GMAT Prep Quantitative Prob (Hard)

Ankur Barasia wrote:I am unable to understand the following problem..........please help me with this one...........it is a GMATPrep prob...

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

a) between 2 and 10
b)between 10 and 20
c) between 20 and 30
d) between 30 and 40
e) above 40

The question has been already answered at the below link -

https://www.beatthegmat.com/prime-nos-t65579.html

Cheers!

Please help me with this question........it seems to me that d) is correct but according to GMATprep b) is correct.

Ankur Barasia wrote:

Please help me with this question........it seems to me that d) is correct but according to GMATprep b) is correct.

Yes, B is the correct answer..This is how -

|x| will always be positive.
If -x|x| > 0, then x has to be negative.

Now take any negative no., say x = -1.

((x - 3)^2)^(1/2) can either be (x - 3) or (3 - x) depending on whether it is the positive root or negative root.

Now we have a supposition that x = -1. Plug it into the Left hand side. We get
((-1-3)^2)^(1/2) = -4

The positive root would be (x - 3) = -4. This is what we have already arrived at.
The negative root would be (3 - x) = 4.

Thus using only the second statement we are able to answer the sufficiency question.

Hope this helps!!

Cheers!

I agree with your solution...........but if we take the positive root....
x-3 = 3-x which means 2x = 6 or x= 3......but in first option X is not equal to 3 so .......positive root is not correct it means we can use only negative root........it that case both sides are equal....

Ankur Barasia wrote:I agree with your solution...........but if we take the positive root....
x-3 = 3-x which means 2x = 6 or x= 3......but in first option X is not equal to 3 so .......positive root is not correct it means we can use only negative root........it that case both sides are equal....

I understand your point. But you cannot simply equate x-3 to 3-x because you are effectively comparing the positive and negative roots of the equation which is not correct. Clearly the two roots can be equated will be possible only when the value of x is 3 which is what statement 1 refutes.

The first statement only tells us that the value of ((x-3)^2)^(1/2) is not equal to 0 because x is not equal to 3, but it does not help us in determining which root of the equation , positive or negative, is correct.

Only statement B helps us in accurately validating that only one of the roots can be correct.

Cheers!