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How many 4-digit numbers have only even digits?

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by Max@Math Revolution » Thu May 17, 2018 12:27 am
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[GMAT math practice question]

How many 4-digit numbers have only even digits?

A. 500
B. 525
C. 600
D. 625
E. 800
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by GMATGuruNY » Thu May 17, 2018 3:00 am
Max@Math Revolution wrote:[GMAT math practice question]

How many 4-digit numbers have only even digits?

A. 500
B. 525
C. 600
D. 625
E. 800
Number of options for the thousands digit = 4. (2, 4, 6, or 8)
Number of options for the hundreds digit = 5. (0, 2, 4, 6, or 8)
Number of options for the tens digit = 5. (0, 2, 4, 6, or 8)
Number of options for the units digit = 5. (0, 2, 4, 6, or 8)
To combine these options, we multiply:
4*5*5*5 = 500.

The correct answer is A.
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by Jeff@TargetTestPrep » Fri May 18, 2018 10:33 am
Max@Math Revolution wrote:[GMAT math practice question]

How many 4-digit numbers have only even digits?

A. 500
B. 525
C. 600
D. 625
E. 800
There are 5 even digits: 0, 2, 4, 6, 8. In a four-digit number, the first digit cannot be 0, so there are only 4 even numbers available. For the second, third, and fourth digits, there are 5 available numbers. Thus, the number of 4-digit numbers containing only even digits is 4 x 5 x 5 x 5 = 500 numbers.

Answer: A

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by Max@Math Revolution » Sun May 20, 2018 5:04 pm
=>

Suppoose abcd is 4-digit number with only even digits.
Then a is one of 2, 4, 6 and 8, and b, c and d may be selected from the digits 0, 2, 4, 6 and 8.
So, there are 4 choices for a, and 5 choices for each of b, c and d.

The total number of 4-digit numbers with only even digits is thus 4*5*5*5 = 500.

Therefore, A is the answer.
Answer: A
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