What is the unit digit in the multiplication of 1× 3× 5× 7× 9× … × 999 ?
- A1
- B3
- C5Correct
- D9
Explanation
The multiplication involves a series of odd numbers: 1, 3, 5, 7, 9, and so on, up to 999.
When determining the unit digit of a product, we only need to consider the unit digits of the numbers being multiplied.
- The series includes the number 5.
- Consider the effect of multiplying 5 by any odd digit:
- 5 x 1 = 5 (unit digit is 5)
- 5 x 3 = 15 (unit digit is 5)
- 5 x 5 = 25 (unit digit is 5)
- 5 x 7 = 35 (unit digit is 5)
- 5 x 9 = 45 (unit digit is 5)
In every case, when 5 is multiplied by an odd number, the unit digit of the product is always 5. Since the entire multiplication consists only of odd numbers and includes 5, the unit digit of the final product will be 5.
Therefore, the correct answer is C.
Related questions
More UPSC Prelims practice from the same subject and topic.
- Prelims 2025CSATQuantitative Aptitude
A natural number N is such that it can be expressed as N = p + q + r , where p, q and r are distinct factors of N. How many numbers below 50 have this property?
- Prelims 2025CSATQuantitative Aptitude
Three prime numbers p, q and r, each less than 20, are such that p - q = q - r . How many distinct possible values can we get for (p + q + r) ?
- Prelims 2025CSATQuantitative Aptitude
How many possible values of (p + q + r) are there satisfying (1)/(p) + (1)/(q) + (1)/(r) = 1 , where p, q and r are natural numbers (not necessarily distinct)?
- Prelims 2025CSATQuantitative Aptitude
A 4-digit number N is such that when divided by 3, 5, 6, 9 leaves a remainder 1, 3, 4, 7 respectively. What is the smallest value of N?
- Prelims 2025CSATQuantitative Aptitude
Consider the first 100 natural numbers. How many of them are not divisible by any one of 2, 3, 5, 7 and 9?
- Prelims 2025CSATQuantitative Aptitude
Let both p and k be prime numbers such that (p² + k) is also a prime number less than 30 What is the number of possible values of k?