All of the stocks on the over-the counter market are designated by either a 4 -letter or 5-letter code that is created by using the 26 letters of tthe alphabet. Which of the following gives the maximum number of different stocks that can be designated with these codes?
A. 2 (26^5)
B. 26 (26^4)
C. 27 (26^4)
D. 26 (26^5)
E. 27 (26^5)
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- Tani
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4-letter codes = 26*26*26*26 (assumes repeating letters are allowed) = 26^4
5-letter codes = 26*26*26*26*26 = 26^5
adding them 26^4 + 26^5 = 26^4 (1 + 26) = 27* 26^4 = C
5-letter codes = 26*26*26*26*26 = 26^5
adding them 26^4 + 26^5 = 26^4 (1 + 26) = 27* 26^4 = C
Tani Wolff
- VivianKerr
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Just to add: Make sure when you add in the final step you don't add the exponents. We can only add the exponents during multiplication. Tricky! ![Smile :)](./images/smilies/smile.png)
Also, this question was nice because it told us the number of options for each digit (26, since it was alphabetical). Sometimes for a numerical code, you will be required to know that each digit has 10 options (the numbers 0 through 9).
![Smile :)](./images/smilies/smile.png)
Also, this question was nice because it told us the number of options for each digit (26, since it was alphabetical). Sometimes for a numerical code, you will be required to know that each digit has 10 options (the numbers 0 through 9).
Vivian Kerr
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Thank you for all the "thanks" and "follows"!![Smile :-)](./images/smilies/smile.png)
GMAT Rockstar, Tutor
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Former Kaplan and Grockit instructor, freelance GMAT content creator, now offering affordable, effective, Skype-tutoring for the GMAT at $150/hr. Contact: [email protected]
Thank you for all the "thanks" and "follows"!
![Smile :-)](./images/smilies/smile.png)
- Tani
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Good point, Vivian - even more complicated, IF they ask for a four digit number, the first digit only has nine options since 0123 counts as a three-digit, not a four digit number.
Tani Wolff