GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Retired Moderator
Joined: 19 Nov 2020
Posts: 326
Given Kudos: 64
GRE 1: Q160 V152
Function f(x) is defined as f(x)=1! + 2! + 3! + ...
[#permalink]
28 Jul 2021, 15:29
28 Jul 2021, 15:29
1
5
Bookmarks
00:00
Question Stats:
62% (01:49) correct
37% (01:00) wrong based on 27 sessions
Hide Show timer Statistics
Function f(x) is defined as f(x)=1! + 2! + 3! + ... x!.
When x=218, the function f(x) is defined as f(218) = 1! + 2! + 3! ... 218! What may be a remainder, if x=218 and f(x)/5?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
When x=218, the function f(x) is defined as f(218) = 1! + 2! + 3! ... 218! What may be a remainder, if x=218 and f(x)/5?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Re: Function f(x) is defined as f(x)=1! + 2! + 3! + ...
[#permalink]
28 Jul 2021, 21:48
28 Jul 2021, 21:48
5
Well, the answer doesn't really require us to care about the factorials after 4! since all of them are multiples of 5 anyway and would have remainder 0 when divided by 5. For example,
9! = 9*8*7*6*5*(4*3*2*1) has '5' in it, and hence a multiple of 5.
So the remainder of f(218)/5 is simply going to be the remainder of [ f(4)/5 ]. Since f(4) equals 33 ( 1! + 2! + 3! + 4!) , we have our remainder as 3. Hence, the answer is D
9! = 9*8*7*6*5*(4*3*2*1) has '5' in it, and hence a multiple of 5.
So the remainder of f(218)/5 is simply going to be the remainder of [ f(4)/5 ]. Since f(4) equals 33 ( 1! + 2! + 3! + 4!) , we have our remainder as 3. Hence, the answer is D
General Discussion
Function f(x) is defined as f(x)=1! + 2! + 3! + ...
[#permalink]
Updated on: 29 Jul 2021, 18:17
Updated on: 29 Jul 2021, 18:17
2
My train of thought here was to look for some sort of pattern as I add factorials and use that to deduce f(218)
1! is 1
2! is 2... 2! + 1! is 3
3! is 6... 3! + 2! + 1! is 9
4! is 24... 4! + 3! + 2! + 1! is 33
5! is 120... 5! + 4! + 3! + 2! + 1! is 153
6! is 720... We can stop right here since we can see a pattern where the ones digit is now 0.
Multiplying a number with a 0 at the ones digit is not going to change the ones digit; it will remain as a 0.
So even though we could add 8! and 9!, they will simply add some large (and annoying to calculate) number that has a 0 at the ones digit.
Ok, since we now know that 5!, 6!, 7!, ..., 218! are going to have a 0 at the ones digit, we know that adding those to 153, while yielding some large number, is simply adding 0 to the ones digit every time.
Thus, the ones will stay as 3 with no change. What is the remainder of a number with a ones digit of 3? It can only be 3 of course!!! (13%5 = 3, 14553%5 = 3, and 12314344983442342423423412348790213%3 = 3)
So the answer here is C
I hope this helps. This is the first question I answered on here.
1! is 1
2! is 2... 2! + 1! is 3
3! is 6... 3! + 2! + 1! is 9
4! is 24... 4! + 3! + 2! + 1! is 33
5! is 120... 5! + 4! + 3! + 2! + 1! is 153
6! is 720... We can stop right here since we can see a pattern where the ones digit is now 0.
Multiplying a number with a 0 at the ones digit is not going to change the ones digit; it will remain as a 0.
So even though we could add 8! and 9!, they will simply add some large (and annoying to calculate) number that has a 0 at the ones digit.
Ok, since we now know that 5!, 6!, 7!, ..., 218! are going to have a 0 at the ones digit, we know that adding those to 153, while yielding some large number, is simply adding 0 to the ones digit every time.
Thus, the ones will stay as 3 with no change. What is the remainder of a number with a ones digit of 3? It can only be 3 of course!!! (13%5 = 3, 14553%5 = 3, and 12314344983442342423423412348790213%3 = 3)
So the answer here is C
I hope this helps. This is the first question I answered on here.
Originally posted by jagjitsatti on 28 Jul 2021, 16:59.
Last edited by jagjitsatti on 29 Jul 2021, 18:17, edited 1 time in total.
Last edited by jagjitsatti on 29 Jul 2021, 18:17, edited 1 time in total.
