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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1055
GPA: 3.39
For each positive integer n, p(n) is defined to be the product of.
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18 Sep 2022, 21:52
18 Sep 2022, 21:52
Expert Reply
00:00
Question Stats:
75% (02:24) correct
25% (02:45) wrong based on 4 sessions
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For each positive integer \(n\), \(p(n)\) is defined to be the product of the digits of \(n\). For example, \(p(724) = 56\) since \(7 * 2 * 4 =56\).
Which of the following statements must be true?
I. \(p(10n) = p(n)\)
II. \(p(n+1) > p(n)\)
III. \(p(2n) = 2p(n)\)
--
A. None
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III
Which of the following statements must be true?
I. \(p(10n) = p(n)\)
II. \(p(n+1) > p(n)\)
III. \(p(2n) = 2p(n)\)
--
A. None
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III
Re: For each positive integer n, p(n) is defined to be the product of.
[#permalink]
21 Sep 2022, 03:51
21 Sep 2022, 03:51
Expert Reply
I) p(10n) = p(n)
p(10n) will always have units digit as 0 --> p(10n) = 0
p(n) can be any integer.
Not a must be true statement
II) p(n + 1) > p(n)
If n = 2; p(n +1) = 3 and p(n) = 2 --> p(n + 1) > p(n)
If n = 9; p(n + 1) = 0 and p(n) = 9 --> p(n + 1) < p(n)
Not a must be true statement
III) p(2n) = 2*p(n)
If n = 12; p(2n) = p(24) = 8 and 2*p(n) = 4
Not a must be true statement
Answer: A
p(10n) will always have units digit as 0 --> p(10n) = 0
p(n) can be any integer.
Not a must be true statement
II) p(n + 1) > p(n)
If n = 2; p(n +1) = 3 and p(n) = 2 --> p(n + 1) > p(n)
If n = 9; p(n + 1) = 0 and p(n) = 9 --> p(n + 1) < p(n)
Not a must be true statement
III) p(2n) = 2*p(n)
If n = 12; p(2n) = p(24) = 8 and 2*p(n) = 4
Not a must be true statement
Answer: A
gmatclubot
Re: For each positive integer n, p(n) is defined to be the product of. [#permalink]
21 Sep 2022, 03:51
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