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If R = 1! + 2! + 3! …. 199!, what is the units digit of R?
- a)0
- b)1
- c)2
- d)3
- e)4
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
If R = 1! + 2! + 3! …. 199!, what is the units digit of R?a)0b)...
Few concepts..
R=1!+2!+3!+4!+5!+6!+7!+8!+9!+10!+.....
1) units digit...
All terms after 4! contain one 5 and one 2 atleast, so units digit of all terms after 4! Will be 0..
So units digit will depend on 1!+2!+3!+4! Only
2) last two digits..
All terms after 9! contain two 5 and two 2 atleast, so last 2- digit of all terms after 9! Will be 00.
So last two digits will depend on 1!+2!+...+9! Only
R=1!+2!+3!+4!+5!+6!+7!+8!+9!+10!+.....
1) units digit...
All terms after 4! contain one 5 and one 2 atleast, so units digit of all terms after 4! Will be 0..
So units digit will depend on 1!+2!+3!+4! Only
2) last two digits..
All terms after 9! contain two 5 and two 2 atleast, so last 2- digit of all terms after 9! Will be 00.
So last two digits will depend on 1!+2!+...+9! Only
Units digit here =1+2+3*2+4*3*2=1+2+6+24=33
Hence 3..
Hence 3..
Most Upvoted Answer
If R = 1! + 2! + 3! …. 199!, what is the units digit of R?a)0b)...
Understanding the Problem
To find the units digit of R, where R = 1! + 2! + 3! + ... + 199!, we need to analyze the units digits of the factorials involved.
Analyzing Factorials
- Factorial Values:
- 1! = 1 (units digit is 1)
- 2! = 2 (units digit is 2)
- 3! = 6 (units digit is 6)
- 4! = 24 (units digit is 4)
- 5! = 120 (units digit is 0)
- Notice the Pattern:
- From 5! onwards, every factorial ends with a zero because they include the factors 2 and 5, which contribute to the multiplication resulting in 10.
Calculating the Units Digit of R
- Significant Contributions:
- The factorials from 5! to 199! all contribute a units digit of 0.
- Therefore, we only need to consider the units digits of 1!, 2!, 3!, and 4!.
- Summing Relevant Factorials:
- Units digit of 1! = 1
- Units digit of 2! = 2
- Units digit of 3! = 6
- Units digit of 4! = 4
- Adding These Units Digits:
- 1 + 2 + 6 + 4 = 13
Final Step: Determine the Units Digit
- Units Digit of 13:
- The units digit of 13 is 3.
Conclusion
The units digit of R = 1! + 2! + 3! + ... + 199! is 3.
Thus, the correct answer is option D.
To find the units digit of R, where R = 1! + 2! + 3! + ... + 199!, we need to analyze the units digits of the factorials involved.
Analyzing Factorials
- Factorial Values:
- 1! = 1 (units digit is 1)
- 2! = 2 (units digit is 2)
- 3! = 6 (units digit is 6)
- 4! = 24 (units digit is 4)
- 5! = 120 (units digit is 0)
- Notice the Pattern:
- From 5! onwards, every factorial ends with a zero because they include the factors 2 and 5, which contribute to the multiplication resulting in 10.
Calculating the Units Digit of R
- Significant Contributions:
- The factorials from 5! to 199! all contribute a units digit of 0.
- Therefore, we only need to consider the units digits of 1!, 2!, 3!, and 4!.
- Summing Relevant Factorials:
- Units digit of 1! = 1
- Units digit of 2! = 2
- Units digit of 3! = 6
- Units digit of 4! = 4
- Adding These Units Digits:
- 1 + 2 + 6 + 4 = 13
Final Step: Determine the Units Digit
- Units Digit of 13:
- The units digit of 13 is 3.
Conclusion
The units digit of R = 1! + 2! + 3! + ... + 199! is 3.
Thus, the correct answer is option D.
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Community Answer
If R = 1! + 2! + 3! …. 199!, what is the units digit of R?a)0b)...
Few concepts..
R=1!+2!+3!+4!+5!+6!+7!+8!+9!+10!+.....
1) units digit...
All terms after 4! contain one 5 and one 2 atleast, so units digit of all terms after 4! Will be 0..
So units digit will depend on 1!+2!+3!+4! Only
2) last two digits..
All terms after 9! contain two 5 and two 2 atleast, so last 2- digit of all terms after 9! Will be 00.
So last two digits will depend on 1!+2!+...+9! Only
R=1!+2!+3!+4!+5!+6!+7!+8!+9!+10!+.....
1) units digit...
All terms after 4! contain one 5 and one 2 atleast, so units digit of all terms after 4! Will be 0..
So units digit will depend on 1!+2!+3!+4! Only
2) last two digits..
All terms after 9! contain two 5 and two 2 atleast, so last 2- digit of all terms after 9! Will be 00.
So last two digits will depend on 1!+2!+...+9! Only
Units digit here =1+2+3*2+4*3*2=1+2+6+24=33
Hence 3..
Hence 3..
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If R = 1! + 2! + 3! …. 199!, what is the units digit of R?a)0b)1c)2d)3e)4Correct answer is option 'D'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about If R = 1! + 2! + 3! …. 199!, what is the units digit of R?a)0b)1c)2d)3e)4Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If R = 1! + 2! + 3! …. 199!, what is the units digit of R?a)0b)1c)2d)3e)4Correct answer is option 'D'. Can you explain this answer?.
If R = 1! + 2! + 3! …. 199!, what is the units digit of R?a)0b)1c)2d)3e)4Correct answer is option 'D'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about If R = 1! + 2! + 3! …. 199!, what is the units digit of R?a)0b)1c)2d)3e)4Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If R = 1! + 2! + 3! …. 199!, what is the units digit of R?a)0b)1c)2d)3e)4Correct answer is option 'D'. Can you explain this answer?.
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