  \sqrt{3}  or on the x-y plane, you go up  \sqrt{3}  for every 1 you go to the right, as is in the picture. Since we know that this is the same length as PO, then the point Q will be  \{\sqrt{3},1\} , thus making s =  \sqrt{3}

FN · Answer

Nope..ans should be 1..
i dont know how to draw it out in word or other text editor..

basically you realize you have 30-60-90 triangle..that is formed at the x-axis

BTW Nihit..you must be doing really well on gmatprep..this is 51 level question..

abhijit_sen · Answer

s^2 + t^2 = 4
(s+sqrt(3))^2 + (t-1)^2 = 8

Solve these two equation and you will get s = 1

These two equations may look intimidating however when you start solving, you can found that they are easy to solve.

jallenmorris · Answer

you're right. I have the numbers correct, but messed up the order. It should be  \{1,\sqrt{3}\}

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