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 Post subject: EXPLANATIONS NEEDED ON TWO QUESTIONS
PostPosted: Mon Nov 29, 2010 6:32 am 
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Joined: Mon Nov 29, 2010 6:24 am
Posts: 2
All of the stocks on the over-the-counter market are designated by either a 4-letter or a 5-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different stocks that can be designated with these codes:
2(26^5)
26(26^4)
27(26^4)
26(26^5)
27(26^5)

The answer is 27(26^4) but I don't know how to solve it. And the same with this question:

When a certain tree was first planted, it was 4 feet tall and the height of the tree increased by a constant amount each year for the next 6 years. At the end of the 6th year, the tree was 1/5 taller than it was at the end of the 4th year. By how many feet did the height of the tree increased each year?

3/10
2/5
1/2
2/3
6/5

The answer is 2/3 this time.

Can someone help me please?

Thanks!


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 Post subject: Re: EXPLANATIONS NEEDED ON TWO QUESTIONS
PostPosted: Wed Mar 02, 2011 10:34 am 
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Joined: Fri Apr 09, 2010 2:11 pm
Posts: 454
1) The number of possible combinations for a 4-letter code is 26 × 26 × 26 × 26 = 26^4
The number of possible combinations for a 5-letter code is 26^5.
The sum of all the possible combinations is 26^4 + 26^5 = 26^4(26 + 1) = 27 × 26^4.

2) If you denote the amount of annual growth by x feet, then you can set up the following equation using the final height of the tree:
4 + 6x = (4 + 4x) × (1 + 1/5)
(6 - 24/5)x = 4/5
6x = 4
x = 2/3


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