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Updated on: 26 Nov 2023, 01:27
Originally posted by NithinRaja on 25 Nov 2023, 21:32.
Last edited by Bunuel on 26 Nov 2023, 01:27, edited 1 time in total.
Last edited by Bunuel on 26 Nov 2023, 01:27, edited 1 time in total.
Renamed the topic and edited the question.
Kudos
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
52% (02:46) correct
48%
(02:44)
wrong
based on 73
sessions
History
Date
Time
Result
Not Attempted Yet
There is a sequence An such that \(A_{n+1}=\frac{n+1}{A_n}\), for positive integer n. What is the number of factors of the product of \(A_n\), where n = 1, 2, 3, 4, 5, 6?
A. 6
B. 8
C. 10
D. 12
E. 15
A. 6
B. 8
C. 10
D. 12
E. 15
27 Nov 2023, 06:27
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\(A_{n+1}=\frac{n+1}{A_n}\) and we need to find the number of factors of the product of \(A_n\), where n = 1, 2, 3, 4, 5, 6?
\(A_6 * A_5 * A_4 * A_3 * A_2 * A_1\) = (\(A_6 * A_5\)) * (\(A_4 * A_3\)) * (\(A_2 * A_1\))
= \(\frac{5+1}{A_5} * A_5 * \frac{3+1}{A_3} * A_3 * \frac{1+1}{A_1} * A_1\)
= 6 * 4 * 2
= 48
= \(2^4 * 3^1\)
=> Number of factors = (4+1) * (1+1) = 5*2 = 10
So, answer will be C
Hope it helps!
Watch the following video to learn the Basics of Factors and Multiples
\(A_6 * A_5 * A_4 * A_3 * A_2 * A_1\) = (\(A_6 * A_5\)) * (\(A_4 * A_3\)) * (\(A_2 * A_1\))
= \(\frac{5+1}{A_5} * A_5 * \frac{3+1}{A_3} * A_3 * \frac{1+1}{A_1} * A_1\)
= 6 * 4 * 2
= 48
= \(2^4 * 3^1\)
=> Number of factors = (4+1) * (1+1) = 5*2 = 10
So, answer will be C
Hope it helps!
Watch the following video to learn the Basics of Factors and Multiples
11 Jan 2025, 11:54
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Hello from the GMAT Club BumpBot!
Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
