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16 Mar 2016, 05:37
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
77% (01:29) correct
23%
(02:08)
wrong
based on 369
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In State X, all vehicle license plates have 2 letters from the 26 letters of the alphabet followed by 3 one digit numbers. How many different license plates can State X have if repetition of letters and numbers is allowed?
A. 23,400
B. 60,840
C. 67,600
D. 608,400
E. 676,000
A. 23,400
B. 60,840
C. 67,600
D. 608,400
E. 676,000
16 Mar 2016, 09:05
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Bunuel
In State X, all vehicle license plates have 2 letters from the 26 letters of the alphabet followed by 3 one digit numbers. How many different license plates can State X have if repetition of letters and numbers is allowed?
A. 23,400
B. 60,840
C. 67,600
D. 608,400
E. 676,000
A. 23,400
B. 60,840
C. 67,600
D. 608,400
E. 676,000
hi,
The choices give us the answer without any calculations--
3 one digits places can take 10*10*10 ways..
so answer should have three 0s in end--...000
only E is f that form
ans E..
Proper solution will be
since repetition is allowed, we can choose 2 places for digits in 26*26
3 digits places can befilled up in 10*10*10 ways
ans= 26*26*10*10*10=676000
ans E
11 Jun 2017, 07:47
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Bunuel
In State X, all vehicle license plates have 2 letters from the 26 letters of the alphabet followed by 3 one digit numbers. How many different license plates can State X have if repetition of letters and numbers is allowed?
A. 23,400
B. 60,840
C. 67,600
D. 608,400
E. 676,000
A. 23,400
B. 60,840
C. 67,600
D. 608,400
E. 676,000
Take the task of creating as license plate and break it into stages.
Stage 1: Select the first character
This must be a letter from the alphabet.
So, we can complete stage 1 in 26 ways
Stage 2: Select the second character
This must be a letter from the alphabet.
Also, since repetitions are allowed, we can complete stage 2 in 26 ways
Stage 3: Select the third character
This must be a digit (0, 1, 2, 3, 4, 5, 6, 7, 8, or 9)
We can complete stage 3 in 10 ways
Stage 4: Select the fourth character
This must be a digit.
Since repetitions are allowed, we can complete stage 4 in 10 ways
Stage 5: Select the fifth character
This must be a digit.
Since repetitions are allowed, we can complete stage 5 in 10 ways
By the Fundamental Counting Principle (FCP), we can complete all 5 stages (and thus create a license plate) in (26)(26)(10)(10)(10) ways
Note, before we perform any calculations, we should recognize that (26)(26)(10)(10)(10) = (26)(26)(1000)
So, the answer must end in 000
Answer:
Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.
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