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What is the number of 4-digit positive integers where all 4 digits are 07 Jul 2021, 06:15
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What is the number of 4-digit positive integers where all 4 digits are less than 5?

A. 450
B. 475
C. 500
D. 600
E. 625
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What is the number of 4-digit positive integers where all 4 digits are 07 Jul 2021, 06:33
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The first digit cannot be zero if we'll have a genuine four-digit number. So we have 4 choices for that digit, but we have 5 choices for each of the remaining three digits, and the answer is (4)(5)(5)(5) = 20*25 = 500.
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What is the number of 4-digit positive integers where all 4 digits are 07 Jul 2021, 06:35
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ANSWER of this Question should be 500


4 * 5*5*5 = 500
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What is the number of 4-digit positive integers where all 4 digits are 07 Jul 2021, 07:16
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IanStewart
The first digit cannot be zero if we'll have a genuine four-digit number. So we have 4 choices for that digit, but we have 5 choices for each of the remaining three digits, and the answer is (4)(5)(5)(5) = 20*25 = 500.
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Hey IanStewart, what do you think about the way this question is worded?
What is the number of 4-digit positive integers, doesn't this mean we shouldn't be counting 0? Though looking at the options one could make out!
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What is the number of 4-digit positive integers where all 4 digits are 07 Jul 2021, 07:24
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Showmeyaa

Hey IanStewart, what do you think about the way this question is worded?
What is the number of 4-digit positive integers, doesn't this mean we shouldn't be counting 0? Though looking at the options one could make out!
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There are minor issues with the wording (that's true of most unofficial questions though) but I think the meaning of the question is unambiguous. The "4-digit positive integers" are the integers strictly between 1000 and 9999 inclusive, so zero is not a four-digit integer, and I wasn't including zero in my solution, because I insisted we not allow zero to be the first (the thousands) digit of the number. So I was only counting numbers like 1000 and 2222 and 4130, and I wasn't counting numbers like 0123 or 0000, which are not four digit numbers.
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What is the number of 4-digit positive integers where all 4 digits are 27 Oct 2022, 07:05
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Hello, I have a question here as well: in a different post, it is said that 0 is not a positive integer, which leads me to saying numbers as 4130 should not be included. What is the ruling opinion on this topic?

Thanks

This is the Post I was relating to: gmatclub/forum/is-zero-a-positive-integer-149242.html
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What is the number of 4-digit positive integers where all 4 digits are 27 Oct 2022, 10:43
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fredmath
Hello, I have a question here as well: in a different post, it is said that 0 is not a positive integer, which leads me to saying numbers as 4130 should not be included. What is the ruling opinion on this topic?

Thanks

This is the Post I was relating to: gmatclub/forum/is-zero-a-positive-integer-149242.html
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Yes, zero is not a positive integer (zero is the only number that is neither positive nor negative). But the question asks us to count how many positive 4-digit integers satisfy a certain property, and a positive 4-digit integer might contain one or more digits that are zero. So 4130, for example, is definitely a positive integer, even if it includes zero as one of its digits.
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