6 PS problems, need help on how to attack them

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1) For every positive even integer n, the funtion h(n) is 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 10 b) between 10 and 20 c) between 20 and 30 d) between 30 and 40 e)greater than 40
I guessed e which was the right answer thinking since last multiplier is 100 which means the answer is a factor of 100 + 1 would make it 01.

2) If n is a positive integer less than 200 and 14n/60 is an integer, then n has how many different positive prime factors? 2, 3, 5, 6, 8 3 is the correct answer

3) A boat traveled upstream a distance of 90 miles at an average speed of (v-3) miles per hour and then traveled the same distance downstream at an average speed of (v+3) miles per hour. If the trip upstream took half an hour longer than the trip downstream, how many hours did it take the boat to travel downstream? 2.5, 2.4, 2.3, 2.2, 2.1 Answer is 2.5

4) Susan drove at an average speed of 30 miles per hour for the first 30 miles of a trip and then at an average speed of 60 miles per hour for the remaining 30 miles of the trip. If she made no stops during the trip, what was susan's average speed, in miles per hour, for the entire trip? 35, 40, 45, 50, 55 Answer is 40. I got 45 i must be missing something important ... When i saw the question, it seemed like it was 2 easy, def. one of those tricky ones but as i was running low on time i just moved forward.

5)To furnish a room in a model home, an interior decorator is to select 2 chairs and 2 tables from a collection of chairs and tables in a warehouse that are all different from each other . If there are 5 chairs in the warehouse and if 150 different combinations are possible, how many tables are in the warehouse? 6, 8, 10, 15, 30 6 is the correct answer.
I started this off as 5 * x = 150 but soon realized the choosing of 2 chairs and 2 tables... so then i tried 5C2 = 10 x nC2 = 150 and it got way too confusing from there.

6) The number of stamps that kaye and alberto had were in the ratio 5:3 respectively. After kaye gave alberto 10 of her stamps, the ratio of the number kaye had to the number alberto had was 7:5. As a result of this gift, kaye had how many more stamps than alberto. 20, 30, 40, 60, 90 40 is the correct answer.
I have trouble when i run into ratio type of problems, i figured out a trick when i was in kaplan course but i do not remember. I started off with
5x-10 / 3x+10 = 7x/5x but it got complicating and i guessed and moved on.

These were from the GMAT PREP, i do not know if the the GMAT prep explains the answers, i could not find the explanations so i am posting them here.

Thanks for ur help[/u]
Source: — Problem Solving |

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by awesomeusername » Thu Jan 22, 2009 9:46 pm
For #2
say n=60 for the sake of making 14n/60 an integer. We know that when n=60, 14n/60 = 14. How many different prime numbers are factors of 60?

2*2*3*5 = 60
2, 3 and 5 are the different prime factors, so the answer is 3.

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by coolguy55220 » Thu Jan 22, 2009 10:27 pm
awesomeusername wrote:For #2
say n=60 for the sake of making 14n/60 an integer. We know that when n=60, 14n/60 = 14. How many different prime numbers are factors of 60?

2*2*3*5 = 60
2, 3 and 5 are the different prime factors, so the answer is 3.
huh... looks easy enough... dunno y i couldnt think of this..

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by coolguy55220 » Fri Jan 23, 2009 1:59 pm
i seem to have a problem with ratio + average speed type of problems. I am not sure how to really start it. Can someone point me in the right direction with one of those problems. I think i can figure it out once i can figure out the right / easiest way to start these.

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by hardik.jadeja » Sat Jan 24, 2009 4:48 am
for the 3rd question

Let downstream travel time be t…
v-3 = 90 / (t + 0.5)…… avg speed while traveling upstream
v-3 = 180/(2t+1)…… (replace 0.5 by ½ and simplify)
v=(180/(2t+1)) + 3…………(1)

v+3= 90/t… avg speed while traveling downstream
v=(90/t) – 3…………(2)

compare 1 and 2
(180/(2t+1)) + 3 = (90/t) – 3

Solve this equation.. you will get t = -3 and t = 5/2

Time cannot be-3 so 5/2 is the answer.

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by hardik.jadeja » Sat Jan 24, 2009 5:22 am
For the 4th question..

Susan traveled first 30 miles in one hour.. (because avg speed is 30miles/hr)
and she traveled last 30 miles in 1/2 hour (because avg speed is 60miles/hr)

so final avg speed is = Total distance/Total time
= 60 miles / 1.5 hours
= 60 * 10/15
= 40 miles/ hr
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5th Question..

we have 5 chairs in the warehouse and we have to choose 2 out of 5..
we can do it in 10 (5C2) diff ways..

150 different combinations are possible of selecting 2 chairs and 2 tables

we know there are 10 diff ways of selecting 2 chairs out of 5..
now let x be the number ways we can select tables then

150 = 10 * x
x = 15.. which means there are 15 diff ways of selecting 2 tables

now let n be the number of tables available in the warehouse then
nC2 has to be 15

6C2 is 15.. so n=6
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6th question

let k be the number of stamps kaye had
and a be the number of stamps alberto had

k/a=5/3 (because the number of stamps that kaye and alberto had were in the ratio 5:3)

so k = (5/3)a..........(1)

After kaye gave alberto 10 of her stamps the equation becomes..
(k-10)/(a+10) = 7/5
if u solve this equation you get
5k = 7a+120
replace the value of k by (5/3)a (check equ (1))
you get a = 90 and k = 150

After kaye gave alberto 10 of her stamps... k becomes 140 and a becomes 100.. diff between the two is 40
so the answer is 40

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by aroon7 » Sat Jan 24, 2009 8:08 am
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i am back!

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by coolguy55220 » Sat Jan 24, 2009 10:27 am
i figured out wat i did wrong for all of them except for the combination problem... i actually was on the right track, just couldnt figured 15 = nc2 wouldnt be the right path so i just guessed an moved on. But now i know..
thx for ur help