How many 4-digit numbers begin with an odd digit and end with an even

Question

How many positive 4-digit numbers begin with an odd digit and end with an even digit ?

A. 250
B. 500
C. 2,000
D. 2,500
E. 5,000

Archit3110 · Answer

odd= 1,3,5,7,9
even= 0,2,4,6,8

5*10*10*5
2500
IMO D

snehaluk · Answer

first 4 digit no is 1000
1000....1999------> in this series there will be total 1000 no.s and 1000/2=500 nos. will end with even digit.

likewise ,
3000....3999----> 500 nos (which will fulfill given constraint)
5000.....5999--->500
7000.....7999--->500
9000.....9999--->500

all nos will sum to 2500 hence ans is option 'D' IMO.

anmit123 · Answer

4 digit number

_ _ _ _

First place can be filled in 5 ways-1/3/5/7/9
Last place can be filled in 5 ways-0/2/4/6/8

Middle two can each be filled in 10 ways (0-9)

5*10*10*5=2500

Ans:D

sbolipombo · Answer

Rationale:
You are looking for all the numbers that start with ODD numbers. These will be the series starting with 1, 3, 5, 7, 9. But these numbers have to end with even numbers. You know that in order for a number to be even it must be divisible by 2. In a string of 1000 to 1999 - this will be half of the string i.e. 500 numbers that are even. 
In total it is the possible odd series (5) multiplied by even numbers in each series (500). The total is 2500.

Sonia2023 · Answer

Bunuel

Can you please clarify whether we need to assume repetition as allowed when nothing is mentioned and when nothing can be inferred from the text of the question?

For instance, in this question, we have taken 10*10 for middle two values assuming repetition.

Please clarify.

Thank you,
Sonia

Bunuel · Answer

In a well-framed GMAT question, any potential ambiguity, such as whether repetition is allowed, would be clarified in the question. If a specific restriction, like "repetition not being allowed", is not mentioned, it usually indicates that the restriction doesn't apply. Therefore, if there's no mention of such a restriction, one can generally assume that repetition is allowed.

Sonia2023 · Answer

Thanks a lot for clarification.

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How many 4-digit numbers begin with an odd digit and end with an even

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How many 4-digit numbers begin with an odd digit and end with an even

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