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g(x) is defined as the product of all even integers k such that 0 < k

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GeminiHeat
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g(x) is defined as the product of all even integers k such that 0 < k [#permalink] New post   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
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B
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g(x) is defined as the product of all even integers k such that 0 < k [#permalink] New post   28 Jul 2021, 03:35
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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

g(x)=g(y) =x!/4^11=x!/2^22
test all answer choices to find 2n and n=22:
(A) 22!/2n, n=22/2+22/4+22/8+22/16=11+5+2+1=19 not a good choice
(B) 24!/2n, n=24/2+24/4+24/8+24/16=12+6+3+1=22 a good choice
(C) 28!/2n, 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
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Re: g(x) is defined as the product of all even integers k such that 0 < k [#permalink] New post   30 Aug 2021, 03:33
Is this a Gmat level or a gre question?
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Re: g(x) is defined as the product of all even integers k such that 0 < k [#permalink] New post   30 Aug 2021, 03:36
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aishumurali wrote:
Is this a Gmat level or a gre question?


Good question.

Frankly is rather on the first side
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mrk9414
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Re: g(x) is defined as the product of all even integers k such that 0 < k [#permalink] New post   01 Sep 2021, 10:23
Carcass wrote:
aishumurali wrote:
Is this a Gmat level or a gre question?


Good question.

Frankly is rather on the first side


Could please explain this solution i could understand it
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Re: g(x) is defined as the product of all even integers k such that 0 < k [#permalink] New post   01 Sep 2021, 11:00
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4^11=2^22. So we have to find a product with atleast 22 2's in it.

in option 1 22 the total no of 2's = [22/2] + [22/4] +[22/8] +[22/16] = 11+5+2+1 = 19
in option 2 24 the total no of 2's = [24/2] + [24/4] +[24/8] +[24/16] = 12+6+3+1 = 22 . Hence B
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Re: g(x) is defined as the product of all even integers k such that 0 < k [#permalink] New post   13 Dec 2024, 06:38
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Re: g(x) is defined as the product of all even integers k such that 0 < k [#permalink]
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