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The number of positive integers less than 1000 having only odd digits is? (A)155
(B)177
(C)55
(D)205
(E)85
The correct answer is (A)155.
Can you explain this answer?
(B)177
(C)55
(D)205
(E)85
The correct answer is (A)155.
Can you explain this answer?
Verified Answer
The number of positive integers less than 1000 having only odd digits ...
Ah this is one of those combinatoric questions that sounds simple but feels impossible to solve without some experience. In these situations, it's good to simplify the question into one that you know you can solve, so instead of going up to 1000, let's just go up to 10. This one is easy, it's just 5 since there's only 5 odd numbers between 1 and 10. Ok now let's increase it up to 100. We already know that there are 5 of these numbers when we have one digit, so we just need to look at the case when there's 2 digits and add these two numbers. If we look at when the tens digit is 1, how many times will the ones digit be odd? Well it's just 5 again! And what about if the tens digit is 3? It's 5 as well. And how often is the tens digit odd? Well it's 5 times because there's 5 odd numbers between 0 and 9. So then we get 5*5 = 25 for the amount of times we have two odd digits. But remember, we need to add 5 from when we only have one digit, so we get 5 + 25 = 30, so there are 30 numbers between 1 and 100 that only have odd digits. We can then extend this idea to 1000 to find out that there are 5*5*5 = 125 three-digit numbers that have only odd digits. Adding this to 5 and 25, we get 5 + 25 + 125 = 155.
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Most Upvoted Answer
The number of positive integers less than 1000 having only odd digits ...
Solution:
We have to find the number of positive integers less than 1000 having only odd digits.
First, we consider the one-digit odd numbers, which are 1, 3, 5, 7, and 9. There are five one-digit odd numbers.
Next, we consider the two-digit odd numbers. The first digit can be any of the five one-digit odd numbers, and the second digit can also be any of the five one-digit odd numbers. Therefore, there are $5\times 5=25$ two-digit odd numbers.
Similarly, we can count the three-digit odd numbers. The first digit can be any of the five one-digit odd numbers, and the second and third digits can also be any of the five one-digit odd numbers. Therefore, there are $5\times 5\times 5=125$ three-digit odd numbers.
Therefore, the total number of positive integers less than 1000 having only odd digits is $5+25+125=\boxed{155}$.
We have to find the number of positive integers less than 1000 having only odd digits.
First, we consider the one-digit odd numbers, which are 1, 3, 5, 7, and 9. There are five one-digit odd numbers.
Next, we consider the two-digit odd numbers. The first digit can be any of the five one-digit odd numbers, and the second digit can also be any of the five one-digit odd numbers. Therefore, there are $5\times 5=25$ two-digit odd numbers.
Similarly, we can count the three-digit odd numbers. The first digit can be any of the five one-digit odd numbers, and the second and third digits can also be any of the five one-digit odd numbers. Therefore, there are $5\times 5\times 5=125$ three-digit odd numbers.
Therefore, the total number of positive integers less than 1000 having only odd digits is $5+25+125=\boxed{155}$.
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The number of positive integers less than 1000 having only odd digits is? (A)155 (B)177 (C)55 (D)205 (E)85 The correct answer is (A)155. Can you explain this answer?
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The number of positive integers less than 1000 having only odd digits is? (A)155 (B)177 (C)55 (D)205 (E)85 The correct answer is (A)155. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about The number of positive integers less than 1000 having only odd digits is? (A)155 (B)177 (C)55 (D)205 (E)85 The correct answer is (A)155. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of positive integers less than 1000 having only odd digits is? (A)155 (B)177 (C)55 (D)205 (E)85 The correct answer is (A)155. Can you explain this answer?.
The number of positive integers less than 1000 having only odd digits is? (A)155 (B)177 (C)55 (D)205 (E)85 The correct answer is (A)155. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about The number of positive integers less than 1000 having only odd digits is? (A)155 (B)177 (C)55 (D)205 (E)85 The correct answer is (A)155. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of positive integers less than 1000 having only odd digits is? (A)155 (B)177 (C)55 (D)205 (E)85 The correct answer is (A)155. Can you explain this answer?.
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