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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1055
GPA: 3.39
g(x) is defined as the product of all even integers k such that 0 < k
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28 Jul 2021, 02:59
28 Jul 2021, 02:59
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g(x) is defined as the product of all even integers k such that 0 < k ≤ x. For example, g(14) = 2 × 4 × 6 × 8 × 10 × 12 × 14. If g(y) is divisible by 4^11, what is the smallest possible value for y?
(A) 22
(B) 24
(C) 28
(D) 32
(E) 44
(A) 22
(B) 24
(C) 28
(D) 32
(E) 44
Retired Moderator
Joined: 19 Nov 2020
Posts: 326
Given Kudos: 64
GRE 1: Q160 V152
g(x) is defined as the product of all even integers k such that 0 < k
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28 Jul 2021, 03:35
28 Jul 2021, 03:35
1
GeminiHeat wrote:
g(x) is defined as the product of all even integers k such that 0 < k ≤ x. For example, g(14) = 2 × 4 × 6 × 8 × 10 × 12 × 14. If g(y) is divisible by 4^11, what is the smallest possible value for y?
(A) 22
(B) 24
(C) 28
(D) 32
(E) 44
(A) 22
(B) 24
(C) 28
(D) 32
(E) 44
\(g(x)=g(y)\) =x!/4^11=x!/2^22
test all answer choices to find \(2^n\) and \(n=22\):
(A) \(22!/2^n\), \(n=22/2 + 22/4 + 22/8 + 22/16 = 11+5+2+1=19\) not a good choice
(B) \(24!/2^n\), \(n=24/2 + 24/4 + 24/8 + 24/16 = 12+6+3+1=22\) a good choice
(C) \(28!/2^n\), \(n=28/2 + 28/4 + 28/8 + 28/16 = 14+7+3+1=25\) not a good choice
choices (D) and (E) are not suitable as well. Hence, answer is B
checking the solution method and answer: \(24=2*4*6*8*10*12*14*16*18*20*22*24\),
2=2^1, 4=2^2, 6=3*2^1, 8=2^3, 10=5*2^1, 12=3*2^2, 14=7*2^1, 16=2^4, 18=9*2^1, 20=5*2^2, 22=11*2^1, 24=3*2^3. Total powers of 2^n result in n=22
Re: g(x) is defined as the product of all even integers k such that 0 < k
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30 Aug 2021, 03:33
30 Aug 2021, 03:33
Is this a Gmat level or a gre question?
