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09 May 2026, 22:18
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
47% (01:50) correct
53%
(02:04)
wrong
based on 15
sessions
History
Date
Time
Result
Not Attempted Yet
What is the remainder when 4! + 5! + 6! + 7! + ··· + 18! + 19! is divided by 50?
(A) 4
(B) 14
(C) 24
(D) 34
(E) 44
(A) 4
(B) 14
(C) 24
(D) 34
(E) 44
10 May 2026, 05:48
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Bookmarks
We need the remainder when
4! + 5! + 6! + ... + 19!
is divided by 50.
Notice that from 10! onward, every factorial is divisible by 50 because it contains enough factors of 2 and 5.
So only calculate:
4! + 5! + 6! + 7! + 8! + 9!
Now find each remainder when divided by 50:
4! = 24
5! = 120 → remainder 20
6! = 720 → remainder 20
7! = 5040 → remainder 40
8! = 40320 → remainder 20
9! = 362880 → remainder 30
Add the remainders:
24 + 20 + 20 + 40 + 20 + 30 = 154
Now divide 154 by 50:
154 leaves remainder 4.
Answer: (A) 4
4! + 5! + 6! + ... + 19!
is divided by 50.
Notice that from 10! onward, every factorial is divisible by 50 because it contains enough factors of 2 and 5.
So only calculate:
4! + 5! + 6! + 7! + 8! + 9!
Now find each remainder when divided by 50:
4! = 24
5! = 120 → remainder 20
6! = 720 → remainder 20
7! = 5040 → remainder 40
8! = 40320 → remainder 20
9! = 362880 → remainder 30
Add the remainders:
24 + 20 + 20 + 40 + 20 + 30 = 154
Now divide 154 by 50:
154 leaves remainder 4.
Answer: (A) 4
