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GMAT Prep 198 #93

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GMAT Prep 198 #93

by Megs17 » Sat Jul 28, 2012 5:27 am
93) Each stack is designated with a 1, 2, and 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 constitutes 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. 8278

I know this has been posted earlier ,but couldn understand.
Thanks.
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by eagleeye » Sat Jul 28, 2012 7:20 am
Megs17 wrote:93) Each stack is designated with a 1, 2, and 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 constitutes 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

I know this has been posted earlier ,but couldn understand.
Thanks.
There are 26 letters in the alphabet (from A to Z).
The question is asking us for all possible combinations of letters when the code has either 1 or 2 or 3 letters.
Now, number of 1 letter codes (such as A, B, W, Z etc.) = 26.
Number of 2 letter codes (such as AA, AB, BA, WX, ZA etc.) = 26*26 (since each letter has 26 options)
Number of 3 letter codes (such as AAA, ABA, BAA, WSF etc.) = 26*26*26.

Total number of possible codes = 26+26*26+26*26*26 = 26(1+26+676) = 26*703 = 18278.
E is correct.
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by Brent@GMATPrepNow » Sat Jul 28, 2012 7:50 am
Megs17 wrote:93) Each stack is designated with a 1, 2, and 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 constitutes 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
eagleeye's solution is great.

I thought I'd just mention one thing about calculating 26+(26x26)+(26x26x26)
On the GMAT, the test-makers would never require us to perform these kinds of lengthy calculations, BUT it's still possible that you could be given answer choices that SUGGEST that we need to actually perform the calculations.

The answer choice here are great in that they might lead you start calculating.
However, if we focus on the units of each part of the calculation, we see a faster way to arrive at the correct answer.

26 has 6 as its units digit
26^2 has 6 as its units digit
26^3 has 6 as its units digit

So, (26)+(26x26)+(26x26x26) = (26)+(___6)+(____6) = _____8

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

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by nailGmat2012 » Sat Jul 28, 2012 4:56 pm
I thought the code on each stack should be something like "A AA AAA" as it says - Each stack is designated with a 1, 2, "AND" 3 letter code.

In that case the answer should have been 26^6.

obviously I've been proved wrong.. but still trying to figure our what I'm missing...
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