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Combinations , permutations ?

This topic has 2 expert replies and 2 member replies
sapuna Senior | Next Rank: 100 Posts
Joined
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Combinations , permutations ?

Post Mon Aug 11, 2014 6:54 am
A ceirtain stock exchange designates each item with a one , two or three letter code where each letter is selected from the 26 letters of the alphabet. If the letters may be repeated and if the same letter used in a different order constitue a different code, how many different stocks is it possible to uniquely designate with these codes ?

2951

8125

15600

16302

18278

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Post Fri Dec 15, 2017 10:32 am
sapuna wrote:
A ceirtain stock exchange designates each item with a one , two or three letter code where each letter is selected from the 26 letters of the alphabet. If the letters may be repeated and if the same letter used in a different order constitue a different code, how many different stocks is it possible to uniquely designate with these codes ?

2951

8125

15600

16302

18278
A 1-digit code can be created in 26 ways, a 2-digit code in 26^2 ways, and a 3-digit code in 26^3 ways.

Thus, the number of ways to create the 3 codes is:

26 + 26^2 + 26^3

We should recognize that 26, 26^2, and 26^3 all have units digits of 6. Thus, the sum of those 3 numbers will have a units digit of 8. The only answer choice that has a units digit of 8 is choice E. Thus, the answer must be 18,278.

Answer: E

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Post Mon Aug 11, 2014 9:44 am
Quote:
A certain stock exchange designates each stock with a one-, two- or three-letter code, where each letter is selected from the 26 letters of the alphabets. If the letter maybe repeated and if the same letters used in different order constitude a different code, how many different stock is it possible to uniquely designate with these codes?

A. 2,951
B. 8,125
C. 15,600
D. 16,302
E. 18,278
My approach is similar to that of Bhoopendra, with a TWIST at the end.

1-letter codes
26 letters, so there are 26 possible codes

2-letter codes
There are 26 options for the 1st letter, and 26 options for the 2nd letter.
So, the number of 2-letter codes = (26)(26) = 26²

3-letter codes
There are 26 options for the 1st letter, 26 options for the 2nd letter, and 26 options for the 3rd letter.
So, the number of 3-letter codes = (26)(26)(26) = 26³

So, the TOTAL number of codes = 26 + 26² + 26³

IMPORTANT: Before we perform ANY calculations, we should first look at the answer choices, because we know that the GMAT test-makers are very reasonable, and they don't care whether we're able make long, tedious calculations. Instead, the test-makers will create the question (or answer choices) so that there's an alternative approach.

The alternative approach here is to recognize that:
26 has 6 as its units digit
26² has 6 as its units digit
26³ has 6 as its units digit

So, (26)+(26²)+(26³) = (26)+(___6)+(____6) = _____8

Since only E has 8 as its units digit, the answer must be E

Cheers,
Brent

_________________
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Post Fri Dec 15, 2017 10:32 am
sapuna wrote:
A ceirtain stock exchange designates each item with a one , two or three letter code where each letter is selected from the 26 letters of the alphabet. If the letters may be repeated and if the same letter used in a different order constitue a different code, how many different stocks is it possible to uniquely designate with these codes ?

2951

8125

15600

16302

18278
A 1-digit code can be created in 26 ways, a 2-digit code in 26^2 ways, and a 3-digit code in 26^3 ways.

Thus, the number of ways to create the 3 codes is:

26 + 26^2 + 26^3

We should recognize that 26, 26^2, and 26^3 all have units digits of 6. Thus, the sum of those 3 numbers will have a units digit of 8. The only answer choice that has a units digit of 8 is choice E. Thus, the answer must be 18,278.

Answer: E

_________________

Scott Woodbury Stewart Founder & CEO
GMAT Quant Self-Study Course - 500+ lessons 3000+ practice problems 800+ HD solutions
5-Day Free Trial 5-DAY FREE, FULL-ACCESS TRIAL TTP QUANT

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Post Mon Aug 11, 2014 9:44 am
Quote:
A certain stock exchange designates each stock with a one-, two- or three-letter code, where each letter is selected from the 26 letters of the alphabets. If the letter maybe repeated and if the same letters used in different order constitude a different code, how many different stock is it possible to uniquely designate with these codes?

A. 2,951
B. 8,125
C. 15,600
D. 16,302
E. 18,278
My approach is similar to that of Bhoopendra, with a TWIST at the end.

1-letter codes
26 letters, so there are 26 possible codes

2-letter codes
There are 26 options for the 1st letter, and 26 options for the 2nd letter.
So, the number of 2-letter codes = (26)(26) = 26²

3-letter codes
There are 26 options for the 1st letter, 26 options for the 2nd letter, and 26 options for the 3rd letter.
So, the number of 3-letter codes = (26)(26)(26) = 26³

So, the TOTAL number of codes = 26 + 26² + 26³

IMPORTANT: Before we perform ANY calculations, we should first look at the answer choices, because we know that the GMAT test-makers are very reasonable, and they don't care whether we're able make long, tedious calculations. Instead, the test-makers will create the question (or answer choices) so that there's an alternative approach.

The alternative approach here is to recognize that:
26 has 6 as its units digit
26² has 6 as its units digit
26³ has 6 as its units digit

So, (26)+(26²)+(26³) = (26)+(___6)+(____6) = _____8

Since only E has 8 as its units digit, the answer must be E

Cheers,
Brent

_________________
Brent Hanneson – Founder of GMATPrepNow.com
Use our video course along with Beat The GMAT's free 60-Day Study Guide

Check out the online reviews of our course
Come see all of our free resources

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