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# A certain stock echange designates each stock with a

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Intern
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Re: A certain stock echange designates each stock with a [#permalink]

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25 Nov 2014, 05:16
00:00

Difficulty:

45% (medium)

Question Stats:

66% (01:29) correct 34% (01:30) wrong based on 328 sessions

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Hi,

I have a doubt. If this question mentioned that same letters used in a different order are considered same code, then how would we solve it?

Thanks
[Reveal] Spoiler: OA

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Manager
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Re: A certain stock echange designates each stock with a [#permalink]

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25 Nov 2014, 05:22
Bunuel wrote:
usre123 wrote:
I dont know why , but I was thinking for one letter, it's 26,
Then for 2 same ones it would be 26^2
2 different ones would mean 26*25 * 2 (because a different order)
3 same would be 26^3, and 3 different would be 26*25*24*3!....Where am I (obviously) double counting?

How is 26^2 the number of two same letter words? How is 26^3 the number of three same letter words? Isn't both 26? AA, BB, CC, ..., ZZ and AAA, BBB, CCC, DDD, ..., ZZZ?

26^2 gives the number of ALL 2-letter words possible, the same way as 26^3 gives the number of ALL 3-letter words possible.

Crystal clear when I read this, thanks!

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Re: A certain stock echange designates each stock with a [#permalink]

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12 May 2015, 07:26
Bunuel wrote:
chicagocubsrule wrote:
A certain stock exchange designates each stock with a 1, 2, or 3 letter code, where each letter is selected from the 26 letters of the alphabet. If the letters may be repeated and if the same letters used in a different order constitute a different code, how many different stocks is it possible to uniquely designate with these codes?

a) 2,951
b) 8,125
c) 15,600
d) 16,302
e) 18,278

1 letter codes = 26
2 letter codes = 26^2
3 letter codes = 26^3

Total = 26 + 26^2 + 26^3

The problem we are faced now is how to get the answer quickly. Note that the units digit of 26+26^2+26^3 would be (6+6+6=18) 8. Only one answer choice has 8 as unit digit: E (18,278). So I believe, even not calculating 26+26^2+26^3, that answer is E.

can not say a word for this excellent
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Re: A certain stock echange designates each stock with a [#permalink]

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19 Apr 2016, 16:50
A certain stock echange designates each stock 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 letters used in a different order constitute a different code, how many different stocks is it possible to uniquely designate with these codes?

A) 2951

B) 8125

C) 15600

D) 16302

E) 18278

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Re: A certain stock echange designates each stock with a [#permalink]

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19 Apr 2016, 18:15
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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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Re: A certain stock echange designates each stock with a [#permalink]

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19 Apr 2016, 21:14
GMATPrepNow wrote:
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

Thanks a lot!

To use this units digit trick is very clever. Is it just possible to use it for adding? I thought about it for a while and it should work for multyplying as well - am I right?

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Re: A certain stock echange designates each stock with a [#permalink]

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19 Apr 2016, 22:11
Flexxice wrote:
A certain stock echange designates each stock 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 letters used in a different order constitute a different code, how many different stocks is it possible to uniquely designate with these codes?

A) 2951

B) 8125

C) 15600

D) 16302

E) 18278

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Re: A certain stock echange designates each stock with a [#permalink]

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14 May 2016, 23:59
chicagocubsrule wrote:
A certain stock exchange designates each stock with a 1, 2, or 3 letter code, where each letter is selected from the 26 letters of the alphabet. If the letters may be repeated and if the same letters used in a different order constitute a different code, how many different stocks is it possible to uniquely designate with these codes?

A. 2,951
B. 8,125
C. 15,600
D. 16,302
E. 18,278

I was able to quickly arrive at the answer when I spotted the 8 in the units digit in the option E.
Looks like the OA marked in the Question post is incorrect. It shows as C is the correct option, while it actually is E.

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Re: A certain stock echange designates each stock with a [#permalink]

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20 Jun 2017, 03:53
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Re: A certain stock echange designates each stock with a [#permalink]

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20 Jun 2017, 19:09
lagomez wrote:
chicagocubsrule wrote:
A certain stock exchange designates each stock with a 1, 2, or 3 letter code, where each letter is selected from the 26 letters of the alphabet. If the letters may be repeated and if the same letters used in a different order constitute a different code, how many different stocks is it possible to uniquely designate with these codes?

a) 2,951
b) 8,125
c) 15,600
d) 16,302
e) 18,278

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.

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GMAT Quant Self-Study Course
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Re: A certain stock echange designates each stock with a   [#permalink] 20 Jun 2017, 19:09
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