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Learn how Kamakshi achieved a GMAT 675 with an impressive 96th %ile in Data Insights. Discover the unique methods and exam strategies that helped her excel in DI along with other sections for a balanced and high score.
20 Mar 2022, 02:49
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D
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Difficulty:
75%
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Question Stats:
50% (02:10) correct
50%
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wrong
based on 145
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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
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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
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Bunuel
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
