3 Questions Are killing me!

Expert replies

zico20: Senior | Next Rank: 100 Posts; Posts: 37; Joined: Wed Feb 11, 2009 7:20 am

by zico20 » Mon Jun 08, 2009 7:52 am

hey fellaz,

can someone help me figure out these two gmat prep questions. they are really bugging me.

1. 6 machines working together at a constant rate can complete a job in 12 days. How many additional machines, each working at the same constant rate are needed to finish the job in 8 days ?

A. 2
B. 3
C. 4
D. 6
E. 7

2. A certain library assess fines for overdue books as follows. after the first day a $0.3 fine is applied. for each additional day, either a $0.10 fine is added or the original fine is doubled whichever amounts to the lower amount. What is the total fine for a book that is overdue on the fourth day?

A. $ 0.6
B. $0.7
C. $0.8
D. $0.9
E. $1.00

3. When a goddamn tree was first planted, it was 4 feet tall and the height of the tree increased by a constant rate each year for 6 years. At the end of the 6th year, the tree was 1/5 taller than its height in the end of the 4th year. By how many feet did the height increase each year?

A. 3/10
B. 2/5
C. 1/2
D. 2/3
E. 6/5

Please advise

Thank you

Source: Beat The GMAT — Problem Solving | Mon Jun 08, 2009 7:52 am

dmateer25: Community Manager; Posts: 1049; Joined: Sun Apr 06, 2008 5:15 pmFollowed by: 27 members; Location: Pittsburgh, PA; Thanked: 113 times; GMAT Score:710

by dmateer25 » Mon Jun 08, 2009 8:51 am

3)

Let x = the constant yearly growth rate

at the end of the 1st year the height is 4 +x

end of 2nd = 4 + 2x and so on

so at the end of the 4th year the height is 4 + 4x

at the end of the 6th year the height is 4 + 6x.

The tree is 1/5 taller at the end of the 6th year so:

4 + 4x + 1/5(4 + 4x) = 4 + 6x
4 + 4x + 4/5 + 4x/5 = 4 + 6x
(4 + 4x)/5 = 2x
4 + 4x = 10x
4 = 6x
x = 4/6 = 2/3

D

dmateer25: Community Manager; Posts: 1049; Joined: Sun Apr 06, 2008 5:15 pmFollowed by: 27 members; Location: Pittsburgh, PA; Thanked: 113 times; GMAT Score:710

by dmateer25 » Mon Jun 08, 2009 8:54 am

1. 6 machines working together at a constant rate can complete a job in 12 days. How many additional machines, each working at the same constant rate are needed to finish the job in 8 days ?

A. 2
B. 3
C. 4
D. 6
E. 7

I am going to assume that 6 machines all work at the same rate.

6(1/x) = 1/12
6/x = 1/12
x = 72

So it takes 1 machine 72 days to finish the job.

How many total machines are needed to finish the job in 8 days:

x(1/72) = 1/8
x/72 = 1/8
8x = 72
x = 9

9 Total machines will finish the job in 8 days.

So we already have 6, we need 3 more machines to finish the job in 8 days.

B

dmateer25: Community Manager; Posts: 1049; Joined: Sun Apr 06, 2008 5:15 pmFollowed by: 27 members; Location: Pittsburgh, PA; Thanked: 113 times; GMAT Score:710

by dmateer25 » Mon Jun 08, 2009 9:00 am

Here you go for #2.

https://www.beatthegmat.com/library-fine ... 22378.html

zico20: Senior | Next Rank: 100 Posts; Posts: 37; Joined: Wed Feb 11, 2009 7:20 am

by zico20 » Mon Jun 08, 2009 11:51 am

Thanks alot guys. it makes alot of sense.

number two is tough. I worked it out so many times and i got answer C when in reality answer B is the correct one!!

thanks anyways

electrico: Senior | Next Rank: 100 Posts; Posts: 53; Joined: Tue Feb 17, 2009 11:14 pm; Location: India; Thanked: 2 times

by electrico » Thu Jun 18, 2009 7:07 pm

1. 6 machines takes 12 Days
=> 1 maching will take 72 days

So, to finish it in 8 Days, we need 72/8 = 9 machine

Additional machines requires = 9 -6 = 3 machine

2. Since we are adding 0.10 for subsequnet days, the double of the previous fine will always be greater than if we add 0.10, beacuse initial fine is 0.30.

so, after 4th day, fine = 0.60

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