Problem Solving Question from GMAT Prep test

[lajohnson2200]

Can someone please explain these questions? They are easy, but I am horrible at math and lost without the explanations.


1. For every positive even integer n, the function h(n) id defined to be 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

a. between 2 and 20
b. between 10 and 20
c. between 20 and 30
d. between 30 and 40
e. greater than 40

The answer is e. But why?



2.) If two sides of a triangle have lengths of 2 and 5, which of the following could be the perimeter of the triangle?

I. 9
II. 15
III. 19

a. none
b. I only
c. II only
d II and III only
I, II, and III

answer is none. why?

Thanks in advance to anyone that helps!

[beat_gmat_09]

Can someone please explain these questions? They are easy, but I am horrible at math and lost without the explanations.


1. For every positive even integer n, the function h(n) id defined to be 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

a. between 2 and 20
b. between 10 and 20
c. between 20 and 30
d. between 30 and 40
e. greater than 40

The answer is e. But why?



2.) If two sides of a triangle have lengths of 2 and 5, which of the following could be the perimeter of the triangle?

I. 9
II. 15
III. 19

a. none
b. I only
c. II only
d II and III only
I, II, and III

answer is none. why?

Thanks in advance to anyone that helps!

@lajohnson2200 , seems that you are new to this forum so i suggest that before posting questions try to do a search, it is possible that same question has been discussed earlier. Both your questions were discussed, below are the links.

1st Problem -
https://www.beatthegmat.com/gmat-prep-nu ... hlight=100

2nd Problem -
https://www.beatthegmat.com/triangles-t24497.html

[lajohnson2200]

Thanks for the quick response. That was indeed my first post, I have been an observer the forum for awhile, but never knew that you could search specific questions. A little slow on the uptake. Thanks for the tip!

[Ian Stewart]

They are easy, but I am horrible at math and lost without the explanations.

Just so you know, those aren't easy questions at all. The first one, about h(n), is probably the most asked question on GMAT forums, in fact, so it might be the hardest question in GMATPrep - certainly among the hardest, anyway.