Forum Home > GMAT > Quantitative > Problem Solving (PS)
Events & Promotions
|
|
GMAT 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.
Dec 1511:00 AM IST
-01:00 PM IST
Attend this free GMAT Algebra Webinar and learn how to master the most challenging Inequalities and Absolute Value problems with ease.
Dec 1410:00 AM EST
-12:00 PM EST
Think a 100% GMAT Verbal score is out of your reach? Target Test Prep will make you think again! Our course uses techniques such as topical study and spaced repetition to maximize knowledge retention and make studying simple and fun.- Dec 14
11:00 AM IST
-01:00 PM IST
Attend this session to learn how to Deconstruct arguments, Pre-Think Author’s Assumptions, and apply Negation Test. 
Dec 1608:00 AM PST
-11:59 PM PST
GMAT Club 12 Days of Christmas is a 4th Annual GMAT Club Winter Competition based on solving questions. This is the Winter GMAT competition on GMAT Club with an amazing opportunity to win over $40,000 worth of prizes!- Dec 17
09:00 AM PST
-10:00 AM PST
Join Manhattan Prep instructor Whitney Garner for a fun—and thorough—review of logic-based (non-math) problems, with a particular emphasis on Data Sufficiency and Two-Parts. - Dec 18
10:00 AM PST
-11:00 AM PST
Here is the essential guide to securing scholarships as an MBA student! In this video, we explore the various types of scholarships available, including need-based and merit-based options.
20 Mar 2022, 02:49
Kudos
Bookmarks
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
52% (02:10) correct
48%
(02:05)
wrong
based on 122
sessions
History
Date
Time
Result
Not Attempted Yet
If n is a positive integer, what is the units digit of the sum of the following series: 1! + 2! + ... + n!? (The series includes every integer between 1 and n, inclusive)
(1) n is divisible by 4.
(2) n^2 + 1 is an odd integer.
Are You Up For the Challenge: 700 Level Questions
(1) n is divisible by 4.
(2) n^2 + 1 is an odd integer.
Are You Up For the Challenge: 700 Level Questions
22 Mar 2022, 04:39
Kudos
Bookmarks
Factorials from 5! onwards will always end in 0. Which means that our focus here is whether \( n = 3\) or whether \(n ≥ 4\). If \(n = 3\) then \(1!+2!+3! = 9\), and if \(n ≥ 4\) then no matter what the actual value of \(n\) is, the units digit will be \(3\).
(1) As \(n\) could be any multiple of \(4\), it means that \(n ≥ 4\) which means that the unit's digit will be \(3\).
SUFFICIENT
(2) \(n^2 + 1 = odd\) tells us that \(n\) is even. As we know that \(n\) cannot be \(2\), it means that \(n ≥ 4\) which means that the unit's digit will be \(3\).
SUFFICIENT
ANSWER D
(1) As \(n\) could be any multiple of \(4\), it means that \(n ≥ 4\) which means that the unit's digit will be \(3\).
SUFFICIENT
(2) \(n^2 + 1 = odd\) tells us that \(n\) is even. As we know that \(n\) cannot be \(2\), it means that \(n ≥ 4\) which means that the unit's digit will be \(3\).
SUFFICIENT
ANSWER D
General Discussion
23 Mar 2022, 14:49
Kudos
Bookmarks
Bunuel
If n is a positive integer, what is the units digit of the sum of the following series: 1! + 2! + ... + n!? (The series includes every integer between 1 and n, inclusive)
(1) n is divisible by 4.
(2) n^2 + 1 is an odd integer.
(1) n is divisible by 4.
(2) n^2 + 1 is an odd integer.
Breaking Down the Info:
Note that as n gets to 5 or higher, the terms after the 4th one don't affect the units digit anymore since those terms always end in 0, due to having a factor of 2 and 5.
Then we only care about whether n >= 5, and if not then we will have to discuss the exact value of n.
Statement 1 Alone:
If n = 4, then the units digit will be some known digit L. As we add more terms, 5!, 6!, 7! ... all of them don't change the unit digit anymore as explained above.
Thus for all n > 4, the units digit will still be L. Then this statement is sufficient.
Statement 2 Alone:
We need n to be even for \(n^2 + 1 -> n + 1\) to be odd. Then n = 2, 4, .... If n = 2, the unit digit is 3. If n = 4, the unit digit is 1 + 2 + 6 + 24 -> 3. Then the unit digit is always 3 using the fact above.
Answer: D
